Review: Semiconductor Quantum Light Sources
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Preprint version of Nature Photonics 1, 215 (2007) 
Review: Semiconductor Quantum Light Sources  
Andrew J Shields  
Toshiba Research Europe Limited, 260 Cambridge Science Park, Cambridge CB4 0WE, UK 
Abstract 
Lasers and LEDs display a statistical distribution in the number of photons emitted in a given time interval.  New 
applications exploiting the quantum properties of light require sources for which either individual photons, or pairs, are 
generated in a regulated stream.  Here we review recent research on single-photon sources based on the emission of a 
single semiconductor quantum dot.  In just a few years remarkable progress has been made in generating 
indistinguishable single-photons and entangled photon pairs using such structures.  It suggests it may be possible to 
realise compact, robust, LED-like semiconductor devices for quantum light generation.   
Applications of Quantum Photonics 
Applying quantum light states to photonic applications allows functionalities that are not possible using ‘ordinary’ 
classical light.  For example, carrying information with single-photons provides a means to test the secrecy of optical 
communications, which could soon be applied to the problem of sharing digital cryptographic keys.1 2 Although secure 
quantum key distribution systems based on weak laser pulses have already been realised for simple point-to-point links, 
true single-photon sources would improve their performance.3 Furthermore, quantum light sources are important for 
future quantum communication protocols such as quantum teleportation. 4   Here quantum networks sharing 
entanglement could be used to distribute keys over longer distance or through more complex topologies.5   
A natural progression would be to use photons for quantum information processing, as well as communication.  In this 
regard it is relatively straightforward to encode and manipulate quantum information on a photon.   On the other hand, 
single-photons do not interact strongly with one-another, a prerequisite for a simple photon logic gate.  In linear optics 
quantum computing67 (LOQC) this problem is solved using projective measurements to induce an effective interaction 
between the photons.  Here triggered sources of single-photons and entangled pairs are required as both the qubit 
carriers, as well as auxiliary sources to test the successful operation of the gates.  Although the component requirements 
for LOQC are challenging, they have recently been relaxed significantly by new theoretical schemes. 7  Quantum light 
states are also likely to become increasingly important for various types of precision optical measurement.8  
For these applications we would ideally like light sources which generate pure single-photon states “on demand” in 
response to an external trigger signal.  Key performance measures for such a source are the efficiency, defined as the 
fraction of photons collected into the experiment or application per trigger, and the second order correlation function at 
zero delay, see text box.  The latter is essentially a measure of the two-photon rate compared to a classical source with 
random emission times of the same average intensity.  In order to construct applications involving more than one 
photon, it is also important that photons emitted from the source (at different times), as well as those from different 
sources, are otherwise indistinguishable.   
In the absence of a convenient triggered single-photon source, most experiments in quantum optics rely on non-linear 
optical processes for generating quantum light states.  Optically pumping a crystal with a χ(2) non-linearity has a finite 
probability of generating a pair of lower energy photons via parametric down conversion.  This may be used to prepare 
photon pairs with time-bin entanglement,9 entangled polarisations,1011 or alternatively single-photon states ‘heralded’ by 
the second photon in the pair.12  A χ(3) non-linearity in a semiconductor has also been used to generate entangled 
pairs.13  As these non-linear processes occur randomly, there is always a finite probability of generating two pairs that 
increases with pump power.  As double pairs degrade the fidelity of quantum optical gates, the pump laser power must 
be restricted to reduce the rate of double pairs to an acceptable level, which has a detrimental effect upon the efficiency 
of the source.14  This means that although down-conversion sources continue to be highly successful in demonstrating 
few photon quantum optical gates, scaling to large numbers may be problematic. Solutions have been proposed based 
on switching multiple sources,15 or storing photons in a switched fibre loop.16    
Ideally we would like a quantum light source that generates exactly one single-photon, or entangled-pair, per excitation 
trigger pulse.  This may be achieved using the emission of a single quantum system.  After relaxation, a quantum 
system is by definition no longer excited and therefore unable to re-emit.  Photon anti-bunching, the tendency of a 
quantum source to emit photons separated in time, was first demonstrated in the resonance fluorescence of a low density 
vapour of Na atoms,17 and subsequently for a single ion.18   
Quantum dots are often referred to as “artificial atoms”, as their electron motion is quantised in all three spatial 
directions, resulting in a discrete energy level spectrum, like that of an atom.  They provide a quantum system which 
can be grown within robust, monolithic semiconductor devices and can be engineered to have a wide range of desired 
properties.  In the following we review recent progress towards the realisation of a semiconductor technology for 
quantum photonics.  An excellent account of the early work can be found in Ref. 19. Space restrictions limit discussion 
of work on other quantised systems. For this we refer the reader to the comprehensive review in Ref 20. 
Optical Properties of Single Quantum Dots 
Nano-scale quantum dots with good optical properties can be fabricated using a natural growth mode of strained layer 
semiconductors.21  When InAs is deposited on GaAs it initially grows as a strained two-dimensional sheet, but beyond 
some critical thickness, tiny islands like those shown in Fig.1a form in order to minimize the surface strain.  
Overgrowth of the islands leads to the coherent incorporation of InxGa1-xAs dots into the crystal structure of the device, 
as can be seen in the cross-sectional image of Fig.1c.  The most intensively studied are small InAs dots on GaAs 
emitting around 900-950nm at low temperatures, which can be conveniently measured with low noise Si single photon 
detectors.    
A less desirable feature of the self-organising technique is that the dots form at random positions on the growth surface.  
However, recently considerable progress has been made on controlling the dot position (Fig.1b) within the device 
structure by patterning nanometer sized pits on the growth surface.2223   
As InGaAs has a lower energy bandgap than GaAs, the quantum dot forms a potential trap for electrons and holes.  If 
sufficiently small, the dot contains just a few quantised levels in the conduction and valence bands, each of which holds 
two electrons or holes of opposite spin.   Illumination by a picosecond laser pulse excites electrons and holes which 
rapidly relax to the lowest lying energy states either side of the bandgap.  A quantum dot can thus capture two electrons 
and two holes to form the biexciton state, which decays by a radiative cascade, as shown schematically in Fig.2a.  One 
of the trapped electrons recombines with one of the holes and generates a first photon (called the biexciton photon, X2).  
This leaves a single electron-hole pair in the dot (the exciton state), which subsequently also recombines to generate a 
second (exciton, X) photon.  The biexciton and exciton photons have distinct energies, as can be seen in the low 
temperature photoluminescence spectrum of Fig.2a, due to the different Coulomb energies of their initial and final 
states.  Often a number of other weaker lines can also be seen due to recombination of charged excitons which form 
intermittently when the dot captures an excess electron or hole.24  Larger quantum dots, with several confined electron 
and hole levels, have a richer optical signature due to the large number of exciton complexes that can be confined.   
High resolution spectroscopy reveals that the X2 and X transitions of a dot are in fact both doublets with linearly 
polarised components parallel to the [110] and [1-10] axes of the semiconductor crystal, labelled here H and V, 
respectively.2526  The origin of this polarisation is an asymmetry in the electron-hole exchange interaction of the dot 
which produces a splitting of the exciton spin states.  The asymmetry derives from an elongation of the dot along one 
crystal axis and in-built strain in the crystal.  It mixes the exciton eigenstates of a symmetric dot with total z-spin Jz = 
+1 and -1 into symmetric and anti-symmetric combinations, which couple to two H or two V polarised photons, 
respectively, as shown in Fig.2.   
The exciton state of the dot has a typical lifetime of ~1ns, which is due purely to radiative decay.  As this is much 
longer than the duration of the exciting laser pulse, or the lifetime of the photo-excited carrier population in the 
surrounding semiconductor, only one X photon can be emitted per laser pulse.  This can be proven, as first reported27 by 
Peter Michler, Atac Imamoglu and their colleagues in Santa Barbara, by measuring the second order correlation 
function, g(2)(τ) of the exciton photoluminescence,2829 see text box.  In fact each of the exciton complexes of the dot 
generates at most one photon per excitation cycle, which allows single-photon emission from also the biexciton or 
charged exciton transitions.30  
Cross-correlation measurements313233  between the X and X2 photons confirm the time correlation expected for the 
cascade in Fig.2a, ie the X photon follows the X2 one.  Indeed the shape of the cross-correlation function for both CW 
and pulsed excitation can be accurately described with a simple rate equation model and the experimentally measured X 
and X2 decay rates.
 34   
Semiconductor Microcavities 
A major advantage of using self-assembled quantum dots for single-photon generation is that they can be easily 
incorporated into cavities using standard semiconductor growth and processing techniques.  Cavity effects are useful for 
directing the emission from the dot into an experiment or application, as well as for modifying the photon emission 
dynamics. 3536 Purcell37 predicted enhanced spontaneous emission from a source in a cavity when its energy coincides 
with that of the cavity mode, due to the greater density of optical states to emit into.  For an ideal cavity, in which the 
emitter is located at the maximum of the electric field with its dipole aligned with the local electric field, the 
enhancement in decay rate is given by Fp = (3/4π
2) (λ/n)3 Q/V, where Q is the quality factor, a measure of the time a 
photon is trapped in the cavity, and V is the effective mode volume.  Thus high photon collection efficiency, and 
simultaneously fast radiative decay, requires small cavities with highly reflecting mirrors and a high degree of structural 
perfection.  However, without controlling the location of the dot in the cavity, as discussed below, it may be difficult to 
achieve the full enhancement predicted by the Purcell formula.   
Figure 3 shows images of some of the single quantum dot cavity structures that have proven most successful.  Pillar 
microcavities, formed by etching cylindrical pillars into semiconductor Bragg mirrors placed either side of the dot layer, 
have shown large Purcell enhancements and have a highly directional emission profile, thus making good single-photon 
sources.38394041 Purcell factors of around 6 have been measured directly,4041 through the rate of cavity-enhanced radiative 
decay compared to that of a dot without cavity, implying a coupling to the cavity mode of β=Fp/(1+Fp)>85%, if we 
assume the leaky modes are unaffected by the cavity.  However, the experimentally determined photon collection 
efficiency, which is a more pertinent parameter for applications, is typically ~10%, due the fact that not all the cavity 
mode can be coupled into an experiment and scattering of the mode by the rough pillar edges.  We can expect that the 
photon collection efficiency will increase with improvements to the processing technology or new designs of 
microcavity.   
Another means of forming a cavity is to etch a series of holes in a suspended slab of semiconductor, so as to form a 
lateral variation in the refractive index which creates a forbidden energy gap for photonic modes in which light cannot 
propagate.42  Photons can then be trapped in a central irregularity in this structure: usually an unetched portion of the 
slab.  Such photonic bandgap defect cavities have been fabricated in Si with Q values approaching 106.4344  High quality 
active cavities have also been demonstrated in GaAs containing InAs quantum dots. 45464748  A radiative lifetime of 86 ps, 
corresponding to a Purcell factor of Fp~12, has been reported.
47  Very recently a lifetime of 60ps was measured for a 
cavity in the strong coupling regeme.48  
If the Q-value is sufficiently large, the system enters the strong coupling regime where the excitation oscillates 
coherently between an exciton in the dot and a photon in the cavity.  The spectral signature of strong coupling, an anti-
crossing between the dot line and the cavity mode, has been observed for quantum dots in pillar microcavities,49 
photonic bandgap defect cavities,50 microdisks51 and microspheres.52  It has been demonstrated for atom cavities that 
strong coupling allows the deterministic generation of single-photons.5354  Single-photon sources in the strong coupling 
regime can be expected to have very high extraction efficiencies and be time-bandwidth limited.55  Encouragingly 
single-photon emission has been reported recently for a dot in a strongly coupled pillar microcavity. 56      
Another interesting recent development is the ability to locate a single quantum dot within the cavity, as this ensures the 
largest possible coupling and removes background emission, as well as other undesirable effects, due to other dots in 
the cavity.  Above we discussed techniques to control the dot position on the growth surface.  The other way is to 
position the cavity around the dot.  One technique combines micro-photoluminescence spectroscopy to locate the dot 
position, with in-situ laser photolithography to pattern markers on the wafer surface.57  An alternative involves growing 
a vertical stack of dots so that their location can be revealed by scanning the wafer surface, 58 as shown in Fig.3.  
Recently this technique has allowed larger coupling energies for a single dot in a photonic bandgap defect cavity.48   
Photon Indistinguishability 
Cavity effects are important for rendering different photons from the source indistinguishable, which is essential for 
many applications in quantum information.  When two identical photons are incident simultaneously on the opposite 
input ports of a 50/50 beamsplitter, they will always exit via the same output port, 59 as shown schematically in Fig.4a. 
This occurs because of a destructive interference in the probability amplitude of the final state in which one photon exits 
through each output port.  The amplitude of the case where both photons are reflected exactly cancels with that where 
both are transmitted, due to the π/2 phase change upon reflection, provided the two photons are entirely identical.   
Two-photon interference of two single-photons emitted successively from a quantum dot in a weakly-coupled pillar 
microcavity was first reported by the Stanford group.60 Fig. 4b shows a schematic of their experiment.  Notice the 
reduction of the co-incidence count rate measured between detectors in either output port, when the two photons are 
injected simultaneously (Fig.4c).  The dip does not extend completely to zero, indicating that the two photons sometime 
exit the beamsplitter in opposite ports.  The measured reduction in co-incidence rate at zero delay of 69%, implies an 
overlap for the single-photon wavepackets of 0.81, after correcting for the imperfect single-photon visibility of the 
interferometer.  Two-photon interference dips of 66% and 75% have been reported by Bennett et al61  and Vauroutsis et 
al. 62   Similar results have been obtained for a single dot in a photonic bandgap defect cavity.63   
This two-photon interference visibility is limited by the finite coherence time of the photons emitted by the quantum 
dot,64 which renders them distinguishable.  The depth of the dip in Fig.4c depends upon the ratio of radiative decay time 
to the coherence time of the dot, ie R=2τdecay/τcoh. When unity, the coherence time is limited by radiative decay and the 
source will display perfect 2-photon interference.  The most successful approach thus far has been to extend τcoh by 
resonant optical excitation of the dot and reduce τdecay using the Purcell effect in a pillar microcavity, to values R~1.5.
the future higher visibilities may be achieved with a larger Purcell enhancement, using a single dot cavity in the strong-
coupling regime or with electrical gating described in the next section.   
A source of indistinguishable single-photons was used by Fattal et al to generate entanglement between post-selected 
pairs. 65 66  This involves simply rotating the polarisation of one of the photons incident on the final beamsplitter in 
Fig.4a by 90o.  By post-selecting the results where the two photons arrive at the beamsplitter at the same time and where 
there is one photon in each output arm (labelled 1 and 2), the measured pairs should correspond to the Bell state 
ψ− =  1/√2 (¦H1 V2 > - ¦V1 H2 >)            Eq.1 
Note that only if the two photons are indistinguishable and thus the entanglement is only in the photon polarisation, are 
the two terms in Eq1 able to interfere. Analysis of the density matrix published by Fattal et al65 reveals a fidelity of the 
post-selected pairs to the state in Eq.1 of 0.69, beyond the classical limit of 0.5.  This source of entangled pairs has an 
importance difference to that based on the biexciton cascade described below.  Post-selection implies that the photons 
are destroyed when this scheme succeeds.  This is a problem for some quantum information applications such as LOQC, 
but could be usefully applied to quantum key distribution.65   
Single-Photon LEDs 
An early proposal for an electrical single-photon source by Kim et al67  was based upon etching a semiconductor 
heterostructure displaying Coulomb blockade. However, the light emission from this etched structure was too weak to 
allow the second-order correlation function to be studied. Recently encouraging progress has been made towards the 
realisation of a single-photon source based on quantising a lateral electrical injection current.6869  However the most 
successful approach so far has been to integrate self-assembled quantum dots into conventional p-i-n doped junctions. 
In the first report of electrically-driven single-photon emission by Yuan et al,70 the electroluminescence of a single dot 
was isolated by forming a micron-diameter emission aperture in the opaque top contact of the p-i-n diode.  Fig.5a shows 
an improved emission aperture single-photon LED after Bennett et al, 71 which incorporates an optical cavity formed 
between a high reflectivity Bragg mirror and the semiconductor/air interface in the aperture. This structure forms a weak 
cavity, which enhances the measured collection efficiency 10-fold compared to devices without a cavity. 72      
Single-photon pulses are generated by exciting the diode with a train of short voltage pulses. The second order 
correlation function g(2)(τ) of either the X or X2  electroluminescence (Fig.5c) shows the suppression of the zero delay 
peak indicative of single-photon emission.71  The finite rate of multi-photon pulses is due mostly to background 
emission from layers other than the dot, which is also seen for non-resonant optical excitation.  Electrical contacts also 
allow the temporal characteristics of the single-photon source to be tailored. By applying a negative bias to the diode 
between the electrical injection pulses, Bennett et al73  reduced the jitter in the photon emission time <100ps. This 
allowed the repetition rate of the single-photon source to be increased to 1.07GHz (Fig.5d) while retaining good single-
photon emission characteristics (Fig.5e).  Electrical gating could provide a technique for producing time-bandwidth-
limited single-photons from quantum dots.   
Another promising approach is to aperture the current flowing through the device.7475  This is achieved by growing a 
thin AlAs layer within the intrinsic region of the p-i-n junction and later exposing the mesa to wet oxidation in a 
furnace, converting the AlAs layer around the outer edge of the mesa to insulating Aluminium oxide.  By careful 
control of the oxidation time, a µm-diameter conducting aperture can be formed within the insulating ring of AlOx.  
Such structures have the advantage of exciting just a single dot within the structure, thereby reducing the amount of 
background emission.  The oxide annulus also confines the optical mode laterally within the structure, potentially 
allowing high photon extraction efficiency.   
Altering the nanostructure or materials that comprise the quantum dot allows considerable control over the emission 
wavelength and other characteristics.  Most of the experimental work done so far has concentrated on small InAs 
quantum dots emitting around 900-950nm, as these have well understood optical properties and can be detected with 
low noise Si single-photon detectors. On the other hand the shallow confinement potentials of this system means they 
emit only at low temperatures.  At shorter wavelengths optically-pumped single-photon emission has been demonstrated 
at ~350nm using GaN/AlGaN,76 500nm using CdSe/ZnSSe77 and 682nm InP/GaInP78 quantum dot.  The former two 
systems have been shown to operate at 200K.   
It is very important for quantum communications to develop sources at longer wavelengths in the fibre optic 
transmission bands at 1.3 and 1.55µm.  This may be achieved using InAs/GaAs heterostructures by depositing more 
InAs to form larger quantum dots. These larger dots offer deeper confinement potentials than those at 900nm and thus 
often display room temperature emission.79 Optically pumped single-photon emission at telecom wavelengths has been 
achieved using a number of techniques to prepare low densities of longer wavelength dots, including a bimodal growth 
mode in MBE to form low densities of large dots,80 ultra-low growth rate MBE81 and MOCVD.82  Recently, the first 
electrically-driven single-photon source at a telecom wavelength has been demonstrated.83   
Generation of Entangled Photons 
By collecting both the X2 and X photons emitted by the biexciton cascade, a single quantum dot may also be used as a 
source of photon pairs.  Polarisation correlation measurements on these pairs discovered that the two photons were 
classically-correlated with the same linear polarisation.848586  This occurs because the cascade can proceed via one of 
two intermediate exciton spin states, as described above and shown in Fig.2a, one of which couples to two H- and the 
other two V-polarised photons.  The emission is thus a statistical mixture of |HX2HX> and |VX2VX>, although exciton 
spin scattering during the cascade (discussed below) ensures there are also some cross-polarised pairs.   
The spin splitting87,88 of the exciton state of the dot distinguishes the H and V polarised pairs and prevents the emission 
of entangled pairs predicted by Benson et al. 89  If this splitting could be removed, the H and V components would 
interfere in appropriately designed experiments.  The emitted 2-photon state should then be written as a superposition of 
HH and VV, which can be recast in either the diagonal (spanned by D, A) or circular (σ+, σ-) polarisation bases, ie  
Φ+ =  1/√2 (¦HX2 HX > + ¦VX2 VX >)   
    =  1/√2 (¦DX2 DX > + ¦ΑX2 ΑX >)   
                 =  1/√2 (¦σ+X2 σ
X > + ¦σ
X >)  Eq.2. 
Equal weighting of the HH and VV terms assumes the source to be unpolarised, as indicated by experimental 
measurements.  
Eq.2 suggests that, for zero exciton spin splitting, the biexciton cascade generates entangled photon pairs, similar to 
those seen for atoms.90  Entanglement of the X or X2 photons was recently observed experimentally for the first time by 
Stevenson, Young and co-workers,9192   using two different schemes to cancel the exciton spin splitting. An alternative 
approach by Akopian et al, 93 using dots with finite exciton splitting, post-selects photons emitted in a narrow spectral 
band where the two polarisation lines overlap.    
The exciton spin splitting depends on the exciton emission energy, tending to zero for InAs dots emitting close to 1.4eV 
and then inverting for higher emission energy. 94 95 These correspond to shallow quantum dots for which the carrier 
wavefunctions extend into the barrier material reducing the electron-hole exchange.  Zero splitting can be achieved by 
either careful control of the growth conditions to achieve dots emitting close to the desired energy, or by annealing 
samples emitting at lower energy.94  The exciton spin splitting may be continuously tuned by applying a magnetic field 
in the plane of the dot.96 It has been observed that the signatures of entanglement then appear only when the exciton 
splitting is close to zero.91  Other promising schemes to tune the exciton splitting are now emerging, including 
application of strain97 and electric field.9899  
Figure 6a plots polarisation correlations reported by Young et al92 for a dot with zero exciton splitting (by control of the 
growth conditions).  Pairs emitted in the same cascade (ie zero delay) shows a very striking positive correlation (co-
polarisation) measuring in either, rectilinear or diagonal bases and anti-correlation (cross-polarisation) when measuring 
in circular basis.  This is exactly the behaviour expected for the entangled state of Eq.2.  In contrast, a dot with finite 
splitting shows polarisation correlation for the rectilinear basis only, with no correlation for diagonal or circular 
measurements, see Figure 6b.  The strong correlations seen for all three bases in Fig.6a could not be produced by any 
classical light source or mixture of classical sources and is proof that the source generates entangled photons. The 
measured92 two-photon density matrix (Fig.6c) projects onto the expected 1/√2 (¦HX2 HX > + ¦VX2 VX >) state with 
fidelity (ie probability) 0.702 ± 0.022, exceeding the classical limit (0.5) by 9 standard deviations.  
Two processes contribute to the ‘wrongly’ correlated pairs which impair the fidelity of the entangled photon source.  
The first of these is due to background emission from layers in the sample other than the dot.  This background 
emission, which is unpolarised and dilutes the entangled photons from the dot, limited the fidelity observed in the first 
report91 of triggered entangled photon pairs from a quantum dot and has been subsequently reduced with better sample 
design.92  The second mechanism, which is an intrinsic feature of the dot, is exciton spin scattering during the biexciton 
cascade.  It is interesting that this process does not seem to depend strongly upon the exciton spin splitting.  It may be 
reduced by suppressing the scattering using resonant excitation or alternatively using cavity effects to reduce the time 
required for the radiative cascade.    
Outlook 
The past several years have seen remarkable progress in quantum light generation using semiconductor devices.  
However, despite considerable progress many challenges still remain.  The structural integrity of cavities must continue 
to improve, thereby enhancing quality factors.  This, combined with the ability to reliably position single dots within the 
cavity, will further enhance photon collection efficiencies and the Rabi energy in the strong coupling regime.  It is also 
important to realise all the benefits of these cavity effects in more practical electrically-driven sources.  Meanwhile 
bandstructure engineering of the quantum dots will allow a wider range of wavelengths to be accessed for both single 
and entangled photon sources, as well as structures that can operate at higher temperatures.  Techniques for fine tuning 
the characteristics of individual emitters will also be important.   
One of the most interesting aspects of semiconductor quantum optics is that we may be able to use quantum dots not 
only as quantum light emitters, but also as the logic and memory elements which are required in quantum information 
processing.  Although LOQC is scalable theoretically, quantum computing with photons would be much easier with a 
useful single-photon non-linearity.  Such non-linearity may be achieved with a quantum dot in a cavity in the strong 
coupling regime.  Encouragingly strong coupling of a single quantum dot with various type of cavity has already been 
observed in the spectral domain.  Eventually it may even be possible to integrate photon emission, logic, memory and 
detection elements into single semiconductor chips to form a photonic integrated circuit for quantum information 
processing.   
The author would like to thank Mark Stevenson, Robert Young, Anthony Bennett, Martin Ward and Andy Hudson for 
their useful comments during the preparation of the manuscript and the UK DTI “Optical Systems for Digital Age”, 
EPSRC and EC Future and Emerging Technologies programmes for supporting research on quantum light sources.   
TextBox : Photon Correlation Measurements 
The photon statistics of light can be studied via the second order correlation function, g(2)(τ), which describes the 
correlation between the intensity of the light field with that after a delay τ and is given by100   
This function can be measured directly using the Hanbury-Brown and Twiss101 interferometer, comprising a 50/50 
beamsplitter and two single-photon detectors, shown in the figure.  For delays much less than the average time between 
detection events (ie for low intensities), the distribution in the delays between clicks in each of the two detectors is 
proportional to g(2)(τ).   
For a continuous light source with random emission times, such as an ideal laser or LED, g(2)(τ)=1.  It shows there is no 
correlation in the emission time of any two photons from the source.  A source for which g(2)(τ=0)>1 is described as 
'bunched' since there is an enhanced probability of two photons being emitted within a short time interval.  Photons 
emitted by quantum light sources are typically 'anti-bunched', (g(2)(τ=0)<1) and tend to be separated in time.   
In communication and computing systems, we are interested in pulsed light sources, for which the emission occurs at 
times defined by an external clock.  In this case g(2)(τ) consists of a series of peaks separated by a clock period. For an 
ideal single-photon source, the peak at zero time delay is absent, g(2)(τ=0)=0;  as the source cannot produce more than 
one photon per excitation period, clearly the two detectors cannot fire simultaneously.   
The figure shows g(2)(τ) recorded for resonant pulsed optical excitation of the X emission of a single quantum dot in a 
pillar microcavity.  Notice the almost complete absence of the peak at zero delay: the definitive signature of a single-
photon source.  The weak peak seen at τ=0 demonstrates that the rate of two-photon emission is 50 times less than that 
of an ideal laser with the same average intensity.  The bunching behaviour observed for the finite delay peaks is 
explained by intermittent trapping of a charge carrier in the dot.102  This trace was taken for quasi-resonant laser 
excitation of the dot which avoids creating carriers in the surrounding semiconductor.  For higher energy laser 
excitation, the suppression in g(2)(0) is typically reduced indicating occasional 2-photon pulses due to emission from the 
layers surrounding the dot, but can be minimised with careful sample design.   
Figure textbox: (a) Schematic of the set-up used for photon correlation measurements, (b) second order correlation 
function of the exciton emission of a single dot in a pillar microcavity.  
Figure Captions 
Figure 1: Self assembled quantum dots (a) Image of a layer of InAs/GaAs self assembled quantum dots recorded in an 
Atomic Force Microscope (AFM).  Each yellow blob corresponds to a dot with typical lateral diameters of 20-30nm and 
a height of 4-8nm.  (b) AFM image23 of a layer of InAs quantum dots whose locations have been seeded by a matrix of 
nanometer sized pits patterned onto the wafer surface.  Under optimal conditions up to 60% of the etch pits contain a 
single dot (Courtesy of P Atkinson & D A Ritchie, Cambridge). (c) Cross-sectional STM image of an InAs dot inside a 
GaAs device (Courtesy of P. Koenraad, Eindhoven).   
Figure 2: Optical spectrum of a quantum dot. (a) Schematic of the biexciton cascade of a quantum dot.  (b) Typical 
photoluminescence spectrum of a single quantum dot showing sharp line emission due to the biexciton X2 and exciton X 
photon emitted by the cascade.   The inset shows the polarisation splitting of the transitions originating from the spin 
splitting of the exciton level. 
Figure 3: SEM images of semiconductor cavities, including pillar microcavities (a)56 and (b), microdisk (c)51 and 
photonic bandgap defect cavities (d)47, (e) and (f).48  (Structures fabricated at Univ Wuerzburg (a), CNRS-LPN (UPR-
20), Marcoussis (b, c, e), Univ Cambridge (d), UCSB/ETHZ Zurich (f))      
Figure 4: Two Photon Interference.  (a) If the two photons are indistinguishable, the two outcomes resulting in one 
photon in either arm interfere destructively. This results in the two photons always exiting the beamsplitter together. (b) 
Schematic of an experiment using two photons emitted successively from a quantum dot, (c) experimental data showing 
suppression of the co-incidence rate in (b) when the delay between input photons is zero due to two-photon 
interference.60  (Courtesy of Y Yamamoto, Stanford Univ.) 
Figure 5: Electrically driven single-photon emission.  (a) Schematic of a single-photon LED. (b) Electroluminescence 
spectra of the device.  Notice the spectra are dominated by the exciton X and biexciton X2 lines, which have linear and 
quadratic dependence on drive current, respectively.  Other weak lines are due to charged excitons. (c) second order 
correlation function recorded for the exciton (i) and biexciton (ii) emission lines, (d) time-resolved electroluminescence 
from a device operate with a 1.07GHz repetition rate, (e) measured (i) and modelled (ii) second order correlation 
function of the biexciton electroluminescence at 1.07GHz.  (adapted from Refs. 71and  73) 
Figure 6: Generation of entangled photons by a quantum dot. (a) Degree of correlation measured for a dot with exciton 
polarisation splitting S=0 µeV in linear (i), diagonal (ii) and circular (iii) polarisation bases as a function of the delay 
between the X and X2 photons (in units of the repetition cycle).  The correlation is defined as the rate of co-polarised 
pairs minus the rate of cross-polarised pairs divided by the total rate.  Notice that the values at finite delay show no 
correlation, as expected for pairs emitted in different laser excitation cycles.  More interesting are the peaks close to 
zero time delay, corresponding to X and X2 photon emitted from the same cascade.  The presence of strong correlations 
for all three types of measurement for the dot with zero exciton splitting can only be explained if the X and X2 
polarisations are entangled. (b) Degree of correlations measured for the dot in (a) subject to in-plane magnetic field so 
as to produce an exciton polarisation splitting of S=25 µeV. Notice that the correlation in diagonal and circular bases 
have vanished, indicating only classical correlations at finite splitting.  (c) Two-photon density matrix of the device 
emission in (a).  The strong off-diagonal terms appear due to entanglement.  (adapted from Ref 92) 
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500 nm 500 nm
Fig. 1 
1375 1380 1385
Detection polarisation:
Vertical
Horizontal
Photon Energy (meV)
1378.0 1378.5 1380.0 1380.5
(b)(a)
Fig. 2 
ground state
500 nm
500nm
(c)(a) (b)
(e) (f)
Fig. 3 
(a) (b)
Fig. 4
substrate/buffer
n-ohmic
contact
InAs QD
insulator
Al p-ohmic
contact
emission
n+ Bragg mirror
cavity layer
contact
metal
p+ GaAs
Semicon/air 
interface
905 910 915
X X-X
x100 0.11µA
12.0µA 
wavelength (nm)
95.1µ A
X+(b)
-40 -20 0 20 40
 Time (ns)
-40 -20 0 20 40
delay (ns)
(ii) X
(c) (i)
-10 -5 5 10
delay (ns)
(i) calculated
(ii) measured
time (ns)
Fig. 5 
-0.05
(c) Real Part Imaginary Part
Errors 
(magnitude)
S = 0µeV
delay period (/12.5ns)
(a)(i)
(ii) 
(iii)
-15 0 15
S = 25µeV
(b)(i)
(iii)
-15 0 15
Fig. 6 
detector
beamsplitter
detector
device 
emission
-40 -20 0 20 40
delay, τ [ns]
(a) (b)
Fig. textbox
