40587572
Inverted spectroscopy and interferometry for quantum-state reconstruction of systems with SU(2) symmetry
We consider how the conventional spectroscopic and interferometric schemes can be rearranged to serve for reconstructing quantum states of physical systems possessing SU(2) symmetry. The discussed systems include a collection of two-level atoms, a two-mode quantized radiation field with a fixed total number of photons, and a single laser-cooled ion in a two-dimensional harmonic trap with a fixed total number of vibrational quanta. In the proposed rearrangement, the standard spectroscopic and interferometric experiments are inverted. Usually one measures an unknown frequency or phase shift using a system prepared in a known quantum state. Our aim is just the inverse, i.e., to use a well-calibrated apparatus with known transformation parameters to measure unknown quantum states.
27052128
Parity-dependent squeezing of light
A parity-dependent squeezing operator is introduced which imposes different SU(1,1) rotations on the even and odd subspaces of the harmonic oscillator Hilbert space. This operator is used to define parity-dependent squeezed states which exhibit highly non-classical properties such as strong antibunching, quadrature squeezing, strong oscillations in the photon-number distribution, etc. In contrast to the usual squeezed states whose Q and Wigner functions are simply Gaussians, the parity-dependent squeezed states have much more complicated Q and Wigner functions that exhibit an interesting interference in phase space. The generation of these states by parity-dependent quadratic Hamiltonians is also discussed.
16820646
Analytic representations based on SU(1,1) coherent states and their applications
We consider two analytic representations of the SU(1,1) Lie group: the representation in the unit disc based on the SU(1,1) Perelomov coherent states and the Barut - Girardello representation based on the eigenstates of the SU(1,1) lowering generator. We show that these representations are related through a Laplace transform. A `weak' resolution of the identity in terms of the Perelomov SU(1,1) coherent states is presented which is valid even when the Bargmann index k is smaller than . Various applications of these results in the context of the two-photon realization of SU(1,1) in quantum optics are also discussed.
39771192
Quantum statistical properties of the radiation field in a cavity with a movable mirror
A quantum system composed of a cavity radiation field interacting with a movable mirror is considered and quantum statistical properties of the field are studied. Such a system can serve, in principle, as an idealized meter for detection of a weak classical force coupled to the mirror which is modelled by a quantum harmonic oscillator. It is shown that the standard quantum limit on the measurement of the mirror position arises naturally from the properties of the system during its dynamical evolution. However, the force detection sensitivity of the system falls short of the corresponding standard quantum limit. We also study the effect of the nonlinear interaction between the moving mirror and the radiation pressure on the quadrature fluctuations of the initially coherent cavity field.
15829252
Factorization of analytic representations in the unit disc and number-phase statistics of a quantum harmonic oscillator
The inner - outer part factorization of analytic representations in the unit disc is used for an effective characterization of the number-phase statistical properties of a quantum harmonic oscillator. It is shown that the factorization is intimately connected with the number-phase Weyl semigroup and its properties. In the Barut - Girardello analytic representation the factorization is implemented as a convolution. Several examples are given which demonstrate the physical significance of the factorization and its role for quantum statistics. In particular, we study the effect of phase-space interference on the factorization properties of a superposition state.
53454093
Phase-space formulation of quantum mechanics and quantum-state reconstruction for physical systems with Lie-group symmetries
We present a detailed discussion of a general theory of phase-space distributions, introduced recently by the authors @J. Phys. A 31 ,L 9 ~1998!#. This theory provides a unified phase-space formulation of quantum mechanics for physical systems possessing Lie-group symmetries. The concept of generalized coherent states and the method of harmonic analysis are used to construct explicitly a family of phase-space functions which are postulated to satisfy the Stratonovich-Weyl correspondence with a generalized tracing condition. The symbol calculus for the phase-space functions is given by means of the generalized twisted product. The phase-space formalism is used to study the problem of the reconstruction of quantum states. In particular, we consider the reconstruction method based on measurements of displaced projectors, which comprises a number of recently proposed quantum-optical schemes and is also related to the standard methods of signal processing. A general group-theoretic description of this method is developed using the technique of harmonic expansions on the phase space. @S1050-2947~99!00702-7#
126351679
A lunar‐based detector to search for relic supernovae antineutrinos
We discuss the motivation for and advantages of a lunar‐based detector capable of observing the relic antineutrino flux from all past supernovae at or close to the lowest theoretical estimates of the magnitude of flux.
124420576
Possible Production of 'Collapsed' Hadronic Matter in Very High-energy Nucleon-nucleon Collisions
We speculate on the possible production of "collapsed" hadrons, i.e., color-singlet, electrically uncharged (or with small integral charge) clusters of quarks and antiquarks, in very-high-energy proton-proton collisions, the intermediate states of which contain relatively large numbers of quarks $q$, antiquarks $\overline{q}$, and gluons $g$. Using a thermodynamic model, we crudely estimate the numbers and kinetic energies of the $q$, $\overline{q}$, and $g$ in the intermediatestate gas mixture, and indicate how the properties of collapsed hadrons might depend on the quantum numbers of the $q$ and $\overline{q}$. A brief discussion of experimental signatures for identification of collapsed hadrons is presented, along with mention of the consequences of possible collapsed-hadron production in the early Universe.
116981125
Multimuon production by neutrinos at FNAL
Data on neutrino interactions involving two, three and four final state muons are summarized and the origins of such events are discussed.
121246612
Scaling-variable distributions in high-energy inelastic neutrino interactions
122124216
Neutrino oscillations and the number of neutrino types
A brief treatment of neutrino oscillations, generalized to an arbitrary number of neutrino types, is given as the basis for design of a feasible experiment to search for neutrino oscillations using the neutrino beam produced at a high-energy proton accelerator.