Periodic Squeezing in the Tavis-Cummings Model

Abstract

By utilizing our previous operator solution [17], we have investigated the squeezing in the radiation field of the Tavis-Cummings model (collective N ? 1 two-level atoms interacting with a resonant single cavity quantized mode). With field and atoms initially in coherent field state strong or weak and atomic coherent state (of few excited atoms), periodic time-dependent squeezing in the field and the macroscopic polarization is expressed in terms of Jacobian elliptic functions of the first kind. The statistical investigations are carried out for the quasiprobability distribution functions (Wigner function and Q function). The distribution function of the field quadrature has a variance less (greater) than that for a coherent state if this quadrature is squeezed (unsqueezed).     

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.     

Non-classical Properties of Even and Odd Coherent States

Abstract

We present a detailed discussion of even and odd coherent states defined as eigenstates of the single mode two-photon annihilation operator a ². We study the non-classical properties such as squeezing, higher-order squeezing, and photon antibunching. Also discussed are the various quantum quasiprobability distributions, namely the P function, which is shown to be highly singular, the Q function, and the Wigner, which can take on negative values for these states. Finally, we present a discussion of a possible mechanism for the generation of such states based on the competition between parametric amplification and the incoherent losses from two-photon resonant absorption.     

Four-photon Coherent States

Abstract

We present a detailed discussion of a type of four-photon coherent state defined as right eigenstates of the operator â ⁴ where â is the usual annihilation operator. There are actually four sets of states that need to be considered, namely those containing as the lowest number states ¦0>, ¦1>, ¦2>, or ¦3>. These correspond to the possible unique superpositions of the ordinary coherent states ¦±α> and ¦±iα>. We discuss the nonclassical properties of these states such as photon antibunching and squeezing. The usual second order squeezing does not exist for these states but higher order squeezing and square field amplitude squeezing do exist. Also discussed are the quasiprobability distributions, namely the P-function, the Q-function and the Wigner function. Finally, a method of generating these states based on the competition between a four-photon parametric process and incoherent losses from four-photon absorption is presented.     

Partial phase state as a nonlinear coherent state and some of its properties

Abstract

One introduces the phase state as a nonlinear coherent state. Some of its properties, such as the sub-Poissonian statistics, the squeezing effects, the phase properties in the Pegg-Barnett formalism and the quasiprobability function of the nonlinear coherent states, are calculated and discussed in this paper. The results show that the phase states are squeezed.     

The Statistical Properties of a Generalized Two-mode Squeezed Operator

Abstract

In this paper we have employed the generalized two-mode squeeze operator to discuss the effect of squeezing on two-mode coherent states, number states and thermal states. By using the Glauber second-order correlation function we examined the statistical properties of these various squeezed states. The statistical investigations are carried out for the quasi-probability distribution functions (Wigner function and Q function). The P representation is also considered.     

Dynamics of a Q-analogue of the Quantum Harmonic Oscillator

Abstract

We analyse the dynamics of the q-deformed quantum harmonic oscillator initially prepared in the q-analogue of the coherent state. Non-trivial behaviour of the mean values of the q-position operator is observed. The squeezing of the second-order moments of this operator is studied.     

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.     

Statistical Properties of the Time Evolution Operator for Two Coupled Oscillators

Abstract

In the present work we study the effects of squeezing on coherent states, number states, and on the thermal field states related to the time evolution operator, which is the result of the Hamiltonian describing the simultaneous non-degenerate parametric amplifier with mixing of two modes a and b via a rotation of their polarization. By using the Glauber second-order correlation function we examined the statistical properties of these various squeezed states. The quasi-probabilities of the W Wigner and Q functions are calculated. The Glauber P representation for the squeezed thermal state explicitly shows the limit of its applicability.     

Phase Fluctuations and Squeezing

Abstract

We investigate the relationship between squeezing and reduced phase fluctuations for various states of the single-mode electromagnetic field, including the strongly-squeezed vacuum and phase states. We find that, although squeezing the fluctuations of the electric field that arise from the vacuum guarantees a more well-defined phase, reducing phase fluctuations does not guarantee a squeezed electric field. We also investigate the evolution of the electric field and its fluctuations for a phase state. Our results show that even though the electric field fluctuations never vanish for a phase state, the times when the electric field changes sign are precisely defined. We also discuss why it is not always possible to attribute physical properties to certain states, such as simple superpositions of phase states.     

Statistical Properties of a New Squeezed Operator Model

Abstract

We introduce a new squeezed operator which is a combination of the two-mode squeezed operator and the two single photon squeezed operator. Here we study the effects of this operator on the photon number sum and difference. The squeezing in the frequency converter model has been examined, and statistical investigations are carried out for the quasi-probability distribution functions (Wigner function and Q-function). An application to the parametric amplifier is given.     

A New Quantum Formalism for Damping and Gain in Harmonic Oscillators

Abstract

A new formulation of loss or gain in the quantum theory of harmonic oscillators is put forward using a non-passive reactive circuit which can be readily quantized. The analysis is based on the electrical circuit theory and demonstrates how a circuit, with negative inductance ? L _n and negative capacitance ? C _n, coupled to a conventional harmonic oscillator circuit, of positive inductance L and positive capacitance C, can act as a source or sink of energy and allow for both gain and loss. Classically this series circuit is indistinguishable in its transients from either a + G or ? G conductance shunted across a main LC oscillator circuit. However, unlike the resistive circuit, this coupled circuit can be quantized, maintaining the uncertainty principle. A two-valued solution is found, dependent on whether the circuits are in a state to receive energy or a state to absorb energy. A full correspondence, including second-order frequency shifts, is found between the quantum and the classical solutions with states which are appropriate to thermodynamic equilibrium of a conductance at a temperature T as well as to the classical-like coherent states. While the accessible mode in the + L + C circuit does not exhibit any squeezing directly, the system as a whole is an example of two-mode squeezing discussed by other authors.     

Interaction of mesoscopic Josephson junction with superposition of even and odd coherent states

Abstract

The interaction of a mesoscopic Josephson junction with superposition of even and odd coherent states is investigated. It is found that the expectation value and the fluctuation of a supercurrent can exhibit dc components. The number of current-voltage steps (CVSs) for the former are less than the latter. For the former the static supercurrent flows in a positive or negative direction, which depends on the phase of the light field. The correlation function and squeezing of the dc components of a supercurrent depend on the value of CVS. For some special value of a CVS, the squeezing disappears.     

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.     

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.     

Effects of the Binomial Field Distribution on Collapse and Revival Phenomena in the Jaynes-Cummings Model

Abstract

The dynamical properties of a two-level atom interacting with a single non-decaying mode of an electromagnetic field in a binomial state are studied. The statistical aspects of the field, such as intensity-intensity correlation and squeezing, are also investigated. The binomial state reduces to a pure number state and a pure coherent state in different limits. Hence it enables us to study how the sinusoidal Rabi oscillations in a pure number state develop to give rise to the phenomenon of collapse and revival which has been studied extensively in the coherent-state field. In addition, the binomial state exhibits squeezing for certain values of parameters, but it is not a minimum-uncertainty-product state.     

N-level Atom Interacting with Single-mode Radiation Field: An Exactly Solvable Model with Multiphoton Transitions and Intensity-dependent Coupling

Abstract

We study the dynamics of an N-level atom coupled in a lossless cavity to a single-mode near-resonant quantized field. The atomic levels are coupled by the multiphoton transitions and the coupling constants between the field and the atomic levels are supposed to be intensity dependent. We find the exact solution for the state vector describing the dynamics of the atom-plus-field system. As an illustration we use the model for studying (i) the time evolution of the atomic occupation probability with the initially coherent field and (ii) the light squeezing, when the cavity field is initially in the vacuum state and the atom is prepared in the atomic ‘coherent state’ (a superposition of atomic states).     

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.     

Intracavity Optical Bistability Driven by Squeezed Light from a Parametric Amplifier

Abstract

We describe the theory of optical bistability when atoms are collectively excited within the cavity of a parametric oscillator. Both optical bistability and parametric amplification can squeeze significantly the cavity-field quantum noise. When they are coupled together we find significant changes both on the mean value bistability and on the spectrum of squeezing as the parametric coupling increases. These are calculated directly from the appropriate master equation for the density matrix using a quantum distribution function (positive P) to develop Fokker—Planck and Ito equations.     

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.