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NASA NTRS1992

Photon number squeezed states in semiconductor lasers

Electromagnetic fields, with the noise on one quadrature component reduced to below the quantum mechanical zero-point fluctuation level and the noise on the other quadrature component enhanced to above it, are currently of great interest in quantum optics because of their potential applications to various precision measurements. Such squeezed states of light are usually produced by imposing nonlinear unitary evolution on coherent (or vacuum) states. On the other hand, squeezed states with reduced photon number noise and enhanced phase noise are generated directly by a constant current-driven semiconductor laser. This is the simplest scheme for the generation of nonclassical light, and so far it has yielded the largest quantum noise reduction. The mutual coupling between a lasing junction and an external electrical circuit provides opportunities for exploring the macroscopic and microscopic quantum effects in open systems.

Yamamoto, Yoshihisa↗
NASA NTRS1993

Squeezed states of damped oscillator chain

The Caldirola-Kanai model of one-dimensional damped oscillator is extended to the chain of coupled parametric oscillators with damping. The correlated and squeezed states for the chain of coupled parametric oscillators with damping are constructed. Based on the concept of the integrals of motion, it is demonstrated how squeezing phenomenon arises due to parametric excitation.

Manko, O. V.↗
NASA NTRS1993

Wave and pseudo-diffusion equations from squeezed states

We show that the probability distributions P(sub n)(q,p;y) := the absolute value squared of (n(p,q;y), which are obtained from squeezed states, obey an interesting partial differential equation, to which we give two intuitive interpretations: as a wave equation in one space dimension; and as a pseudo-diffusion equation. We also study the corresponding Wehrl entropies S(sub n)(y), and we show that they have minima at zero squeezing, y = 0.

Daboul, Jamil↗
NASA NTRS1994

Supersymmetry and radial squeezed states for Rydberg wave packets

Atomic supersymmetry provides an analytical effective-potential model useful for describing certain aspects of Rydberg atoms. Experiments have recently demonstrated the existence of Rydberg wave packets localized in the radial coordinated with p-state angular distribution. This paper shows how atomic supersymmetry can be used to treat radial Rydberg wave packets via a particular analytical type of squeezed state, called a radial squeezed state.

Bluhm, Robert↗
NASA NTRS1994

Phase space flow of particles in squeezed states

The manipulation of noise and uncertainty in squeezed states is governed by the wave nature of the quantum mechanical particles in these states. This paper uses a deterministic model of quantum mechanics in which real guiding waves control the flow of localized particles. This model will be used to examine the phase space flow of particles in typical squeezed states.

Ceperley, Peter H.↗
NASA NTRS1994

Understanding squeezing of quantum states with the Wigner function

The Wigner function is argued to be the only natural phase space function evolving classically under quadratic Hamiltonians with time-dependent bilinear part. This is used to understand graphically how certain quadratic time-dependent Hamiltonians induce squeezing of quantum states. The Wigner representation is also used to generalize Ehrenfest's theorem to the quantum uncertainties. This makes it possible to deduce features of the quantum evolution, such as squeezing, from the classical evolution, whatever the Hamiltonian.

Royer, Antoine↗
NASA NTRS1994

Applications of squeezed states: Bogoliubov transformations and wavelets to the statistical mechanics of water and its bubbles

The squeezed states or Bogoliubov transformations and wavelets are applied to two problems in nonrelativistic statistical mechanics: the dielectric response of liquid water, epsilon(q-vector,w), and the bubble formation in water during insonnification. The wavelets are special phase-space windows which cover the domain and range of L(exp 1) intersection of L(exp 2) of classical causal, finite energy solutions. The multiresolution of discrete wavelets in phase space gives a decomposition into regions of time and scales of frequency thereby allowing the renormalization group to be applied to new systems in addition to the tired 'usual suspects' of the Ising models and lattice gasses. The Bogoliubov transformation: squeeze transformation is applied to the dipolaron collective mode in water and to the gas produced by the explosive cavitation process in bubble formation.

Defacio, Brian↗
NASA NTRS1994

Some rules for polydimensional squeezing

The review of the following results is presented: For mixed state light of N-mode electromagnetic field described by Wigner function which has generic Gaussian form, the photon distribution function is obtained and expressed explicitly in terms of Hermite polynomials of 2N-variables. The momenta of this distribution are calculated and expressed as functions of matrix invariants of the dispersion matrix. The role of new uncertainty relation depending on photon state mixing parameter is elucidated. New sum rules for Hermite polynomials of several variables are found. The photon statistics of polymode even and odd coherent light and squeezed polymode Schroedinger cat light is given explicitly. Photon distribution for polymode squeezed number states expressed in terms of multivariable Hermite polynomials is discussed.

Manko, Vladimir I.↗
NASA NTRS1994

Time-dependent variational approach in terms of squeezed coherent states: Implication to semi-classical approximation

A general framework for time-dependent variational approach in terms of squeezed coherent states is constructed with the aim of describing quantal systems by means of classical mechanics including higher order quantal effects with the aid of canonicity conditions developed in the time-dependent Hartree-Fock theory. The Maslov phase occurring in a semi-classical quantization rule is investigated in this framework. In the limit of a semi-classical approximation in this approach, it is definitely shown that the Maslov phase has a geometric nature analogous to the Berry phase. It is also indicated that this squeezed coherent state approach is a possible way to go beyond the usual WKB approximation.

Tsue, Yasuhiko↗
NASA NTRS1994

Quantum amplification and quantum optical tapping with squeezed states and correlated quantum states

Quantum fluctuations in a nondegenerate optical parametric amplifier (NOPA) are investigated experimentally with a squeezed state coupled into the internal idler mode of the NOPA. Reductions of the inherent quantum noise of the amplifier are observed with a minimum noise level 0.7 dB below the usual noise level of the amplifier with its idler mode in a vacuum state. With two correlated quantum fields as the amplifier's inputs and proper adjustment of the gain of the amplifier, it is shown that the amplifier's intrinsic quantum noise can be completely suppressed so that noise-free amplification is achieved. It is also shown that the NOPA, when coupled to either a squeezed state or a nonclassically correlated state, can realize quantum tapping of optical information.

Ou, Z. Y.↗
NASA NTRS1996

Two Different Squeeze Transformations

Lorentz boosts are squeeze transformations. While these transformations are similar to those in squeezed states of light, they are fundamentally different from both physical and mathematical points of view. The difference is illustrated in terms of two coupled harmonic oscillators, and in terms of the covariant harmonic oscillator formalism.

Han, D.↗
NASA NTRS1996

The Total Gaussian Class of Quasiprobabilities and its Relation to Squeezed-State Excitations

The class of quasiprobabilities obtainable from the Wigner quasiprobability by convolutions with the general class of Gaussian functions is investigated. It can be described by a three-dimensional, in general, complex vector parameter with the property of additivity when composing convolutions. The diagonal representation of this class of quasiprobabilities is connected with a generalization of the displaced Fock states in direction of squeezing. The subclass with real vector parameter is considered more in detail. It is related to the most important kinds of boson operator ordering. The properties of a specific set of discrete excitations of squeezed coherent states are given.

Wuensche, Alfred↗
NASA NTRS1996

Q (Alpha) Function and Squeezing Effect

The relation of squeezing and Q(alpha) function is discussed in this paper. By means of Q function, the squeezing of field with gaussian Q(alpha) function or negative P(a)function is also discussed in detail.

Yunjie, Xia↗
NASA NTRS1996

Observation of Two-Photon Excitation for Three-Level Atoms in a Squeezed Vacuum

The two-photon transition (6S(sub 1/2) yields 6D(sub 5/2)) of atomic Cesium is investigated for excitation with squeezed vacuum generated via nondegenerate parametric down conversion. The two-photon excitation rate (R) is observed to have a non-quadratic dependence of R = aI(exp 2) + bI on the incident photon flux (I), reflecting the nonclassical correlations of the squeezed vacuum field.

Edamatsu, K.↗
NASA NTRS1996

Optimal Signal Filtration in Optical Sensors with Natural Squeezing of Vacuum Noises

The structure of optimal receiver is discussed for optical sensor measuring a small displacement of probe mass. Due to nonlinear interaction of the field and the mirror, a reflected wave is in squeezed state (natural squeezing), two quadratures of which are correlated and therefore one can increase signal-to-noise ratio and overcome the SQL. A measurement procedure realizing such correlation processing of two quadratures is clarified. The required combination of quadratures can be produced via mixing of pump field reflected from the mirror with local oscillator phase modulated field in duel-detector homodyne scheme. Such measurement procedure could be useful not only for resonant bar gravitational detector but for laser longbase interferometric detectors as well.

Gusev, A. V.↗