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.     

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.     

Two-mode Squeezed Pair Coherent States

Abstract

The properties of states generated by the application of the two-mode squeeze operator to the pair coherent states are studied. These states are the two-mode analogues of the single-mode squeezed states generated by the application of the single-mode squeeze operator to an ordinary coherent state. In the present case there are correlations between the modes and strong non-classical properties are to be expected. We study the statistical properties of the photon number distributions, squeezing, violations of the Cauchy-Schwartz inequality, quasiprobability distributions and the phase distributions.     

Squeezed States Generated by Boson Creation Operator

Using the normal ordering techniques of an operator, we show that a general squeezed state may be expressed in the form N exp [1/2 ξ â σ² m nâ σ] S 0 ¢, where S 0 ¢ is the vacuum state. We obtain the normalization constant N and various other representations. We also discuss conditions for squeezing and photon antibunching.     

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.     

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.     

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.     

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.     

Squeezed displaced fock states and non-diagonal P representation

Abstract

An R representation with a squeezed displaced-Fock-states (SDFSs) basis is introduced. A non-diagonal P representation for the density operator with SDFS basis is defined. The special cases for the fields, chaotic and laser, are calculated. The Pegg–Barnett phase distribution is given and compared with the radial integration of the generalized P function. The Fokker–Planck equation for the damped harmonic oscillator is considered, and its steady-state solution is given.     

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.     

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.     

The Interaction of Displaced Number State and Squeezed Number State Fields with Two-level Atoms

Abstract

The time-evolution of a single two-level atom in a single-mode high-Q cavity is sensitive to the quantum fluctuations of the cavity radiation field and to its photon statistics: this sensitivity is realizable experimentally in the Rydberg atom micromaser. We study the effects of the interaction of a two-level atom with two new non-classical radiation fields: the squeezed number state and the displaced number state realizable by nonlinear and linear transformations of field number states which have an initially precise occupation number. The time-varying field fluctuations caused by the atomic interaction are described using the Q-function quasi-probability.     

Orthonormalized Eigenstates of Operator a k and Their Squeezing Properties

Abstract

The orthonormalized eigenstates of the higher powers, a ^k (k  3), of the annihilation operator a were obtained. We discuss the mathematical properties and the squeezing properties of the orthonormalized eigenstates of a ^k. We prove that these orthonormalized eigenstates of a ^k construct a complete representation, that none of them have the squeezed effect in the usual sense, and that higher-order squeezing can be found.     

Homodyne tomography of classical and non-classical light

Abstract

States with explicit quantum character, such as squeezed vacuum and bright squeezed light, as well as coherent states and incoherent superpositions of coherent states were generated and analysed by tomographical methods. Wigner functions, photon-number distributions, density matrices and phase distributions were reconstructed with high accuracy. Features such as photon number oscillations, sub-Poissonian and super-Poissonian photon statistics, bifurcations of the phase distribution, and loss of coherence were observed, demonstrating the usefulness of quantum state reconstruction as an analysing tool in quantum optics experiments.     

Superposition Phases and Squeezing

Abstract

Quadrature variances of a radiation field depend not only on the photon number distribution in the field but also on the relative phases of the photon number probability amplitudes. Two fields with the same photon number distribution can show different degrees of squeezing if photon number states are superposed with different relative phases. It is thus possible, for example, for a radiation field with Poissonian photon statistics to exhibit squeezed quadrature fluctuations. Since different relative superposition phases in general yield different maximum and minimum values of the quadrature variances, measurement of the variances can yield information concerning the relative phases between different number states.     

Squeezing Properties and Photon Statistics in Multiphoton Processes with Radiative Damping of the Atomic Levels

Abstract

A model for the master equation of multiphoton processes with radiative damping of the atomic levels is proposed and a matrix method employed to solve exactly the rate equations for the matrix elements of the reduced density operator in the Fock representation. This model has been applied to the study of the low-noise properties of squeezed light in an all-optical transmission link formed from alternating sections of linear and nonlinear attenuating fibre and optical amplifiers. When the attenuators present radiative damping of the atomic levels (the lower atomic state is not the ground state) the signal-to-noise ratio is enhanced with respect to the case in which the lower atomic level is the ground state. The enhancement is improved when the input light is squeezed. The statistical properties of linear and two-photon amplification with an absorption process which exhibits radiative damping have also been analysed for coherent and squeezed inputs. The second-order fluctuations are reduced when radiative damping in the absorption process is considered except in the case of two-photon absorption for small values of the saturation parameter s_a . When the value of this parameter is increased the behaviour of the fluctuations changes and the noise is reduced. These results could be of interest in all-optical transmission links and are improved when the input light is squeezed.     

Generation of amplitude squeezed states of light from phase squeezed coherent states

Abstract

We propose a scheme to generate a displaced macroscopic superposition of phase squeezed coherent states by incorporating an optical parametric oscillator (OPO) and a nonlinear Kerr medium in a Mach-Zhender interferometer configuration. We show that the phase squeezed coherent state generated by the OPO evolves into a macroscopic superposition of phase squeezed coherent states on spending a specific amount of time inside a Kerr medium. The phase space displacement is achieved by the interference of the intense reference beam with the signal in the final beam splitter of the interferometer. The noise of the reference beam contaminating the signal is prevented by making this beam splitter highly reflective. We have calculated the photon number uncertainty of the outcoming beam and have shown that it is smaller than the usual amplitude squeezed coherent state's value.     

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.     

Pulse Position Modulation and Extended Pulse Position Modulation with Squeezed Light

Abstract

It is shown that the performance of optical communication systems that use pulse position modulation and direct photon counting can be improved with the use of squeezed states. The effect of noise is studied. An improved version of the pulse position modulation called extended position modulation is also considered.     

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.