On the Squeezing of Coherent States by the Multiphoton Jaynes-Cummings Hamiltonian with an Intensity-dependent Coupling

Abstract

The squeezing properties of the multiphoton Hamiltonian with intensity-dependent coupling are evaluated for the [xcirc] and [pcirc] _x quadratures, for the initial state of a coherent electromagnetic field and an atom in the ground state. Two measures of squeezing: the percentage of total squeezing and the squeezing time-period percentage, are introduced. Interesting squeezing properties with respect to [xcirc] are observed for real coherent states when the time evolution of the above measures and of the time-averaged squeezing are analysed. The multiphoton intensity-dependent coupling Hamiltonian is found to be almost independent of the specific powers of the annihilation and creation operators, as long as the sum of the powers is kept constant.     

Effective Dipole Squeezing in the Non-degenerate Two-photon Jaynes-Cummings Model with Superposition State Preparation

Abstract

Effective dipole squeezing in the non-degenerate two-photon Jaynes-Cummings model for atom and fields initially prepared in superposition of states is investigated. It is shown that the squeezing can be exhibited in certain periods of time but it cannot be achieved for atomic spontaneous radiation processes.     

Squeezing of Spectral Components in the Jaynes-Cummings Model

Abstract

Squeezing of spectral components of a fluorescence field in the framework of the Jaynes-Cummings model has been studied. It has been shown that squeezing is observed only in sidebands of the fluorescence field. The degree of squeezing increases as the intensity of the cavity mode is increased. Contrary to squeezing in the cavity mode (see Kuklinski and Madajczyk [14] a large degree of squeezing in sidebands of the fluorescence field is observed in the short-time limit.     

Entropy squeezing for a two-level atom

Abstract

The usual definition of squeezing, based on the Heisenberg uncertainty principle, measures uncertainty in terms of the standard deviation. It can run into difficulties when applied to squeezing in the two-level atom. An alternative definition of squeezing is presented for this system, based on information entropy theory, which overcomes the disadvantages of the definition based on the Heisenberg uncertainty relation. The utility of this definition is illustrated by examining squeezing in the information entropy of a two-level atom in the Jaynes-Cummings model, and in resonance fluorescence.     

Propagation of Squeezed Light in Dielectrics

Abstract

We model the propagation of squeezed light through a dielectric medium. Frequency-dependent absorption reduces the level of squeezing and may decrease the squeezing bandwidth. Dispersion dephases the squeezing at different frequencies within the spectrum.     

Squeezing in Multiphoton Absorption

Abstract

The conditions for obtaining squeezing by single-beam multiphoton absorption are examined. For an initial coherent light the amount of squeezing is calculated in the second order of interaction time using the master-equation formalism. A limit formula for the amount of squeezing is found in the case of an initial strong coherent beam. The results are compared with the exact numerical calculations and some remarks are made on the short-time approximation in multiphoton absorption.     

Coherent States of a Harmonic Oscillator in a Finite-dimensional Hilbert Space and Their Squeezing Properties

Abstract

New coherent states of a harmonic oscillator in a finite-dimensional Fock space are introduced. Some properties of these coherent states are discussed. The second-order squeezing of these coherent states with respect to the quadrature operators is studied in detail. In particular, for a two-state system the arbitrary higher-order squeezing of these states is investigated. It is shown that these coherent states exhibit much richer squeezing properties than the coherent states of a usual harmonic oscillator in an infinite-dimensional Fock space. It is found that these coherent states have not only second-order squeezing but also higher-order squeezing with respect to the quadrature operators of the field under consideration.     

Statistical Properties of the Even Binomial State

Abstract

In this paper we introduce the even binomal state, which interpolates between the even number state and the even coherent state. We consider the effect of this state on the Glauber second order correlation function. Both squeezing phenomena are discussed, i.e., normal squeezing and amplitude squared squeezing. The quasiprobability distribution functions (Wigner function and Q function) for such a state are also examined.     

Light Squeezing in the Jaynes-Cummings Model with Intensity-dependent Coupling

Abstract

We have found that in the intensity-dependent-coupling Jaynes-Cummings model with the coherent radiation field light squeezing exhibits periodical revivals. The influence of the initial states of the atom on the squeezing of light is investigated in detail.     

The Influence of Phase-destroying and Absorption Processes on Squeezing

Abstract

The already well known sensitivity of genuine quantum effects to loss processes is investigated for squeezing. Owing to the phase dependence of its quantum fluctuations, a squeezed state is extraordinarily fragile with respect to phase-destroying processes. This sensitivity increases with increasing degree of squeezing. A present coherent photon number enhances this disturbing effect.     

Sub-Poissonian Photon Statistics and Higher-order Squeezing in the Light Amplifier with Input Binomial States

Abstract

We make a comparison between the necessary and sufficient conditions on the gain of the linear amplifier under which the light output exhibits sub-Poissonian photon statistics or squeezing and exact numerical results, obtained by solving the master equation by means of matrix procedures, and find good agreement. We find numerically that higher-order squeezing persists in a region in which sub-Poissonian statistics and second-order squeezing have already disappeared, for certain parameter ranges of input binomial states.     

Non-classical Features in the Three-level Jaynes-Cummings Model

Abstract

The eigenfunctions and eigenenergies of the system composed of a cascade three-level atom and bichromatic or monochromatic field with arbitrary detunings are presented. The development of the state vector of the system with arbitrary initial conditions is obtained. The development of the quantum fluctuations and the second-order coherence degree for the field is calculated. The dependence of the squeezing and antibunching on the detunings, initial intensities and initial squeezing is studied. The contribution of single-photon and two-photon transitions to, and the influence of, the a.c. Stark effect on the squeezing are discussed.     

Squeezing with Rydberg Atoms

Abstract

It is shown that some 17 Rydberg Na atoms initially placed into a coherent atomic state and super-radiating into a low-Q microwave cavity at temperatures T ? 0·4 K will show modest squeezing in the fluorescence field, the squeezing arising from terms oscillating at twice the cavity frequency. It is also shown that similar numbers of Rydberg atoms undergoing resonance fluorescence in a coherent single-mode microwave driving field and without any cavity will show more substantial squeezing in the fluorescence field.     

Squeezed States for Interferometric Gravitational-wave Detectors

Abstract

The possibility of using squeezed states for improving the shot-noise limit of the strain sensitivity of Michelson interferometers is discussed. We find that the spectrum of squeezing required depends on the method of stabilization used in the experiment. Details are given for the widely used phase-modulation technique (which also allows for recycling of the field), where we find an important application for broadband (‘two-mode’) squeezing.     

Squeezing from Raman Scattering in Optical Parametric Oscillators

Abstract

The squeezing properties of the Raman scattering process which takes place when the lower output frequency from a non-degenerate optical parametric interaction approaches a resonance of the nonlinear medium placed inside an optical resonant cavity are presented. The linear stability analysis is performed and the spectrum for the output fields is given in terms of the quadrature phase components in the Wigner representation. Perfect squeezing for the amplitude difference between the output Stokes and anti-Stokes modes at the Hopf bifurcation point is obtained.     

Entropy squeezing of a degenerate two-photon process with a nonlinear medium

Abstract

This paper presents new results on some aspects of the properties of the entropy squeezing in the time development of a degenerate two-photon of a single-mode interacting with a two-level system with a nonlinear medium. A general analytic expression for the density matrix is obtained on the basis of a Hamiltonian generalized in that it includes nonlinear effects and Stark shifts, by means of which we identify and numerically demonstrate the region of parameters where significantly large squeezing can be obtained. The influence of various parameters on the entropy squeezing are explored. It is shown that features of the entropy squeezing were influenced significantly by changing the nonlinear medium, Stark shift and the detuning. The results show that, certain amounts of the nonlinear effect yield the superstructure of atomic Rabi oscillation and changes the quasiperiod of the entropy evolution and atomic inversion.     

SU(1, 1) and SU(2) Squeezing in Trilinear Optical Processes

Abstract

The squeezing properties in terms of SU(1, 1) and SU(2) operators for the case of trilinear processes are studied. The initial state of the system is supposed to be a coherent state in one of the modes and number states in the remaining modes. It is pointed out that in several cases a considerable amount of squeezing can be achieved. Due to the common mathematical structure the case of a two-mode coupler with intensity dependent coupling is also analysed.     

Influence of squeezing bandwidths on resonance fluorescence

Abstract

We present an analytical technique for investigating the behaviour of a coherently driven atom damped by a squeezed vacuum with finite squeezing bandwidth. A master equation and analytic expressions for the fluorescent spectrum are derived for the simple case of a two-level atom exactly resonant with the frequencies of both the squeezed field and the driving field. Suitable choices of driving strength, phase and squeezing source lead to either sub-natural lincwidths of the Rabi sidebands or a sub-natural linewidth of the central spectral peak or indeed sub-natural linewidths of all three spectral peaks when squeezing bandwidths are taken into account. We also establish the remarkable result that in the strong driving regime, the width of the central peak of the fluorescent spectrum depends solely on the squeezing found at the Rabi sideband frequencies.     

Squeezed Atomic Light Amplifiers

Abstract

Various authors have shown that for a particular type of atomic light amplifier, which can be identified as an unsqueezed amplifier, squeezing in the output is destroyed for gains greater than 2, and if the input is classical light then there are no non-classical effects (squeezing or sub-Poisson photon statistics) in the output for any value of the gain; however, these results are not necessarily true for a squeezed amplifier. Here we investigate single-stage and multi-stage squeezed atomic light amplifiers and show that the above non-classical effects can occur even with a coherent-state input. We find that the output of a multistage squeezed amplifier can be squeezed in principle for any desired gain, and that when this amplifier is used as an attenuator, output light can in principle be produced with any desired amount of squeezing for any input.     

Squeezing in Correlated Quantum Systems

Abstract

We discuss the connection between quantum correlations and squeezing in simple quantum optical systems. We illustrate this connection by a study of two-mode states of light produced by parametric down-conversion and similar two-photon processes. The intermode correlations in these systems are shown to be responsible for modifications in photon-number sum and difference operators, and for squeezing in the superpositions of the two modes. The disappearance of the diagonal coherent-state quasiprobability function P(α) when non-classical light properties are important is noted, and alternative and better-behaved Wigner functions and coherent-state expectation Q-functions for the two-mode system are developed.