Georges Descombes
email: georges.descombes@cnam.fr

Serge Boudigues

Modelling of waste heat recovery for combined heat and power applications

Keywords: gas turbine, internal combustion engine, combined cycles, combined heat and power plants, cogeneration, efficiency

The current environmental context dictates to reduce the pollutant emissions by improving thermal efficiency of the energy production units. The authors present some studies of cogeneration applications using gas turbines and thermal engines. The on-going research concerns a detailed study of thermodynamic modelling cycles with energy recovery. These combined cycles with gas turbine and ICE can generate a potential increase of about 10% of the energy efficiency. They will generate a technological complexity and the over-charge must be estimated. At last, the authors insist on the necessary synergy between gas turbines and thermal engines.

Introduction

The expression of the efficiency η of a thermal engine arises from the combination of both laws of thermodynamics (relation 1) where T and T 0 are the average exchange temperatures between the active fluid and the sources [1, 2]. The amount of heat generated by the combustion reaction is q, ∆ i S k are the entropy production generated by the irreversibilities of the energy transformation on each engine subassembly k. The thermal efficiency can then be written by reference to Carnot, following relation [START_REF] Lallemand | Thermodynamique appliquée, bilans entropiques et exergétiques[END_REF], as the product of the Carnot efficiency η c and of the exergetic efficiency η ex which depends on the level of losses given by the term of entropy production ∆ i S. The chemical energy En is split up into two contributions described by relations 3 to 5. The exergy Ex (4) of the heat flux q at the temperature T corresponds to the mechanical energy produced on the engine crankshaft. The anergy An [START_REF] Trémoulière | Etude de la modélisation des transferts thermiques dans la chambre de combustion d'un moteur Diesel[END_REF] represents the thermal energy which is lost due to the intrinsic term T T q 0 on one hand and by the major entropy production ∆ i S due to the irreversibilities on the other hand [START_REF] Mc Govern | Exergy analysis, a different perspective on energy, Part I, The concept of exergy[END_REF][START_REF] Mc Govern | Exergy analysis, a different perspective on energy, Part II, Rational efficiency and some examples of exergy analysis[END_REF].

An Ex En + = (3) S T T T q Ex i ∆ - - = 0 0 1 (4) S T T T q An k k i k k ∆ + = 0 0 (5)
The global energy balance [START_REF] Mc Govern | Exergy analysis, a different perspective on energy, Part I, The concept of exergy[END_REF] shows that a fraction of these anergy A n can be used partially for energy recovery applications. The energy balance applied in open system on a steady state operating condition (relation 6) shows that if the fraction E x of the chemical energy E n of the fuel is transformed into mechanical work, the anergy A n rejected as heat to the outside remains preponderant, U being the internal energy, V the velocity of fluid particle, P its pressure and Vol its volume.

[ ]

2 2 2 1 1 1 1 2 2 2 2 2 2 1 2 1 V Vol P U V Vol P U En An Ex - - - + + = + = ∆ → (6)
Relations [START_REF] Volz | Analyse de la conduction de la chaleur aux temps ultra-courts[END_REF] and ( 8) describe the entropy evolution balance in steady state operation of the engine where dA n represents the energy which is not transformed into work, TdS the entropy variation at the temperature level T which results from the convective contribution d e S of the heat and mass transfer to the outside and of the internal entropy production d i S. In this relation [START_REF] Kawamura | Combustion and combustion chamber for a low heat rejection engine[END_REF], q k is the thermal power exchanged at the local entropic temperature T k by each of the engine subassembly k with the outside, m the gas mixture mass flow rate, Si the source term of internal entropy defined as a flux, the indices 1 and 2 identifying the energetic states of the matter transfer at the inlet and at the outlet of the thermal engine.

dAn TdS = (7) ∆ + - + = k i k k k S m S m S T q k 2 2 1 1 0 (8)
The associated modeling of the heat exchanges by convection and radiation with the outside is most often based on correlations established in steady state (relation 9). Many authors assume that the energy radiated to the walls of the engine during combustion represents only a small fraction of the order of 4 to 20 % of the total energy released during the cycle [START_REF] Trémoulière | Etude de la modélisation des transferts thermiques dans la chambre de combustion d'un moteur Diesel[END_REF]. The convective flux density to the walls is restricted, with this simplification that remains to be proved, to the formulation [START_REF] Peyrard | Les moteurs Diesel adiabatiques[END_REF] in which ϕ is the flux density, h i the internal heat transfer coefficient, T g and T w the respective gas and wall temperatures. The heat transfer coefficient h i is evaluated from correlation [START_REF] Giraud | Contribution à l' étude de l' isolation thermique d' un moteur suralimenté à allumage par compression[END_REF] between the non dimensional numbers Nusselt N u , Prandtl P r and Reynolds R e in which the velocity is taken as the mean piston speed. In this simplified modeling, which supposes a steady-flow forced-convection heat-transfer approach, the Prandtl number varies little and is about 0.7 for gases.

[

] [ ] ∞ ∞ - + - = + = A w A w g dA T T dA T T V h dt d dt dq 4 4 2 2 εσ (9) [ ] T T h w g - = ϕ (10) R kP Nu q e p r = (11)
The application of the above mentioned balances (1) to [START_REF] Giraud | Contribution à l' étude de l' isolation thermique d' un moteur suralimenté à allumage par compression[END_REF] in full load operation for a Diesel engine (Fig. 1) shows that a noticeable part of the thermal energy provided by the combustion reaction is rejected to the cylinder outside as energy not transformed into work (Fig. 2). An exergetic analysis is then necessary to calculate the efficiency of the devices aiming at recovering at least a portion of this thermal energy at the exhaust of the engine and in its cooling system [3, 4, 6, 7].

Energy recovery

Concept of thermal insulation

The engine cylinder head and cylinders can operate correctly only if they are cooled by water circulation. This cooling is considered as an unavoidable drawback, harmful to the engine efficiency. A currently widespread but however wrong idea is that the heat transferred to the cylinder walls can be transformed into work. A premature analysis can lead to wrong conclusions, by stating that one can reduce the anergy An transferred to the engine cooling circuit to increase the mechanical exergy production Ex, keeping the same internal energy variation ∆U (relation 8). This led to some attempts of thermal insulation developed in the sole objective of improvement of engine thermal efficiency. The reduction of this heat transfer at the water cooling jackets mostly led to deceiving results. Results were on the contrary encouraging when the objective was to increase the thermal energy level recoverable at the engine exhaust [6, 8, 9] (Fig. 3).

As a matter of fact, the experiments show that a reduction of the anergy An transferred to the cooling circuit of the engine whose general shape of the thermodynamic cycle most often leads to an increase of the internal energy of the gases rejected in the exhaust. The production of mechanical exergy Ex is maintained at best, but it is also often degraded [START_REF] Peyrard | Les moteurs Diesel adiabatiques[END_REF][START_REF] Giraud | Contribution à l' étude de l' isolation thermique d' un moteur suralimenté à allumage par compression[END_REF]. Moreover, Diesel [START_REF] Diesel | Le moteur thermique système Diesel[END_REF] has considered a combined isothermal and adiabatic compression cycle in his initial report, before recommending his famous constant pressure cycle.

The analysis of the energy balance of a thermal engine shows more than of the chemical energy is lost depending upon the application. A usual case of energy recovery concerns the simultaneous production of electrical energy and thermal energy [START_REF] Magnet | International business conference on cogeneration, note SEMT PIELSTICK, RIO de JANEIRO[END_REF][START_REF] Haushalter | La cogénération par moteurs alternatifs[END_REF]. That is the case of the cogeneration applications such as the production of steam and hot water on one hand and trigeneration with additional cold energy production on the other hand.

The experience shows that the comparative efficiency of energy recovery applications between gas turbines and thermal engines is a function of output of the machines [START_REF] Sinatov | Turbocharging helps to Diesel engine in cogeneration and combined cycles[END_REF][START_REF] Grone | Prime mover systems for Diesel power plants[END_REF]. In a first approach, the thermal efficiency of a Diesel engine is better than the efficiency of a single gas turbine in the range of the low output power, particularly at partial loads. This trend inverses for a range of output power, which is higher than some MW and more.

Gas turbine

Figure 4 shows the diagram of a usual scheme applied to a cogenerated gas turbine used in a power plant unit [START_REF] Grone | Prime mover systems for Diesel power plants[END_REF]. In this example, the electrical power is equal to 1000 kW and the thermal losses are mostly concentred in the exhaust gas. The mass flow rate of the exhaust gas is 5.45 kg/s and the thermal recovery power is equal to 2175 kW when the exhaust gas are water-cooled form 500°C to 150°C. The mass flow rate of the hot water is equal to 95000 kg/h and the saturated steam production at 0,4 MPa is about 33000 kg/h. The overall efficiency of the power plant unit can reach 80%.

Diesel engine

Figure 5 shows the diagram case of an industrial turbocharged Diesel engine with energy recovery on water and oil cooling, exhaust and supercharging circuits. This thermal unit produces electrical energy and hot water to an urban city [START_REF] Magnet | International business conference on cogeneration, note SEMT PIELSTICK, RIO de JANEIRO[END_REF][START_REF] Marque | Production combinée de force, chaleur et froid, rapport de l'association technique de l'industrie du gaz en France[END_REF]. The thermal efficiency of the engines is equal to 45%. The engine with 18 cylinders operates on heavy-duty fuel with a viscosity equal to 180 centistokes at 50°C and a sulphur content less than 1.5%. The electrical power is equal to 38.5MW. The cogeneration process allows to obtain a simultaneous thermal power equal to 30MW of hot pressurized water at 120°C and 1MW of water at low temperature at 70°C. The overall efficiency of this power plant unit is around 80% and the annual fuel saving compared with a non-cogeneration application is about 10 000 tonnes equivalent petroleum.

Waste energy compared

We have seen that the major source of heat losses within a gas turbine is concentrated on the exhaust gas unlike an ICE, which imposes a more complicated technology to recover waste energy. Then, the levels of the temperature and the exhaust mass flow rate of the gas turbine can be adapted on the same machine as a function of user's needs with a simple branch circuit on the heat exchangers [START_REF] Boudigues | Contribution à l' optimisation des performances d' unités de production d' énergie cogénérées[END_REF][START_REF] Boudigues | Production d'énergie par cogénération et optimisation du cycle thermodynamique[END_REF]. The cogeneration efficiency Ec (relation 12) which is the ratio between recovery thermal energy E th and mechanical work E m, is higher in a gas turbine than thermal engines. This cogeneration efficiency, which can be evolved from 2 to 6, is distinctly higher than the cogeneration efficiency of an ICE which is about 0.5 to 2, but to the detriment for the gas turbine for its higher fuel consumption [START_REF] Boudigues | Contribution à l' optimisation des performances d' unités de production d' énergie cogénérées[END_REF][START_REF] Boudigues | Production d'énergie par cogénération et optimisation du cycle thermodynamique[END_REF].

E E Ec m th = (12)

Combined cycles with gas turbine

It is possible to model a series of cogenerated cycles having real industrial application possibilities [START_REF] Boudigues | Contribution à l' optimisation des performances d' unités de production d' énergie cogénérées[END_REF][START_REF] Boudigues | Production d'énergie par cogénération et optimisation du cycle thermodynamique[END_REF] and all the results of modelling program which are presented use systematically the thermodynamic balances (1) to [START_REF] Giraud | Contribution à l' étude de l' isolation thermique d' un moteur suralimenté à allumage par compression[END_REF]. The first simulation (Fig. 6) concerns the evolutive range of waste heat recovery as a function of the ratio of the thermal energy recovered on the exhaust gas which is taken on the turbine circuit. The entropic diagram illustrates the case without derivation and with derivation toward the inlet of the combustion chamber (Fig. 7).

The performance of the machine can evolve as a function of the mass flow, which is by-passed in the exchanger (Fig. 8). The outlet temperature is a function of the level of the by-passed exhaust gas at the exchanger. The outlet temperature reaches a maximum value of 900K when non derivation is realised.

It is a linear decreasing function of the by pass ratio and the thermal energy is also maximum when there is no derivation. The calculation results give a potential increase of the thermal efficiency about 20% from 0.4 to 0.482. The ratio of the recovery thermal energy and mechanical work increases to 40% when the levels of gas temperature evolve from 500 to 900K.

Combined cycles with I.C.E.

Depressurised cycle

Fig. 9 illustrates the schematic diagram applied to an ICE and Fig. 10 shows the thermodynamic depressurised cycle which is proposed in this application.

The calculation is done for an exhaust temperature of 1200K before variable geometry turbine. The pressure at the exit of the turbine is equal to 0.069 MPa and the temperature is 980K. Additional mechanical energy production realised on the rotor of the turbomachinery increases progressively from 2% to 8% of the energy generated on the crankshaft as a function of the load. In last, thermal energy recovery is realized in order to feed an exterior circuit.

The depressurised cycle is realised without preliminary compression [18, 19] and the heat is supplied at constant pressure P 0 . The under expansion is realised until a level inferior to the ambient pressure (point D). An amount of thermal energy can be extracted from (D) to (E) for a cogeneration application at constant pressure. A cooling or non cooling compression can be operated until atmospheric pressure P 0 (point F).

For a maximum temperature of the cycle that is fixed by the technology of the material, the level of pressure at the end of expansion is of course low compared to a classical cycle with exchanger. The density of the flow is also low and imposes the usage of a larger geometry of turbine and compressor to transfer the mass flow rate. We note that this increasing of the dimension of the machine is an advantage to decrease the losses within the blades and therefore the rotating speed is reduced by a factor of 3.

Over expansion cycle Over expansion cycle [18, 19

] is illustrated at first on a combined and power scheme (Fig. 11). The thermodynamic cycle is presented in Fig. 12. This cycle consists of a preliminary compression (A-B) followed by a heat transfer at constant pressure (B-C). The expansion of the combustion gas is realised in three steps. Mechanical energy produced between (C-D) is used to compress the turbocharging air (A-B).

The work produced between (D-E) corresponds to the mechanical energy to be supplied to an exterior electrical circuit. The under expansion (E-F) correspond to the mechanical energy needed to operate the second compressor (G-H) that will recompress the gas from the under expansion until ambient pressure P o . The expanded gas at point F are cooled at constant pressure until G by means of an exchanger that extracts energy for cogeneration. This cycle can improve the output power of the energy production unit as well as its efficiency by the choice of an optimum expansion ratio, which is a function of temperature levels and pressure ratio of the machine. Figure 13 illustrates the diagram of the combined cycle machine. Fig. 14 shows the thermodynamic over-expansion cycle. The modelling is led with an efficiency of the exchanger equal to 0.9 and the pressure losses progress from 2 to 7% in accordance with the studied application.

The level of temperature at the exhaust gas of the engine is fixed at 1000K and the cycle of the power unit is an over expansion cycle. The ratio of recovered thermal energy to work production is illustrated as a function of the temperature and the calculation shows that an additional recovery can be obtained. The optimal point is a function of the temperature level, pressure ratio and the amount of exchangers and the calculations show a potential thermal energy recovery from 10 % of the mechanical power.

Modelling results compared

The objective of depressurised and over-expansion cycles is to increase the turbocharging rate as well as the efficiencies. Table 1 illustrates the comparison between depressurised, over-expansion and simple exchanger cycles, taking into account frictional, mechanical and aerodynamic losses, variations in specific heat values (C p ) and exact calculation of the Fuel / Air ratio (F/A). Optimum flow rate, efficiency, F/A ratio and rotational speed values are given for a power of 50 kW and a heat exchanger efficiency of 85%.

The technology of the exchanger cycle is the simplest, but with higher consummation and pollution rates and its angular rotational speed stays prohibitive for a power of 56 kW. The depressurised cycle can be suitable for a power range higher than 50 kW with a rotating speed reduced by a factor of 1,5-2 for the turbomachinery. The performances of the over expansion cycle are the best, but this expansion cycle is more suitable for a range of output power which is higher than 150 kW and more.

Cycle

Conclusion

In this work, waste heat recovery aiming to increase the availability of the combined cycles and cogeneration has been studied. Non usual depressurised and over-expansion cycles have been studied and they can improve sensibly the efficiency of the power unit. Calculations show that thermal efficiency of the engine is increased by 4 to 5 points on its optimum working condition. These cycles can be used on a thermal engine with high supercharging at lean burn conditions, with cogeneration applications to produce cold energy and additional electrical energy.

The next step of this study will concern experimental work of the performances of a supercharging and combined unit.

A variable geometry turbine dedicated to operate on an over expansion cycle will be realised. The authors intention has been also to suggest a real synergy between alternative engines and gas turbines in thermal and mechanical energy production domain. At last, Georges Descombes would like to honour the memory of Professor Serge Boudigues.

Fig. 1 .Fig. 2 .Fig. 3 .Fig. 4 .Fig. 5 .Fig. 6 .Fig. 7 .Fig. 8 .Fig. 9 .Fig. 10 .Fig. 11 .Fig. 12 .Fig. 13 .Fig. 14 .

 1234567891011121314 Fig. 1. Thermodynamic cycle of a volumetric engine

Table 1 .

 1 Compared performances of thermodynamic cycles

		Mass flow	Efficiency	Fuel / Air	Speed (rpm)
		rate		ratio	rotor
		(g/s)
	Exchanger	229	0,409	0,0127	64000
	Depressurised	194	0,414	0,0147	31000
	Over	193	0,431	0,0143	46000
	expansion


H Grote
email: hartmut.grote@aei.mpg.de

The GEO 600 Status

Keywords: numbers: 04.80.Nn, 95.55.Ym, 95.75.Kk

The British-German gravitational-wave detector GEO 600 has concluded a long observational period called Astrowatch, which lasted from November 2007 to July 2009. Together with the LIGO-H2 detector, GEO 600 was kept observing, while other detectors of the world-wide network of laser-interferometers like LIGO(L1 and H1) and Virgo were upgraded. A fraction of the time during the astrowatch period was set apart for noise investigations and experiments preparing future upgrades. Even with these investigations GEO 600 reached an observation time of 86.0 % of the overall time, such that a total of 522 days worth of data were collected. The average sensitivity was roughly a factor of 2 lower than that of the LIGO-H2 detector for frequencies above 500 Hz. In July 2009 GEO 600 has started an upgrade program called GEO-HF. Within this program we aim at improving the sensitivity by a number of sequential upgrades, like tuned signal recycling, DC readout, output mode-cleaning, injection of squeezed vacuum states, and the increase of circulating light power. Tuned signal recycling and DC readout have already been implemented and can be operated robustly, due to a new technique associated with the automatic alignment system.

Introduction

The GEO 600 detector [START_REF] Grote | The status of GEO 600[END_REF] is part of the world-wide network of laser interferometers aiming at the direct detection of gravitational waves at audio-band frequencies. While the GEO detector is shorter in arm-length by factors of 5 and 6.7 with respect to Virgo [START_REF]Amaldi 2009[END_REF] and LIGO [START_REF] Abbott | LIGO: the Laser Interferometer Gravitational-Wave Observatory[END_REF], it uses so-called advanced techniques which are planned to be implemented, in future upgrades of the other detectors. These are in particular monolithic suspensions, signal recycling, and electro-static test mass actuators, which have been described elsewhere. (See for example [START_REF] Grote | The status of GEO 600[END_REF] and the references therein.)

In this paper, a very brief overview of GEO 600 is given in section 2, followed by a description of the data collecting time within the astrowatch period in section 3. In section 4 we describe investigations during and after the astrowatch period, and in section 5 an outlook of planned the upgrades is given.

The GEO 600 detector

A simplified layout of the GEO 600 interferometer is shown in Figure 1. The light of a master-slave laser system is filtered by two sequential input mode cleaners (MC1 and MC2), ring cavities of about 8 meters round-trip length consisting of 3 mirrors each. The stabilised and filtered light leaving the mode cleaners is injected into the main part of the interferometer, consisting of a Michelson interferometer with single folded arms of 600 meters length, a power recycling mirror (MPR), and a signal recycling mirror (MSR). Up to September 2009 GEO has been operating with detuned signal recycling at a detuning frequency of 530 Hz [START_REF] Hild | Demonstration and comparison of tuned and detuned signal recycling in a large-scale gravitational wave detector[END_REF], and with a heterodyne readout technique, using Schnupp modulation [START_REF] Schnupp | Presentation at European Collaboration Meeting on Interferometric Detection of Gravitational Waves[END_REF], and operation of the Michelson at the dark fringe condition. In detuned signal recycling, the output of the heterodyne detector appears in two quadratures, which have to be combined in a frequency dependent way, to yield a single data stream of strain measurement [START_REF] Hewitson | Optimal time-domain combination of the two calibrated output quadratures of GEO 600[END_REF].

Astrowatch

From November 2007 to July 2009 GEO 600 operated in the so-called astrowatch mode, collecting data for most of the time. The aim of this mode was to have some interferometric detectors online, while others were upgrading their instruments. The LIGO-H2 detector took part in the astrowatch program from February 2008 to the end of May 2009. While the overall sensitivity of GEO 600 and LIGO-H2 was lower than that of LIGO-L1/H1 and Virgo in 2007, the data is valuable for searches triggered by astronomical events that are detected in the electro-magnetic or particle domain, as for example gamma-ray bursts and neutrinos. Typical sensitivities of the GEO 600 and the LIGO-H2 detector during astrowatch are shown in figure 2.

Figure 3 shows the daily duty-factors of GEO 600 over the time from 1. November 2007 to 1. July 2009. The fraction of the total time (or duty factor ) of the astrowatch period when GEO 600 was in the locked state, is 92.4 %. The locked state is characterised by properly resonating light fields in all of the optical cavities, while the science mode state needs some requirements in addition, as for example a stable on-line calibration and the absence of people from the main experimental hall. The overall fraction of science time obtained in astrowatch is 86.0 %, which corresponds to a total of 522 days of well calibrated and characterized science data collected in the period between November 2007 and July 2009.

To keep GEO 600 in the data collecting mode, typically there were operators on the site on normal working hours during astrowatch, while the detector was working fully automated at night and at weekends. Over weekends, operators were on schedule to intervene, if the detector would not re-lock automatically after a loss of lock, or if any other error occurred that could be remotely sensed. We did not have operators on In the locked state, all light fields are resonating in their respective optical cavities. To qualify the data for science mode, more conditions have to be met, like absence of people from the main building, minimum fit quality of the calibration parameters, and some others. duty at night. Investigating the cases where the detector could not re-lock on its own at night showed, that we lost about 1.5 % of the total science time due to not having assigned night shifts, which seems perfectly acceptable.

The end of the atsrowatch period marks the end of about 3.5 years of predominant data taking mode in GEO 600. In the time from January 2006 to October 2007 GEO has collected 421 days of science data within the fifth science run (S5) of the LIGO scientific collaboration. Together with the data taken in the astrowatch period, this makes up 943 days of science data.

Investigations and experiments during and after Astrowatch

Detuned heterodyne noise budget

Investigation of the actual limiting noise sources of the interferometer sensitivity is an essential activity to facilitate further progress. While a standard set of noise projections can be done in a highly automated way, new noise sources have to be taken into account from time to time, in case there is unexplained noise in the sensitivity curve. Over the last years, the GEO detector has seen unexplained noise in the frequency band from about 100 Hz to 600 Hz, at only slightly varying levels. In [START_REF] Grote | The status of GEO 600[END_REF] we have described the investigation of laser frequency noise, oscillator phase noise, and scattered light noise. Since then we have started investigation of phase-and amplitude noise of the signal recycling modulation sidebands. To yield a control signal for the microscopic position of the signal recycling mirror, GEO uses a dedicated phase modulation of the light incident to the PR cavity at a frequency of about 9 MHz, chosen to resonate within the power recycling cavity.

While it could be shown that phase noise of this modulation signal does not limit the strain sensitivity, it turned out that amplitude noise of this modulation was coupling to the strain signal at least for a number of lines in the frequency range of 30 Hz to 300 Hz. The amplitude noise on the RF modulation was caused by GEOs digital control system, coupling to the RF modulation by electro-magnetic pickup. Mitigation of this noise was possible by better electro-magnetic shielding of the signal recycling modulation path against the GEO control system. Due to lack of the proper hardware, we have not yet investigated the coupling of the noise floor of the signal recycling modulation's amplitude noise. Currently, hardware is under construction to fill this gap. Besides the improvement in the signal recycling modulation path, there have also been improvements in the modulation path used for the power recycling control loop. Another field of investigation was the reduction of phase noise in the electronic demodulation path for the strain signal. Here we applied a cancellation technique, where we electrically subtract a sine wave of fixed amplitude and phase from the signal that enters the main frequency mixer. A small improvement around 10-20 % of the strain noise above 1 kHz resultet from this.

Figure 4 shows the noise budget of GEO 600 after the end of astrowatch in August 2009, with GEO operating with heterodyne readout and a signal recycling detuning of 530 Hz. Compared to the noise budget shown in [START_REF] Grote | The status of GEO 600[END_REF] from 2007, the unexplained noise has reduced from a factor 3 at 150 Hz to about a factor of 2, and also has been reduced at higher frequencies. Even though this is a nice improvement of the situation, the GEO sensitivity as shown in figure 4 was still not stationary over long times, and there have been times with yet additional unexplained noise, behaving like a system with two more-or-less stationary noise states.

Tuned signal recycling and DC readout

Tuned signal recycling and DC readout [START_REF] Hild | DC-readout of a signal-recycled gravitational wave detector[END_REF][START_REF] Degallaix | Commissioning of the tuned DC readout at[END_REF] are two major changes in the detector configuration which are the first part of the upgrades within the program called GEO-HF (see also section 5). To study the implementation of tuned signal recycling and DC readout in GEO, we occasionally conducted experiments already during the astrowatch period. These experiments mainly aimed at establishing the combined operation of tuned signal recycling and DC readout (also denoted as tuned DC readout). Tuned signal recycling needs a modification of control loops, and a dedicated acquisition technique to reach the nominal operating point. DC readout needs a change of the operating point of the Michelson interferometer and changes of readout electronics and detector calibration. Both operating conditions are incorporated in the automated locking procedure. After the stable operation of tuned DC readout was established (see also next section), we could start to study the noise budget of this configuration.

Figure 5 shows the noise budget of the detector in the tuned DC configuration, as of September 2009. Essentially there is almost no unexplained noise at all frequencies. This is an important result, in particular since the strain sensitivity obtained in tuned DC readout around 200-300 Hz is comparable to the sensitivity in detuned heterodyne mode, while in the latter condition, the noise cannot be fully explained. Further investigations are needed to confirm this result and interpret it with respect to the unknown noise sources in the detuned heterodyne condition. It seems that the unexplained noise sources in the latter configuration may not be present in the tuned DC readout configuration, but more quantitative analysis is pending.

The 2f beam centering technique

While we could test DC readout operation in GEO for a while, this configuration never was as robust as the heterodyne readout. The typical lock length in DC readout was always clearly less than an hour, and DC readout was hardly possible to lock under windy conditions at all. Investigation of this phenomenon lead to the fact that the beam motion on the wavefront sensor at the antisymmetric port (which is used to generate control signals for the differential alignment mode of the Michelson interferometer) was critical for the stability of the DC readout. This can be understood by the fact, that in DC readout, there is a first-order coupling of the beam position on the wavefront sensor to the alignment signal (obtained on this wavefront sensor) itself. On the photodiode, the offset from the dark fringe condition of the Michelson causes a common signal at the Michelson modulation frequency across the whole area of the anti-symmetric port beam. If this beam is perfectly centered on the wavefront sensor, the common mode terms are suppressed by subtraction of the signals from each of the two half-planes of the two lateral dimensions, resulting in proper error signals for the Michelson alignment. A lateral displacement of the anti-symmetric port beam on the wavefront sensor then generates a fake alignment signal, resulting in a misalignment of the Michelson interferometer, apparently compromising its stability.

Obviously, it is difficult to predict at which level this problem would show up for any interferometer, as it depends on several factors:

• The amount of dark fringe offset determines the linear coupling coefficient of beam motion to the generated alignment signal.

• The amount of beam motion is determined to a large extent by suspension design parameters, and by the global control loops which align the mirrors.

• more external factors like the actual seismic noise level or air currents on beam paths can further increase the beam motion.

If the influence of these factors cannot be reduced, an obvious solution is the attempt to actively control the beam position on its corresponding wavefront sensor. In GEO we have always been following this strategy for almost all of the wavefront sensors, regardless of the fact that normally (i.e. non-DC-readout conditions) the beam positions only couple in second order terms to the corresponding alignment signals. In the detuned heterodyne configuration of GEO we have used the overall power distribution across the anti-symmetric port beam to generate a control signal for the active steering of this beam. In this configuration, the overall power is dominated by the modulation sidebands used for the heterodyne readout, and even without DC readout this increased the robustness of the lock. This strategy failed for DC readout. One obvious reason for this was, that we reduced the level of the modulation sidebands, but although we experimented with large dark-fringe offsets, causing the anti-symmetric port beam to be dominated by carrier power, the lock was never very robust, and the overall power of the anti-symmetric port beam could not be used for the beam-centering. A general problem of the usage of the overall power is the presence of higher-order TEM modes (here: at the anti-symmetric port), which result from imperfections of the mirror surfaces within the interferometer and from thermal lensing effects. These higher order modes can be a function of the alignment, laser power, non-stationary heat distribution within the test-masses, and dark fringe offset, just to name some.

To potentially improve the error signal for the anti-symmetric port beam centering, we now only detect the spatial distribution of the light power of the modulation sidebands present at the anti-symmetric port. At least in the case of GEO, these sidebands are nice TEM00 modes, yielding the proper reference frame for the wavefront sensor, as the sidebands are used as a local oscillator for the heterodyne beat with the main carrier beam. The power of the modulation sidebands on the four quadrants of the photodiode is detected by measuring the amplitudes of the photocurrents at twice the modulation frequency. Therefore, we call this 2f beam centering technique.

Controlling the centering of the anti-symmetric port beam on the wavefront sensor with this signal, the DC readout extremely increased in robustness. It now can be operated in high-seismic-noise conditions, and appears to be of similar stability as the heterodyne readout in GEO.

GEO-HF

With the beginning of the S6 science run within the LIGO scientific collaboration and the VSR2 science run on July, 7 th 2009, the upgrade program of the GEO detector has started. Within this program we aim at an increase of the strain sensitivity of GEO by a number of sequential upgrades: All of these upgrades are independent from each other, at least as far as implementation and control is concerned. Therefore, we plan to establish full locking and analysis of the actual sensitivity after each upgrade step, including data taking to gain experience with the then actual new configurations. Figure 6 shows the potential strain sensitivity of GEO 600, together with shot noise limited sensitivity curves for the individual upgrade steps of GEO, and two sources of expected thermal noise. More details about GEO-HF can be found in [START_REF] Lück | The transition to GEO-HF[END_REF].

Data taking periods from 2011 to 2015

As far as it can be foreseen now, in the period from 2011 to 2015 GEO 600 will be the only interferometer in the world that can be on-line for astrophysical observations for a substantial amount of time. The three LIGO interferometers as well as Virgo will be upgrading to the advanced versions of their instruments. Therefore, current planning is, that GEO will spend more and more time in observation mode, as all the upgrades foreseen for GEO-HF at this time are implemented, and the sensitivity would approach the planned goal.

Confidential: not forFigure 1 .

 1 Figure 1. Simplified optical layout of the GEO 600 detector. GEO 600 is a powerand signal recycled Michelson interferometer with single folded arms within 600 m long beam tubes. See more details in the text.

Figure 2 .

 2 Figure2. Typical strain sensitivities of the GEO 600-and the LIGO-H2 detector in astrowatch. Above 500 Hz, GEO is roughly within a factor of 2 of the LIGO-H2 sensitivity.

Figure 3 .

 3 Figure 3.Daily fractions of locked time and science mose time (duty factors) for the astrowatch period. In the locked state, all light fields are resonating in their respective optical cavities. To qualify the data for science mode, more conditions have to be met, like absence of people from the main building, minimum fit quality of the calibration parameters, and some others.

Figure 4 .

 4 Figure 4. The GEO 600 noise budget in the configuration of detuned signal recycling and heterodyne readout, as used during the astrowatch period. The trace 'sum of the noise' is the uncorrelated sum of all other noise source shown in the graph. There is a gap of unexplained noise between the actual sensitivity (h) and the sum of the noises.

Figure 5 .

 5 Figure 5. The GEO 600 noise budget in the configuration of tuned signal recycling DC readout, as of September 2009. The trace 'sum of the noise' roughly matches the observed sensitivity h. There is almost no unexplained noise.

•

  Tuned signal recycling and DC readout • Implementation of an output mode-cleaner • Injection of squeezed vacuum into the anti-symmetric port • Reduction of the signal recycling mirror reflectivity • Light power increase

Figure 6 .

 6 Figure 6. The potential strain sensitivity of GEO-HF and shot noise limited sensitivites of the individual upgrade steps of GEO-HF. Also shown are expected coating thermal noise, thermo-refractive noise of the bemsplitter of GEO, and the actual sensitivity curve as of August 2009.

Acknowledgments

The authors are grateful for support from the Science and Technology Facilities Council (STFC), the University of Glasgow in the UK, the Bundesministerium für Bildung und Forschung (BMBF), and the state of Lower Saxony in Germany. This work was partly supported by DFG grant SFB/Transregio 7 Gravitational Wave Astronomy.


Benjamin Sheard
email: benjamin.sheard@aei.mpg.de

Gerhard Heinzel

Karsten Danzmann

LISA long arm interferometry: an alternative frequency pre-stabilisation system

Keywords: numbers: 04.80.Nn, 07.60.Ly, 07.87.+v, 95.55.Ym

Laser frequency noise is a significant noise source which couples into the main science measurement of the Laser Interferometer Space Antenna via the mismatch between the interferometer arm lengths. In this paper we discuss the application of unequal pathlength heterodyne Mach-Zehnder interferometer to measure and actively stablise the master laser frequency as used in LISA Pathfinder. In comparison to an optical cavity or atomic reference the technique has a wide operating range and does not require a complex lock acquisition procedure. Frequency tuning can be provided by purely electronic means and does not require physically changing the pathlength (or resonance frequency) of the frequency reference and can therefore be combined with arm locking in a straightforward manner.

Introduction

The Laser Interferometer Space Antenna (LISA) aims to to detect gravitational waves in the 100 µHz to 1 Hz frequency band by measuring the distances between freely-falling proof masses enclosed within three identical spacecraft in a triangular constellation [1]. The 5 million km inter-spacecraft distances will be measured using laser interferometry with close to shot-noise limited precision. Whilst the orbits of the spacecraft are designed to keep the separation between the three spacecraft equal and as constant as possible without station keeping, a slowly changing mismatch on the order of ±60 000 km is unavoidable [START_REF] Povoleri | AIP Conf. Proc[END_REF]. This large arm length mismatch couples laser frequency noise to the differential single-pass length measurement between two adjacent arms according to the following expression

S x (f ) = sinc 2πf ∆L c -1 ∆L ν S ν (f ) (1)
Where ∆L is arm length mismatch, ν is the laser frequency, c is the speed of light, S x (f ) is the displacement amplitude spectral density in m/ √ Hz and S ν (f ) is the frequency amplitude spectral density in Hz/ √ Hz. For f c(2π∆L) -1 Equation 1 can be approximated by

S x (f ) ≈ ∆L ν S ν (f ) (2)
The coupling into the phase measurement is therefore

S φ (f ) ≈ 2π ∆L c S ν (f ) (3)
In the baseline configuration where offset phase locking is used, a single interferometer arm is essentially a Mach-Zehnder interferometer with an enormous mismatch of 10 million km. The coupling of the laser frequency noise to a single arm measurement is on the order of 210 rad/Hz. With the baseline pre-stabilised frequency noise level of 30 Hz/ √ Hz [START_REF] Heinzel | [END_REF] the phase noise of the beatnote to be measured is 6 300 rad/ √ Hz. This comparitively large phase noise must be measured by the phasemeter with a fidelity of approximately 6 µrad/ √ Hz [START_REF] Shaddock | AIP Conf. Proc[END_REF][START_REF] Wand | AIP Conf. Proc[END_REF]. It is only after subsequent active stabilisation with arm-locking and processing the raw measurements using a post-processing technique called time-delay interferometry (see e.g. [START_REF] Tinto | [END_REF]7]) that the laser frequency noise is removed.

Time delay interferometry (TDI) "synthesises" an equal arm length interferometer by appropriately combining the raw signals with delayed versions of the same signals. To process the raw data using TDI requires an accurate knowledge of the propagation delay in each arm. The main phase measurement observes the picometre level fluctuations only in the measurement band and does not directly provide a measurement of the absolute propagation delay. One approach is to implement a dedicated ranging system using pseudo-random codes which are phase modulated onto the main carrier. The absolute separation of the spacecraft can be determined by tracking the phase of these codes at the receiving spacecraft. Preliminary results with a laboratory prototype have shown sub-metre resolution [8].

An alternative method of inferring the propagation delay is to minimise the noise power in the TDI outputs [9]. An extension of this approach is to modulate the laser frequency at the edge of the measurement band and adjust the delays used in TDI to minimise this peak in the final output [START_REF] Spero | Range measurement for LISA 8th Edoardo Amaldi Conference[END_REF]. Initial estimates of the resolution are on the sub-metre level. Assuming that a contribution of 4 pm/ √ Hz is allocated to residual frequency noise, Equation 1 may be inverted to compute the allowable laser frequency noise for a given arm length mismatch. Figure 1 shows this for a mismatch of 60 000 km and for TDI combined with 1 m ranging accuracy (which corresponds to a 2 m effective arm length mismatch in the worst case). A free-runnning laser will not meet the requirement with a 1 m ranging accuracy and additional stabilisation is needed.

There are number of possible ways to stabilise the laser frequency including stabilisation to a reference cavity [12] or atomic reference [START_REF] Leonhardt | [END_REF], and arm locking [13]. A tunable pre-stabilisation system is desirable if arm locking is used. Sideband locking can be used with a fixed reference cavity in order to combine the frequency stability of the reference cavity with tunabilty [14].

In this paper we analyse an alternative laser frequency pre-stabilisation system, based on that used in the LISA technology package (LTP) on board LISA Pathfinder [15,16]. Unlike stabilisation to a reference cavity or an atomic reference no electro-optic modulators, acousto-optic modulators or high power RF electronics are required. The main additional components are a few extra beamsplitters and mirrors on the optical bench and a few extra photodetectors and phasemeter channels. The cleanliness requirements are the same as that of the main optical bench and no additional thermally stable vacuum chamber would be required.

"LTP-style" frequency pre-stabilisation

Figure 2 shows a schematic of how an "LTP-style" pre-stabilisation could be implemented on the LISA optical bench. The reference interferometer measures the phase difference (φ R ) between the lasers on adjacent optical benches in one LISA satellite. This reference interferometer already exists in the current LISA optical bench design. To measure the frequency noise of the master laser an additional interferometer with unequal pathlengths, as will be implemented in LISA Pathfinder [15,16], can be placed on the optical bench. The additional components required include

• Single-element photodetectors (2x for redundancy)

• Fast (≥ MHz) phasemeter channels (2x for redundancy)

• Beam-splitter(s) and mirrors on the optical bench

The main difference between this system and that of LTP is that the beatnote is generated by interference with an offset phase-locked laser at a variable frequency difference of 2 . . . 20 MHz rather than interference between two beams produced by acousto-optic modulators at a constant frequency difference of 1 . . . 2 kHz.

The output of this additional interferometer (φ F ) can not only be used to measure the frequency fluctuations of the laser but also to actively stabilise the master laser frequency. Thus, in the proposed configuration there are two control loops:

• (φ R -frequency offset) locks the slave laser to the master laser as in the LISA baseline

• (φ F -φ R -tuning bias)

locks the master laser absolute frequency

The laser from the adjacent optical bench (the slave laser) is offset phase locked to the master with high gain/bandwidth with a constant offset:

ν s = ν M + f het (4)
with 2 MHz ≤ f het ≤ 20 MHz. Such a phase locking arrangement will be used in any case.

After phase locking the closed loop phase noise of the slave laser is given by (in the frequency domain):

P s|cl = G 1 1 + G 1 P M - G 1 1 + G 1 1 + 1 1 + G 1 P s|fr (5)
where:

• P s|fr -free running slave laser phase noise

• P s|cl -closed loop slave laser phase noise

• P M -master laser phase noise

• 1 -error point noise (sensor noise) for loop 1

• G 1 -controller transfer function for loop 1 (e.g. PI controller)

Equation 5 shows that in the high gain limit:

• The free-running slave phase noise is suppressed,

• The performance is limited by sensor noise 1 ,

• The slave laser tracks the master laser phase noise with accuracy G1 1+G1 (≈ 1 in the high gain limit). Offset phase locking the slave laser fixes the beatnote frequency for both the φ R and φ F interferometers to the chosen frequency offset, but does not have any effect on the frequency of the master laser. The master laser can be freely tuned, while the slave laser tracks these changes. Thus the first loop only controls the frequency difference between the two lasers.

Master laser frequency control loop

Measuring the phase of the beatnote for the φ F interferometer produces the following error signal for the second control loop (used to stabilise the master laser frequency):

E 2 = 2 -P M exp (-jωτ ) + P s|cl (6)
This assumes that the length (propagation delay) for the slave laser to φ F is identical to the delay for φ R . The master laser has an additional propagation delay of τ = ∆L/c for φ F compared to φ R . Subtracting the residual error point of slave laser control loop (E1) from the error point of the second control loop for the master laser (E2) results in the following combined error signal

E 2 -E 1 = 1 -e -jωτ P M + 2 -1 (7)
which is independent of the slave laser controller, simplifing the design of the controller for the master laser.

For frequencies below the inverse delay time τ -1 the transducer gain of the mismatched pathlength interferometer is

δΦ F δν M ≈ 2π∆L c = 2πτ, (8)
thus providing an error signal which can be used to control the frequency of the master laser. The error signal for the master laser frequency is immediately available for any operating point.

The closed-loop master laser noise is then given by:

P M|cl = P M|fr 1 + L 2 + G 2 1 + L 2 1 - G 2 1 + L 2 2 (9)
where G 2 is the controller transfer function for the master laser controller and

L 2 = G 2 [1 -exp(-jωτ )] is the loop gain.
Introducing an offset, 2 , to the error point of the master laser control loop can be used to tune the master laser frequency (which the slave laser tracks due to the offsetphase lock). For large controller gain and frequencies low compared to the inverse delay time the frequency tuning response is

∂ν M|cl ∂ 2 ≈ -1 2πτ [Hz/rad] (10)

Performance estimation

Like an optical cavity the performance is ultimately limited by the stability of the reference, in this case the pathlength stability of the Mach-Zehnder. Figure 3 shows the predicted system performance assuming a 50 cm pathlength mismatch and a typical free-running NPRO laser frequency noise (10 kHz/ √ Hz at 1 Hz with 1/f noise shape). The assumed combined phasemeter and pathlength noise is

i = 2π λ × 1 pm/ √ Hz × 1 + 2.8 mHz f Hz 4 (11)
The phasemeter/pathlength noise of the two channels is assumed to be uncorrelated. The closed loop frequency noise level intersects the free running noise level at approximately 10 Hz for typical Nd:YAG NPRO lasers. For closed loop bandwidths above this frequency the closed loop noise level would be higher than the free running laser which has a potential impact on the performance of other subsystems (e.g. phasemeter). Therefore in the proposed design the bandwidth of the second loop is restricted to approximately 20 Hz.

In this simple model the closed loop frequency is limited primarily by the phasemeter noise of the two phasemeter channels used and results in a closed loop frequency noise level for the master laser of approximately 800 . . . 830 Hz/ √ Hz in the 10 mHz to 1 Hz range.

The performance shown in Figure 3 almost meets the 4 pm/ √ Hz requirement for 1 m ranging accuracy (2 m effective arm length difference) even without arm locking. In combination with arm locking the frequency noise is several orders of magnitude below the requirement [START_REF]The LISA Frequency Control Study Team 2009 LISA Frequency Control Whitepaper[END_REF]. The performance could potentially be improved by increasing the arm length mismatch or by improving the phasemeter performance.

Frequency tunability

Figure 4 shows the frequency tuning response for injecting offsets into the master laser frequency control loop (solid blue curve). Notice that for this input the bandwidth is restricted by the limited loop bandwidth used in order reduce the degradation of the laser noise above 10 Hz. The dashed green curve shows the frequency tuning response for the input labelled Z in Figure 2, scaled by a factor of 1/(2πτ ) in order to compensate for the gain of the interferometer. The sum is shown as the dashed red curve which is flat. Thus injecting the same signal into the offset and directly to the laser (compensating for the interferometer gain) provides a high bandwidth frequency actuation for implementing arm locking. The achievable tuning bandwidth with this approach is limited by the laser frequency actuators and processing delay of the phasemeter and controller electronics.

Conclusion

An analysis of an LTP-style unequal arm length Mach-Zehnder interferometer as alternative frequency pre-stabilisation system for LISA was presented. The ultimate performance of the technique with LISA-like hardware remains to be experimentally verified.

Figure 1 .

 1 Figure 1. Frequency noise requirements for an arm length mismatch of 60 000 km (20 µHz/ √ Hz at 0.1 Hz) and with TDI combined with 1 m rangning accuracy (560 Hz/ √ Hz at 0.1 Hz). Also shown for comparison is the typical free-running laser frequency for Nd:YAG NPRO lasers.

Figure 2 .

 2 Figure 2. Simplified system layout. The interferometer readout labeled φ R exists in the current LISA optical bench design. The interferometer readout labeled φ F is the readout for the proposed additional interferometer for measuring and actively suppressing the laser frequency noise.

Figure 3 .

 3 Figure 3. Closed loop frequency noise (solid blue trace) assuming a 50 cm pathlength mismatch.

Figure 4 .

 4 Figure 4. Frequency tuning response.

Acknowledgments

The authors thank the LISA Frequency Control Study Team for useful discussions. We acknowledge support by the Deutsches Zentrum für Luft-und Raumfahrt (DLR) (reference 50 OQ 0601) and QUEST (Centre for Quantum Engineering and Space-Time Research).


The monolithic suspension for the interferometer Virgo M Lorenzini 1 on behalf of Virgo Collaboration

Keywords: numbers: 04.80.Nn, 43.40.Cw, 62.40.+i, 46.50.+a

Monolithic fused silica suspensions are needed to reduce the suspension thermal noise level in future, ground-based gravitational waves interferometric detectors. We present the status of the monolithic suspension system which will be employed for the test masses of the Virgo+ detector. Two fully monolithic suspensions have been realized using a spare Virgo mirror, so the assembling pipeline was checked; moreover, a very reliable recovery procedure was developed, to allow an efficient and fast (about a week) suspension repairing in case of wires failure. The performances of a full scale prototype of the last suspension stage, suspending an aluminum dummy mass, were tested and the mechanical behaviour of the suspension is currently studied in vacuum. The obtained results, crucial to finalize the design of the silica suspension elements for the advanced version of the interferometer, are reported.

Introduction

Suspension thermal noise, coming from the thermal excitation of the mechanical degrees of freedom of the wires that suspend the test masses, is a limit to present day sensitivity of ground based gravitational waves interferometric detectors at low frequency. Virgo [1] is a 3 km long arm power-recycled Michelson interferometer located near Pisa (Italy). In Virgo, suspending elements are C85 steel wires, 0.2 mm thick, which pass below the mirrors in a cradle-like arrangement [2]. Spurious contact losses and the high structural loss of steel (φ 10 -4 ) make this solution unsuitable for future detectors. Fused silica has a very low loss level (φ 10 -9 [3,4]) at room temperature and high tensile strength, thus it has been suggested as ideal material for the suspension wires. Fused silica wires, connected to the mirror in a monolithic arrangement, have been installed in the German-British GEO600 detector [5]; and now advanced ground based gravitational waves interferometric detectors, such as Advanced LIGO (USA) [6] and Advanced Virgo [START_REF]Advanced Virgo Baseline Design[END_REF], are planning to install monolithic suspensions. The monolithic design for the "intermediate" advanced version of Virgo, called Virgo+ [START_REF] Tournefier E On | [END_REF], is being finalized and is detailed in the following sections.

The monolithic suspensions for Virgo+

Virgo is now in scientific data taking mode in coincidence with LIGOs. Due to the need of collecting as much scientific data as possible, the upgrade to Virgo+ was decided to be realized in steps, its commissioning being performed in parallel with scientific acquisition. Therefore, a shutdown is planned at the beginning of 2010 to install a new last stage of suspensions including monolithic arrangement of new mirrors.

The installation of monolithic suspensions will allow a relevant reduction of thermal noise level in the frequency region around 30-40 Hz. A new model [START_REF] Piergiovanni | Virgo Document[END_REF] of the suspension noise has been developed to take into account the contribution to the noise due to the upper suspension stage, which becomes relevant since losses in fused silica wires are expected to be very low. Nevertheless, the gain in using the monolithic solution is evident (see figure 1). With the monolithic suspensions it is possible to extend the average sight distance for the BNS inspiral from 13 Mpc up to 47 Mpc and for the BBH inspiral from 44 Mpc up to 394 Mpc, consequently increasing the observation rate up to 10 -1 /year for BNS [START_REF] Puppo | Virgo+MS sensitivity curve[END_REF]. In order to have a fully monolithic stage, fused silica wires have to be properly attached to the mirror. This is possible by means of suitable "ears" silicate bonded to the mirror sides. Moreover, they have to be clamped in a proper way to the upper stage of suspension. These simple requests lead to some critical technical point:

• thin silica wires produced from pure material must have a diameter of the order of hundreds of microns ‡. The working load for such wires is in the range of GPa, while ‡ The suspension wires optimal diameter results as a compromise between the optimization of the dilution factor and the limit imposed by the breaking load. Moreover, requests on violin and bouncing modes frequencies are set by control issues, thus for Virgo+, the chosen wires diameter is 280 µm.

for commercially available Suprasil R silica [START_REF]Trade mark from Heraeus Quarzglas[END_REF] the reported breaking stress is of the order of 50 MPa. Therefore, silica must be annealed to increase the maximum load to GPa. Also, after the production, one must avoid that anything touches the wires, since any scratch on them will abruptly decrease their breaking stress.

• suspension wires geometrical and dynamical parameters determine the statics of the suspended masses and the mirrors position control strategy §. Therefore, each of these parameters should be kept within a specified range.

• ears-to-mirrors and wires-to-ears connections must be not only easily operated and quality-controlled, but they must allow an efficient recovery action in case of failure. Further, they have not to spoil the silica wires performances in terms of low mechanical loss and high breaking stress. The same can be stated for the connections among the wires and the clamps on the payload.

• the payload recoil mass must be made of a dielectric material, in order to avoid eddy currents and magnetization effects due to the actuation coils.

Realization of a monolithic suspension

Silica parts composing the monolithic suspension can be joined using two methods, welding and chemical bonding. Welding is performed by locally heating the parts; bonding requires that a specific chemical technique, called silicate bonding [3,[START_REF] Gwo | Ultra precision and reliable bonding method United States Patent n o US 6284085 B1[END_REF][START_REF] Sneddon | [END_REF], be operated on very flat silica surfaces ( λ 10 to λ 4 depending on the process) to be glued together. Experience was collected that welding can be hardly performed in the neighborhood of a silicate bonded surface; otherwise, the bonded surface is deformed by the heat flux and the bonding strength is compromised. As a consequence, in some cases, direct welding of wires to ears, bonded to the masses, can be troublesome. Moreover, the latter technique makes difficult to recover the arrangement in case of wire failure.

The solution adopted for Virgo+ is a three steps operation, conceived for avoiding the use of welding tools in the vicinity of bonded ears. Referring to figure 2, the steps are:

• mirror is shaped by machining two flats on its curved sides. On the flats, two silica ears are silicate bonded, with grooves for the insertion of suspension elements (figure 2 (a)). The large bonding surface assures an adequate shear strength.

• a silica wire is produced with the lower tip welded to a silica piece named anchor, while the upper end is welded to a silica cone (figure 2 (b)). Each wire is tested to check for its strength and compliance to specifications.

• four wires are placed on the mirror by inserting the anchor under the bonded ear, within the groove, and silicate bonding the anchor to the ear (figure 2 (c)). Anchor top surface is optically flattened to allow silicate bonding. The upper cones of the wires are clamped to the payload making use of tight steel clamps (figure 2 (d)). § The geometry of the wires should be optimized in order to minimize the angular-to-translation couplings, thus simplifying the control issues (see section 3.2.3). The last two steps are performed in a clean chamber, at different levels of cleanliness up to 100 class around the mirror. Once the mirror is successfully suspended, it is safely blocked and the complete stage is assembled, including the reference mass.

Mirrors preparation

Virgo+ mirrors are 100 mm thick with a diameter of 350 mm, and a weight of 20.3 kg. Mirrors are prepared in LMA Lyon clean rooms [14]. After the coating procedure the lateral flats are cleaned and the silica supports (ears) are glued with the silicate bonding technique (KOH in H 2 O with a concentration of 1:250). Four magnets are glued on silica cylindrical supports through the cerama bond, then the supports are placed on the mirror surface with the anti-reflective coating through the silicate bonding. On Virgo+ mirrors the markers are not used any more. After the glueing procedure the mirrors are stored in the LMA cleaning room for one month.

Wires production and test

Silica wires, welded to anchors and cones as previously described, are produced and validated in a three tasks pipeline.

3.2.1. Wire pulling with CO 2 laser machine Silica wires are produced starting from high purity, 1.5 mm thick fused silica cylindrical bars commercially available (suitable material is Suprasil R ). Wires are obtained by melting the central region of a bar and subsequently pulling the two ends apart. In order to get reproducible results, the pulling has to be done in a controlled way. A machine for pulling fused silica wires using a 100 W CO 2 laser, developed at the University of Glasgow [START_REF] Heptonstall | LIGO technical[END_REF], has been assembled in a dedicated laser room at the site of the Virgo experiment. A schematic view of the functional parts of the machine is given in figure 3. Consider a silica rod clamped as in figure. The laser beam is delivered onto the fused silica rod by a series of gold coated mirrors. Thanks to the rotating and conic mirrors, the beam hit the rod continuously all around its axis, assuring an homogeneous local heating. The machine includes two arms connected to vertical sleighs which are moved by software controlled motors. Once the rod is melt by the laser, the upper arm pulls it upward following a given velocity profile and the wire is produced. The geometry of the pulled wire depends critically on the chosen velocity profile. Since the melting involves a small volume of the rod, from which the material is driven away, new material must be melt in order to feed the wire. Therefore, during the operation, the melting point must be shifted downward, and this is achieved by moving the conic mirror fixed to the lower arm. The machine can also be used for local welding, in which case it can be manually operated to get accurate results.

For the integration in the monolithic design, first of all a silica rod is welded at the ends to a silica anchor and to a silica cone. Then, the rod is annealed to melt structural imperfections and cracks. Finally, the wire is pulled from the rod as described. The profile of the obtained wire is very reproducible (within 10 µm), and its diameter (280 µm) is remarkably constant along the wire, except at the ends where a conic neck is formed.

Strength test

As soon as the wire is produced, it undergoes a safety load test. Being the working load about 5 kg, all the wires are tested by holding 10 kg for 30 min; if this test is successful, the wire is validated and passes to the following step.

The relevancy of this test is critical. Our experience proved that, if the pulling procedure is correctly followed, wire failure at the load test is very unlikely.

Geometrical and dynamical characterization

Mirrors statics needs and control issues directly fix requests on the wire geometry and dynamics. At low frequencies, the dynamical behaviour of the suspending wire is simply represented by a three-segment model [START_REF] Piergiovanni | Amaldi 8 poster[END_REF] (see figure 4) whose parameters are the two lengths λ t and λ b , called bending lengths, and the distance L among these points, when the wire is loaded. An important request is that both the top and bottom bending points must lie on the horizontal plane of the center of mass, respectively of the payload marionette and of the suspended mass; in fact, the mirror longitudinal to pitch coupling is minimized in this condition. In addition, the first violin frequency f V and the bouncing mode frequency f B of the wire, both depending on the load, must match the Virgo+ specifications. Hence, after the strength test, the wire length is accurately measured. A specific tool, developed at INFN laboratory in Firenze [START_REF] Piergiovanni | Amaldi 8 poster[END_REF][START_REF] Cagnoli | [END_REF], allows the wire bending lengths to be determined within 0.1 mm accuracy. Also f V and f B are measured while the wire is suspended to this tool.

The payload and assembling structure

The monolithic suspension payload is composed by the new design marionette and recoil mass (RM), which inherit all the specifications given by the Virgo style payload [START_REF] Bernardini | [END_REF], including the setup needed for the mirror local control purposes. Moreover, it must follow the requirements to ease the fused silica fibers installation and to avoid their breaking during the assembly and operation phases. For this reason the amagnetic stainless steel marionette has four cuts to allow the lateral insertion of the wires, and the holes, where the wires pass through, are widened to reduce the possibility of contact with the marionette body. The marionette arms are made of Tecapeek R , a dielectric material, to remove the eddy current and magnetization effects due to the coils.

The new RM is designed to surround the mirror and protect it in case of suspension failure, and also to support the coils which act on the magnets glued on the mirror. A Remember that, due to the presence of the necks, the wire cannot be simply modeled as a cylinder. relevant change that has been implemented is to position the markers for the local control on the coil supports of the reaction mass. The new RM is composed by two main parts tightly fastened together to form a single stiff piece: an inner structure made of the dielectric Tecapeek R CF30 and an outer structure made of AISI316L steel. The aim is to remove the eddy current effects between the magnets, the coils and the RM body and to keep its stiffness and the weight similar to the present Virgo one (see figure 5). The RM design includes a small lateral mirror used for an optical lever which monitors the lateral position.

The assembly structure (see figure 5) is designed to ease the transportation and insertion in the tower of the whole monolithic suspension. The design follows all the requirements for positioning and handling all the payload pieces, starting from the clean room until when the payload is hung to the superattenuator. The most delicate phase of the payload assembly is when each silica fiber is transported and fixed to the marionette. Once all the payload is assembled, every component is blocked: in particular the mirror is blocked to its RM with the safety stops, and to the structure by a vacuum lid on its front side which protects it also from the pollution during the transportation.

Dissipation measurements

Table 1-left shows a summary of the expected and measured quality factors on a 1:1 scale dummy monolithic suspension realized in a vacuum chamber. The quality factor of the pendulum mode (0.58 Hz) appears to be lower than the expected one. For this reason a series of tests has been made to understand the dominant losses in the measurement. Possible loss sources can be introduced by the upper cone clamping system, the anchor to ear bonding, the recoil of the suspension structure or other frictional processes affecting the system. 3.4.1. Anchors bonding A FEM simulation was performed to evaluate the losses due to the bonded region of the ears. In the simulation the fraction of elastic energy lost in the bonded zone during the mirror oscillation was calculated. The result is a value of Q pendulum ears = 2.2 × 10 12 for the pendulum mode and φ drum ears = 2.9 × 10 8 for the mirror drum mode [START_REF] Puppo | FEM of the strain energy stored in the Hydroxide-Catalysis Bonded ears of the mirrors for Virgo+[END_REF]. As a consequence the losses due to the bonded region are negligible for both the suspension and mirror thermal noise.

Upper clamp

To evaluate if the losses due to the upper clamp system were predominant, two tests were performed:

• a silica rod of 1.5 mm was welded to the upper clamp system and then put in a vacuum chamber. The Q measurements give a mean value of Q = 1 • 10 7 . This value is the one expected for the silica rod.

• an upper clamp with a Virgo+ standard silica wire was used to suspend different weights to verify the behaviour of the pendulum quality factor. Table 1-right shows the results for 1 kg. The measured values are dominated by recoil losses, as detailed in the following.

For the explored Q values no evidence of extra losses induced by the clamp were found.

Recoil losses

Comparing the measurements in tables 1-left and 1-right, it is interesting to see that the quality factor of the pendulum mode decreases with the inverse ratio of the suspended masses. It seems to fit the recoil losses model. The recoil losses are given by the following equation:

Q Rec = kl M gθ (1)
where k is the spring constant of the structure (at the pendulum frequency), θ is the phase angle between the force applied to the structure and its displacement, l is the length of the fiber loaded with the mass M . All these parameters are listed in [START_REF] Cagnoli | [END_REF].

The ratio between the two quality factor measurements is consistent with the inverse ratio of the masses of the two suspensions: 22 kg for the first suspension and 1 kg for the second. Other measurements with 3 and 5 kg are in course to verify if the Q scales linearly with the mass.

Conclusions

Monolithic suspensions will reduce the suspension thermal noise at low frequency in Virgo+. The complete suspension stages are going to be installed in the interferometer at the beginning of 2010. The suspension design and the realization steps have been successfully validated; the developed technique allows the suspension to be easily realized and rapidly recovered in case of wire failure. In the new local control design, the markers have been moved from the mirrors to the recoil mass. An estimation of the suspension pendulum quality factor is currently ongoing in order to understand if losses introduced by the wires clamping system can be neglected; at present, the measurements are probably limited by recoil losses in the suspension support. The latter point will be carefully investigated by exploiting the dependence of the pendulum quality factor on the suspended mass.

Figure 1 .

 1 Figure 1. Sensitivity curves of Virgo+ in the frequency region where the suspension thermal noise contributions are predominant. It is evident the gain in sensitivity due to the MS (red curve) with respect to the present one (blue curve) with steel wires.For a more detailed description of the curve refer to[START_REF] Puppo | Virgo+MS sensitivity curve[END_REF].

Figure 2 .

 2 Figure 2. Sketch of the steps followed to realize a monolithic suspension, as detailed in the text.

Figure 3 .

 3 Figure 3. Schematic view of the CO 2 laser machine employed for pulling the silica wires.

Figure 4 .

 4 Figure 4. Scheme of the three-segment model of a silica wire. M and I C are respectively the mass and the moment of inertia of the suspended mass. The model includes two angles θ and φ, describing the two low frequency resonances of the wire pendulum motion.

Figure 5 .

 5 Figure 5. Sketch of the MS payload and of the assembly structure.

Table 1 .

 1 (Left) Measured and theoretical quality factors for the monolithic dummy suspension (22 Kg). (Right) Measured and theoretical quality factors for one silica wire loaded with 1 kg.

	Q P endulumM eas 2.5 • 10 6	Q P endulumM eas 6 • 10 7
	Q P endulumT heor 2 • 10 9 Q RecoilT heor 4 • 10 7 Q Gas 9 • 10 7 Q SilicateBonding 3 • 10 8	Q P endulumT heor 9 • 10 8 Q RecoilT heor 8 • 10 8 Q Gas 8 • 10 8


Henning Vahlbruch

Alexander Khalaidovski

Nico Lastzka

Christian Gräf

Karsten Danzmann

Roman Schnabel
email: roman.schnabel@aei.mpg.de

The GEO 600 squeezed light source

published or not. The documents may come

Introduction

Photon shot-noise is a limiting noise source in laser interferometric gravitational wave (GW) detectors. The signal to shot-noise ratio can be improved by increasing the laser power. For this reason the planned Advanced LIGO detectors are designed to store about a megawatt of optical power inside the interferometer arms [1]. At such high laser powers thermally induced optical waveform distortion due to light absorption and the excitation of parasitic instabilities might become an issue [2,3]. Alternatively, the signal to shot-noise ratio can also be improved by 'squeezing' the shot-noise as proposed by Caves in 1981 [4]. In this case, the laser power inside the interferometer is not increased. In order to squeeze the shot-noise of a Michelson interferometer that is operated close to a dark fringe, squeezed (vacuum) states of light have to be injected into the signal output port. A squeezed state is a quantum state whose uncertainty in one of the field quadratures is reduced compared to the vacuum state, while the noise in the conjugate quadrature is increased. Later it was realized that squeezed states of light can also be used to reduce the overall quantum noise in interferometers including radiation pressure noise, thereby beating the standard-quantum-limit (SQL) [START_REF] Unruh | Quantum Optics, Experimental Gravitation, and Measurement Theory[END_REF][START_REF] Jaekel | [END_REF]. Theoretical analysis of Gea-Banacloche and Leuchs [7] and Harms et al. [8,9] suggested that squeezing is broadly compatible with interferometer recycling techniques [START_REF] Drever | Quantum Optics, Experimental Gravitation, and Measurement Theory[END_REF][START_REF] Meers | [END_REF] thereby further promoting the application of squeezed states in GW-detectors.

The first observation of squeezed states was done by Slusher et al. [13] in 1985. Since then different techniques for the generation of squeezed light have evolved. One of the most successful approaches for squeezed light generation is optical parametric amplification (OPA), also called parametric down-conversion, based on second-order nonlinear crystals. Common materials like MgO:LiNbO 3 or periodicly poled potassium titanyl phosphate (PPKTP) can be used to produce

Squeezing resonator

Diagnostic

Second Harmonic Generation (SHG)

Beam Dump

Electro optical modulator EOM x

Figure 1. Schematic of the complete optical setup of the GEO 600 squeezed light source including control lasers and diagnostic tools. Squeezed states of light at audio-band Fourier frequencies around the carrier frequency ω 0 are produced inside a nonlinear squeezing resonator via parametric down-conversion. The squeezing resonator contains a birefringent nonlinear crystal that is pumped with a green laser beam at 532 nm. Two auxiliary laser beams are also focussed into the crystal and serve as control beams for piezo-electric length stabilization of the cavity and the green pump phase. A balanced homodyne detector was used to characterize the squeezed light output. squeezing at the carrier wavelength of today's GW-detectors operating at 1064 nm. Ground based detectors require a broadband squeezed field in the detection band from about 10 Hz up to 10 kHz. Squeezed states were combined in table top experiments with interferometer recycling techniques [14,15], were demonstrated at audio frequencies [16,17,18,19], and were tested on a suspended GW prototype interferometer [20]. A coherent control scheme for the generation and stable control of squeezed vacuum states was also developed for the application in GW-detectors [18,21]. The progress achieved, now provides all the techniques for a first squeezed light upgrade of a large-scale signal-recycled gravitational wave detector at shot-noise limited frequencies as envisaged in [9].

In this paper we present a detailed description of the recently assembled GEO 600 squeezed light source. The optical layout and also elements of the control scheme are presented. Our first measurements demonstrate up to 9 dB squeezing over the complete detection bandwidth of ground-based GW-detectors.

Experimental

The schematic of the optical setup for the GEO 600 squeezed light source is shown in Figure 1. For clarity optical components like lenses, wave plates and steering mirrors etc. are omitted. The optical setup is partly based on earlier experiments presented in [18]- [22]. The device has been set up in a class 100 cleanroom in order to avoid dust particles and light scattering. Most optical components like steering mirrors and lenses have super-polished surfaces. The custommade breadboard of the GEO 600 squeezed light source has the dimensions of 135 cm x 113 cm. A thickness of about 5 cm (2 inches) in combination with a steel bottom plate and an aluminum inner structure and top plate was chosen to provide a high mechanical stability at a reasonable weight (approximately 70 kg). The dimensions of the breadboard are adapted to the available space on the GEO 600 detection bench where the squeezed light source will be operated. The now fully assembled squeezed light source, as shown in Fig. 3, has a weight of about 130 kg.

Squeezed-light laser resonator

The squeezed-light laser resonator ('squeezing resonator' in short) was set up as a standing-wave hemilithic cavity containing a plano-convex PPKTP crystal of about 10 mm length. The convex crystal surface is high-reflectivity coated for the fundamental and second-harmonic wavelengths at 1064 nm and 532 nm, respectively. The planar crystal surface is anti-reflection coated for both wavelengths. The coupling mirror of the standing-wave cavity is a piezo-actuated external mirror with a power reflectivity of R=92 % at 1064 nm and is placed in front of the planar crystal surface at a distance of approximately 20 mm. The resonator is singly resonant and has a Finesse of about 75 at 1064 nm. The PPKTP crystal is temperature stabilized to the phase matching temperature of the fundamental, down-converted squeezed (vacuum) field and the second harmonic pump field. Figure 2 shows a photograph of the quasi-monolithic squeezing resonator housing accommodating the nonlinear crystal, peltier and piezo elements as well as the out-coupling mirror.

Diagnostic homodyne detector

The GEO 600 squeezed light source features an integrated diagnostic balanced homodyne detector (BHD) which could be used to characterize the performance of the squeezed light decoupled from the GEO 600 interferometer. The required local oscillator beam of about 500 µW at 1064 nm is picked off from the main Nd:YAG laser (2 W, Mephisto from Innolight) and is injected into a spatial mode cleaning traveling-wave resonator. This cavity is held on resonance using the PDH-technique at a RF-modulation frequency of 76.5 MHz with a control bandwidth of 10 kHz. The transmitted beam interferes with the squeezed beam on a 50/50 beamsplitter with a fringe visibility of 98.6 %. Each beamsplitter output field is detected with a single high quantum efficiency photodiode. Both photo currents are subtracted from each other before electronic signal amplification.

Preparation of pump and control laser fields

The GEO 600 squeezed light source requires altogether four different laser frequencies as illustrated in Figure 1. A main laser at 1064 nm provides the optical reference frequency ω 0 . Two more laser fields at about 1064 nm have frequency offsets of more than 10 MHz with respect to ω 0 and serves as optical control fields. The fourth laser provides the second-harmonic pump field for the parametric down-conversion process at precisely 2ω 0 . All four laser fields are modematched and injected into the squeezing resonator. We now discuss the preparation and purpose of the four laser fields in more detail.

Main local oscillator beam at fundamental frequency ω 0 -The main laser source at frequency ω 0 will finally be phase locked to the GEO 600 laser source. This main laser provides the input field for the second harmonic generator and also serves as a local oscillator beam for homodyne detection of the generated squeezed vacuum field. Additionally, a small fraction of this laser beam is used for the initial alignment of the squeezing resonator. Subsequently this resonators length is stabilized using the light transmitted through the resonator, which is detected on the photodiode PD Alignment (see Figure 1). A RF-demodulation scheme deliveres a squeezing resonator length error signal, which is fed back onto the piezo-actuated cavity outcoupling mirror. If an intense alignment beam (about 100 mW) is injected, a sufficient amount of infrared photons at 1064 nm gets frequency doubled in order to align the green pump path in the counter direction comfortably. This counter propagating green field (compared to the pump beam) is monitored with either the photodiode PD P umpBeam or PD M C532trans . This offers an ideal alignment procedure of this beam path, which could otherwise only be adjusted by measuring the parametric gain inside the squeezed light source. This latter method can be quite imprecise and time consuming. Nevertheless, the parametric gain can alternatively be monitored using the DC-output of the photodetector PD Alignment . Please note that during the use of this alignment beam only squeezed states at Fourier frequencies in the MHz regime can be generated due to the technical laser noise carried with this beam at lower Fourier frequencies. Therefore, the alignment beam was switched off after the described alignment procedure.

Second harmonic pump field -The main laser frequency is frequency doubled by employing a second harmonic generator (SHG). This SHG produces the necessary pump field for the squeezing resonator at the frequency 2ω 0 . The design of the SHG is almost identical to the squeezed light source except that the nonlinear medium was MgO:LiNbO 3 instead of PPKTP. About 35 mW of pump power are required to achieve an appropriate parametric (de-)amplification factor. After being generated in the SHG, the pump field is guided to a ring-cavity. This mode cleaner has a Finesse of 555 and a linewidth (FWHM) of 1,3 MHz. The purpose of this resonator is to attenuate high frequency phase noise, which is inherent on the green beam due to RF-phasemodulation used for locking the SHG cavity length. It has been shown that phase noise on the green pump beam can deteriorate the squeezing strength [23,24]. Utilizing the photo diode PD M C532 an error signal for the cavity length control is generated via the Pound-Drever-Hall technique at a modulation frequency of 120 MHz, which is much higher compared to the cavity linewidth.

Squeezing resonator length control beam -A second NPRO-laser source (200 mW, Innolight Mephisto OEM Product Line), which is frequency locked to the main laser on the squeezing breadboard, serves for the cavity length control of the squeezed light source. Using the orthogonal polarization (p-polarization) for locking the cavity length, no technical laser noise is introduced into the squeezed beam at the fundamental frequency (ω 0 , s-polarization). Due to the birefringence of the nonlinear crystal inside the squeezed light source, however, this coherent control beam has to be frequency shifted to be simultaneously resonant with the generated s-polarized squeezed field. The frequency offset was determined to approximately 12.6 MHz. This was measured while injecting both the alignment beam at frequency ω 0 and the frequency shifted control beam. While scanning the cavity length, both orthogonally polarized TEM 00 Airy-peaks had to be overlapped. For monitoring the simultaneously resonant Airy-peaks, the photodetector PD Alignment was used.

Squeezing angle control beam -A third NPRO-laser (again with an output power of 200 mW) is set up for coherent control of the squeezing ellipse orientation with respect to the diagnostic homodyne detector. For this it is sufficient to inject only 25µW into the squeezed light source cavity in order to generate clear error signals. This auxiliary laser is again frequency locked to the main laser using a PLL with an offset frequency of 15.2 MHz. Operating on the GEO site, this coherent control field will finally be used to stabilize the phase relation between the squeezed vacuum field and the GEO 600 interferometer signal output field. Furthermore, this coherent control field will be used to set up an auto alignment system for the squeezed beam into the interferometer. Two locking loops are set up for full coherent control of the squeezed vacuum beam using this coherent control beam. The first loop stabilizes the relative phase between the injected control beam and the green pump field. To this end, an error signal is obtained by detecting a fraction of the (frequency shifted) light, which is back-reflected from the squeezed light source. Thus the photocurrent of the photodetector PD GreenP hase has to be demodulated at twice the offset frequency [18,19]. The feedback is applied to a phase shifter device in the green pump path with a unity gain frequency of 6 kHz. A second control loop is set up in order to stabilize the phase relation between the squeezed vacuum field and the local oscillator beam of the homodyne detector. The error signal is extracted from the subtracted photocurrents of both homodyne photo diodes via RF-demodulation at the coherent control beam offset frequency. A phase shifter in the local oscillator beam path serves as an actuator. The locking bandwidth of this control loop is about 10 kHz.

Results and discussion

In Figure 4, quantum noise measurements of the diagnostic balanced homodyne detector in the frequency band from 10 Hz up to 10 kHz are shown. Trace (a) represents a shot-noise measurement performed with the signal input port blocked of the homodyne detector. The local oscillator intensity was 500 µW throughout all the measurements. This LO power delivered a large dark noise clearance of 17 dB. When the squeezed states from our source are mode-matched into the homodyne detector signal input port the noise level changes according to the quantum noise variance of these states. Trace (b) shows the variance of the squeezed quantum noise and trace (c) the variance of the anti-squeezed noise. In order to perform these measurements, the local oscillator phase was stabilized to either the squeezed or the anti-squeezed field quadrature of the signal input, respectively. For the upgrade of GEO 600 one is obviously interested in the stabilization of the phase between the squeezed field and the GEO 600 signal field in such a way that the finally detected quantum noise is squeezed. Nevertheless, a full characterization of the squeezed field is only possible through the measurement of both the squeezed and anti-squeezed quadrature field variances. The squeezing level achieved in the detection band from 10 Hz to 10 kHz is at least 8 dB below the shot-noise level. At several frequencies, squeezing of up to 9 dB is observed. The corresponding anti-squeezing level was measured to be 14 dB above the shotnoise level over the entire bandwidth (trace (c)). From these measurements a total optical loss of approximately 10 % on the squeezed laser field can be derived. This loss value includes the homodyne detection efficiency of approximately 95 %. Thus, if the squeezed states are directly guided into the signal output port of GEO 600, the diagnostic homodyne detector loss can be subtracted, and more than 10 dB squeezing will be injected into the GW-detector.

In the following we estimate the expected nonclassical sensitivity improvement of the future squeezed-light enhanced GEO 600 detector assuming that additional optical loss will reduce the squeezing strength. We consider frequencies at which GEO 600 is currently shot-noise limited, i.e. above a few hundred Hertz. We estimate the additional optical loss for the squeezed field to 10 % up to 15 %. Here, we consider (i) a non-perfect mode matching to the GEO 600 signal-recycling The corresponding anti-squeezing (c) was 14 dB above the shot-noise level. The electronic dark noise (not shown) was 17 dB below the shot-noise and was not subtracted from the measured data. The peaks at 50 Hz and 100 Hz were due to the electric mains supply.

cavity, (ii) loss in the input Faraday isolator, (iii) non-perfect dielectric coatings of GEO 600 optics, and (iv) the non-perfect photo-diode quantum efficiency. From these assumptions we conclude, that finally a 6 dB nonclassical sensitivity improvement of GEO 600 might be reachable. This number corresponds to a sensitivity improvement that is equivalent to an increase in laser power by a factor of 4, without however, the unwanted side-effects from a higher thermal load.

Conclusion

We presented a detailed description of the optical setup of the GEO 600 squeezed light source and showed first measurement results. Up to 9 dB of squeezing over the entire bandwidth of the earth-based gravitational wave detectors was demonstrated. To the best of our knowledge, this is the highest measured squeezing value at audio frequencies observed so far. Our result also belongs to the highest squeezing values ever measured. At radio frequencies (MHz) only recently slightly higher values between 9 dB and 11.5 dB were reported [22,23,25]. We have estimated the additional optical loss for the squeezed-light field when injected into GEO 600 and come to the conclusion that a non-classical detector sensitivity improvement of 6 dB might be possible for the shot-noise limited band of GEO 600. After a long-term test the squeezed light source will be ready for the implementation in GEO 600.

  Photo diode (1064nm) (PD) Photo diode (532nm) (PD)Piezo-actuated mirror Faraday Isolator

Figure 2 .

 2 Figure 2. Photograph showing the housing of the nonlinear squeezing resonator. Nonlinear crystal, peltier and piezo-elements as well as the out-coupling mirror are embedded in a compact quasi-monolithic design for a high intrinsic mechanical stability.

Figure 3 .

 3 Figure 3. Photograph of the GEO 600 squeezed light source. The breadboard dimensions are 135 cm x 113 cm. The three Nd:YAG Lasers are located on the upper left, at the bottom left the squeezing resonator and on the bottom right the homodyne detector with its covering box is shown. The total weight of the complete system is approximately 130 kg.

Figure 4 .

 4 Figure 4. Quantum noise measurements performed with a balanced homodyne detector (BHD) using a 500 µW local oscillator power. Trace (a) constitutes the shot-noise (vacuum noise) reference of the BHD, measured with the squeezed light input blocked. Trace (b) shows the observed squeezed quantum noise from our source. A nonclassical noise suppression of up to 9 dB below shot-noise (a) was measured throughout the complete spectrum from 10 Hz up to 10 kHz.The corresponding anti-squeezing (c) was 14 dB above the shot-noise level. The electronic dark noise (not shown) was 17 dB below the shot-noise and was not subtracted from the measured data. The peaks at 50 Hz and 100 Hz were due to the electric mains supply.

Acknowledgments

This work has been supported by the Deutsche Forschungsgemeinschaft (DFG) through Sonderforschungsbereich 407 and the Centre for Quantum Engineering and Space-Time Research QUEST.