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.     

Quantum statistical properties of superposition of squeezed and displaced states with thermal noise

Abstract

The effect of thermal noise is studied on the statistical behaviour of the superposition of squeezed and displaced number states. In our analysis we have employed the s-parametrized characteristic function. For such superposition states exact expressions for quasiprobability distribution functions, normalized second-order correlation function, photon-number distribution and phase space distribution are obtained and discussed in detail.     

Thermal Coherent States and Thermal Squeezed States

Abstract

Various definitions of thermal coherent states and thermal squeezed states are compared and interrelated. Different ordering of squeezing, displacement and thermalizing operators is discussed in order to establish a relation between all definitions. A one-to-one correspondence is exhibited between general Gaussian density matrices in coordinate space and thermal squeezed states.     

Properties of Squeezed Binomial States and Squeezed Negative Binomial States

Abstract

The effect of squeezing on binomial states and on negative binomial states is studied in terms of second-order correlation functions and quasi-probabilities of Wigner and Q-functions. The photon number distribution of these states is also discussed. The results presented for squeezed binomial (negative binomial) states may be useful for studying a transition from squeezed coherent states to squeezed number (quasi-thermal) states.     

Ordered moments and relation to Radon transform of Wigner quasiprobability

Abstract

It is shown that the symmetrically ordered moments of boson operators for a single boson mode can be reconstructed from the corresponding moments of the Radon transform of the Wigner quasiprobability for discrete sets of equidistant inequivalent angles which solve the circle division problem. This reconstruction is sometimes simpler than the corresponding reconstruction of the normally ordered moments where one first has to multiply the Radon transform with Hermite polynomials in comparison to power functions for symmetrically ordered moments and then to integrate. The connection to the reconstruction for the general class of s-ordered moments is established. The transition from discrete sets of angles to integration over angles via averaging over the discrete angles is made. The results are applied to displaced squeezed thermal states. It is shown how the ordered moments for these states can be explicitly found from the calculated Radon transform of the Wigner quasiprobability. The obtained formulae for these moments possess independent interest since they contribute to the discussion of the properties of the most general class of states with quasiprobabilities of Gaussian form with many possible special cases as, for example, squeezed coherent states and squeezed thermal states.     

Wigner Functions for Coherent and Squeezed States with Thermal Noise

Abstract

A generalized Wigner function W _T(α, ) including the thermal degrees of freedom is presented to calculate the ‘reduced’ Wigner functions for all kinds of coherent and squeezed states with thermal noise by the formalism of thermofield dynamics. The results show that the different definitions of coherent and squeezed state with the same corresponding density matrix give rise to the same reduced Wigner function. By our method, the reduced Wigner function can be calculated for an arbitrary vector in the thermal Fock space, of which the density matrix is too complicated to use.     

Two-mode Squeezed Gaussons

Abstract

Two-mode squeezed Gaussons are non-classical states of light which are intermediate between single-mode and two-mode squeezed states. They may be prepared by coherently mixing two single-mode squeezed states at a beam-splitter or via a frequency converter. When equally squeezed single-mode squeezed states are incident on a 50/50 beam-splitter the output will range between a two-mode squeezed state and two single-mode squeezed states as the phase of the input squeezed light is varied. This behaviour is reflected when the properties of such states are investigated.     

Thermal and squeezed vacuum Jaynes–Cummings models with a Kerr medium

Abstract

The dynamics of the Jaynes–Cummings (JCM) model with a nonlinear Kerr medium at initially thermal and squeezed vacuum fields is discussed. At a special choice of the detuning the Rabi frequency can have a minimum at the initial mean photon number [nbar]. Then the situation becomes especially interesting and instead of the first-order ‘usual’ revivals resembling those manifested by the standard coherent JCM, the nonlinear JCM exhibits second-order revivals, also for initially thermal and squeezed vacuum fields, at least for not too large [nbar]. The revival times are highly sensitive to the nature of [nbar]. In the first case the revival period of the oscillations is dependent on whether [nbar] is integer or non-integer (situation similar to an initially coherent field) while in the latter case it depends additionally on the parity of the integer [nbar]. Moreover, for the squeezed vacuum model appearance of the revivals at an integer [nbar] is accelerated when compared to coherent and thermal models.     

Influence of Resqueezing on Nonclassical Photon Statistics

Abstract

The nonclassical photon statistics of one-mode and two-mode combination squeezed states introduced recently by Fan, which have less fluctuation in one quadrature phase than the usual two-mode squeezed states, is discussed. It is found that increasing the degree of two-mode squeezing cannot always increase the photon antibunching depth of these generalized two-mode squeezed states.     

Quantum statistics and dynamics of nonlinear couplers with nonlinear exchange

Abstract

In this paper we derive the quantum statistical and dynamical properties of nonlinear optical couplers composed of two nonlinear waveguides operating by second subharmonic generation, which are coupled linearly through evanescent waves and nonlinearly through non-degenerate optical parametric interaction. Main attention is paid to generation and transmission of non-classical light, based on a discussion of the squeezing phenomenon, the normalized second-order correlation function and quasiprobability distribution functions. Initially coherent, number and thermal states of optical beams are considered. In particular, results are discussed with dependence on the strength of the nonlinear coupling relatively to the linear coupling. We show that if the Fock state |1〉 enters the first waveguide and the vacuume state |0〉 enters the second waveguide, the coupler can serve as a generator of squeezed vacuum state governed by the coupler parameters. Further, if thermal fields enter initially the waveguides the coupler plays a similar role as a microwave Josephson-junction parametric amplifier to generate squeezed thermal light.     

Experimental preparation and measurement of quantum states of motion of a trapped atom

Abstract

We report the creation and full determination of several quantum states of motion of a ⁹Be⁺ ion bound in a RF (Paul) trap. The states are coherently prepared from an ion which has been initially laser cooled to the zero-point of motion. We create states having both classical and non-classical character including thermal, number, coherent, squeezed, and ?Schrödinger cat‘ states. The motional quantum state is fully reconstructed using two novel schemes that determine the density matrix in the number state basis or the Wigner function. Our techniques allow well controlled experiments decoherence and related phenomena on the quantum-classical borderline.     

Bunching and Antibunching Effects in a System of N Two-level Atoms

Abstract

The problem of exhibiting bunching and antibunching phenomena for a system of N two-level atoms in interaction with light is investigated. The conditions for the change from bunching to antibunching and vice versa are obtained for resonance, and for time-independent and time-dependent coupling constant. The conditions for the case of resonance and time-independent coupling constant are investigated for both generalized coherent states and squeezed coherent states.     

Non-classical Properties of Two-mode SU(1, 1) Coherent States

Abstract

We examine the non-classical properties of two-mode coherent states based on different unitary irreducible representations of SU(1, 1). Such states are generated by the action of the two-mode squeezing operator on initial states of the field containing arbitrary numbers of photons in each of the two modes. If the initial state of the field is a two-mode vacuum state, the final state is of course the two-mode squeezed vacuum. An initial occupation generalizes the idea of a squeezed vacuum to the SU(1, 1) coherent states. We show that fields in such states have remarkable quantum properties such as sub-Poissonian statistics, violations of the Cauchy-Schwarz inequality, strong correlations in the photon number fluctuations and squeezing. Using information theory formalism, we show that these coherent states are less correlated than the usual two-mode squeezed vacuum. Moreover, we show that an initial coherent amplitude contribution, in a large amplitude limit, can result in the reduction of correlations between modes.     

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.     

Interaction of Squeezed Light with Two-level Atoms

Abstract

We investigate some of the fundamental features of the interaction of squeezed light with two-level atoms in the framework of the Jaynes-Cummings model. We start our analysis by calculating the collapses and revivals of the atomic inversion. We discuss the degree of purity of the field (given by the entropy) and its disentanglement from the atomic source. The connection with the evolution of the Q-function is also made. We notice that contrary to the coherent state case, the field turns into a nearly pure (squeezed) state at the revival time as if the field was prepared in a coherent state. The field also becomes a superposition of squeezed states at half of the revival time, and this is confirmed by investigating the photon number distribution. The phase properties of the field are discussed using the Pegg-Barnett formalism.     

Time Evolution of Stable Squeezed States

Abstract

It is shown using a straightforward approach that, for a single mode of an electromagnetic field, only quadratic Hamiltonians can preserve squeezed states for all time. The time-evolution equations for the parameters of a stable squeezed state are given for arbitrary quadratic Hamiltonians. It is also pointed out that there is no single Hamiltonian that preserves minimum uncertainty for all squeezed minimum-uncertainty states.     

Phase Properties of Squeezed Number States

Abstract

We have studied the phase properties of the squeezed number states by evaluating the expression for the phase probability distribution and the phase variance. In addition, the expression for the photon number distribution of the squeezed phase states has been evaluated.     

Squeezing in Finite Superpositions of Photon-number States without the Vacuum

Abstract

We show that a finite superposition of photon-number states without the vacuum state can lead to squeezed fluctuations. The properties of these states are discussed.     

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.