Dynamics of a deformed atom cavity field system in presence of a Kerr-like medium

In this paper, we investigate the interaction between a vee-type three-level atom and a single mode of the electromagnetic field in the presence of a nonlinear Kerr-like medium and an intensity-dependent coupling. We have elucidated the system by a nonlinear Hamiltonian constructed from the standard Jaynes–Cummings model by deforming the field operators and adding some nonlinear terms. Using the initial conditions that the atom is prepared in an excited state and the field is in a coherent state, the state vector of the entire system is determined analytically. The time evolution of nonclassical properties such as Mandel Q, quantum entanglement and position-momentum uncertainty relation (squeezing) of the field are investigated. The quasiprobability distributions are also computed for the resultant state. The effects of the detuning parameters, generalized Kerr medium and intensity-dependent coupling on the previous nonclassicality signs are analysed, in detail.     

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.     

Non-conditioned generation of Schrödinger cat states in a cavity

We investigate the dynamics of a two-level atom in a cavity filled with a nonlinear medium. We show that the atom-field detuning δ and the nonlinear parameter χ⁽³⁾ may be combined to yield a periodic dynamics, allowing the generation of almost exact superpositions of coherent states (Schrödinger cats). By analysing the atomic inversion and the field purity, we verify that any initial atom-field state is recovered at each revival time, and that a coherent field interacting with an excited atom evolves to a superposition of coherent states at each collapse time. We show that a mixed field state (statistical mixture of two coherent states) evolves towards an almost pure field state as well (Schrödinger cat). We discuss the validity of these results by using the field fidelity and the Wigner function.     

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.     

Fock states generation in a kicked cavity with a nonlinear medium

Abstract

We discuss a model of a cavity filled with a passive nonlinear ?Kerr‘ medium and periodically kicked by a series of ultra-short laser pulses. The nonlinear medium is described by the (2q ? 1)th nonlinearity X ^(2q?1). We find analytical formulas describing the field states inside the cavity. We show that such a system can produce, depending on the order of the nonlinearity, superpositions of several Fock states with the small photon numbers (0,1; 0,1,2; etc). In particular, the one-photon state can be approached during the evolution of the system with X ⁽³⁾ nonlinearity provided the cavity losses are negligible. The purity of states generated in this process, however, can be seriously degraded by the cavity damping. We perform numerical calculations to validate our analytical results.     

Evolution of Coherent States in a Dispersionless Fibre with Saturable Nonlinearity and the Generation of Macroscopic Quantum-superposition States

Abstract

We study the evolution of a initially coherent state of an electromagnetic field propagating in a Kerr medium with saturable nonlinearity. By using the quantum phase distribution formalism, we analyse the dependence of the output signal phase configuration upon input field amplitude. We observe that the saturation of the nonlinear contribution of the refractive index of the propagation medium introduces interference effects that compromise the observation of macroscopically well distinguishable components of the output state. For input amplitudes much larger than a characteristic saturation amplitude the final state differs from the input state only by an overall phase shift. Possible relevance of the present results in the experimental search of Schrödinger cat-like states using semiconductor-doped glass optical fibres is discussed.     

SU(1,1) Squeezing of SU(1,1) Generalized Coherent States

Abstract

In this paper we have introduced a new class of the SU(1,1) coherent states which are the eigenstates of the generalized annihilation operator K_. We have also studied the SU(1,1) squeezing of the SU(1,1) generalized coherent states interacting with a nonlinear medium modelled as an anharmonic oscillator.     

Quantum Dynamics of a Nonlinear Birefringent Model with Anticorrelated Field States

Abstract

In this paper, anticorrelated field states with a binomial distribution over orthogonal polarizations, interacting with a nonlinear birefringent medium, are discussed. The field states are the SU(2) coherent states, where the angular momentum operators are realized as bilinear products of the boson operators associated with the two polarizations. The system discussed here provides an optical realization of a nonlinear rotator. We study the quantum dynamics of the statistical properties of the field and the evolution of the degree of polarization.     

Entangled Coherent States with Variable Weighting

Abstract

Entangled coherent states, with arbitrary weighting of the two product coherent states in the superposition, might be produced by incorporating an optical bistable device in a coupled cavity configuration. This scheme is contrasted with the entangled coherent states that arise due to interaction in an optical Kerr medium and produce only equally weighted entanglements. The entanglement is shown to occur, not between coherent states, but between states which closely approximate coherent states. An interaction which does produce entanglement between true coherent states is introduced but is shown to be unphysical.     

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.     

Non-classical behaviour and switching in Kerr nonlinear couplers

Abstract

Directional nonlinear couplers composed of two Kerr nonlinear waveguides are studied. Quantum consistent solutions of the equations of motion are obtained showing the collapses and revivals of the field mode amplitudes. The approximate method is also adopted for the contradirectional geometry and the switching accompanied by collapses of the modes is revealed. Kerr couplers with varying linear coefficients are examined and possible controls of the switching of modes, for instance, digital switching and fast switching are demonstrated. The two-mode squeezing of vacuum fluctuations and the generation of pure states are shown.     

Phase distribution and superstructures on the phase correlation of copropagating electromagnetic fields

Abstract

The phase distribution and phase correlation of two initially coherent electromagnetic field modes copropagating through a lossless nonlinear medium are investigated. We show that the number of distinguishable components in the phase distribution depends on the set of nonlinear parameters through a simple relation and that it is connected with the number of entangled field states as well as the number of components that a single field state acquires after propagating through the medium. The phase correlation between the two field modes is shown to exhibit a rich pattern of collapses and revivals, similar to those observed in the quantum inversion of several generalizations of the Jaynes-Cummings model and is related to beats of the various eigenstates of the total Hamiltonian.     

Revival Hamiltonians,Phase Operators and Non-Gaussian Squeezed States

Abstract

The phase operators P ^± of the electromagnetic field, whose classical analogues are exp (? iθ), θ being the classical phase, and the number operator N associated with a harmonic oscillator mode are used to construct a class of operators T _m = N(P ^?)^m and T ⁺ _m = (P ⁺)^m N, m = 1, 2,…. It is shown that T _m, T ⁺ _m and N satisfy a simple algebra. T _m and T ⁺ _m are used to construct model Hamiltonians H _m describing the coupling of a two-level atom to a field that leads to decay and exact revivals in the atomic dynamics. In the second part of the paper, a family of unitary operators U _m is constructed in terms of T _m and T ⁺ _m. For m = 1 and m = 2 the states generated by U _m from the vacuum are non-Gaussian squeezed states. The variance properties of the squeezed states so constructed are analysed and compared with those of the Gaussian squeezed states. It is shown that the non-Gaussian squeezed states constructed in this paper have small values for the variance product that rise only logarithmically with for large values of , the mean number of quanta.     

Kerr nonlinear coupler with varying linear coupling coefficient

Abstract

We investigate a codirectional nonlinear coupler composed of two Kerr nonlinear waveguides. Unlike the conventional device, the linear coupling between the guides is supposed to be a variable function of the propagation distance. We calculate quantum statistical and dynamical properties of the Kerr nonlinear coupler with a coherent input and analyse the influence of coupling variation on oscillations in mean photon number. The possibility to control the switching characteristics and principal squeezing effect by adjusting the form of coupling function is shown.     

Entanglement of a new type of two-mode photon-added entangled coherent state

We introduce a new entangled state, which is composed of two photon-added coherent states. We discuss the entanglement of this state by using several sufficient entanglement criteria, such as higher-order entanglement criterion, EPR criterion, SU(1,1) algebra and Cauchy–Schwarz inequality. These criteria reflect some entanglement effects of this new state, but fail to find the degree of entanglement directly. Thus, we use the covariance to measure the entanglement in this state. Our findings show that the degree of entanglement decreases with the increasing of photon-number and the amplitude of the coherent states. One interesting result is that the new entangled state becomes a maximally entangled state when the photon-added number is 1 and the amplitude of the coherent states is zero, which is just one of the four Bell states.     

Finite energy states generation by periodically pulsed nonlinear oscillator

Abstract

A system comprising an anharmonic oscillator interacting with an external filed is discussed. The oscillator is assumed to be driven by a series of ultra-short external coherent pulses, and is initially in the vacuum state. It is shown that despite strong and permanent external excitations and lack of damping processes, for sufficiently short times between two subsequent pulses the system's evolution is restricted to a finite set of Fock n-photon states. Consequently, the mean energy of photons remains finite and the system evolves similarly to displaced Kerr states. The dynamics of the mean energy of photons is compared to that of its classical counterparts.     

Quantum phase measurements and non-classical polarization states of light

Abstract

In our paper we consider the non-classical behaviour of both the Hermitian (observable) Stokes parameters of light and the phase difference of two modes that describe the quantum polarization states of optical field. To characterize the degree of polarization of light we introduce a new quantity taking into account the quantum properties of different quantum states of two orthogonally polarized modes. The problem of determination of the phase difference in two modes of optical field for the quantum polarization states of light is discussed. To describe in general such a quantum field we introduce two pairs of the phase operators: the phase angles for the Stokes parameters of light in a three-dimensional picture of the Poincaré sphere. We also consider a special type of the eight-port polarization interferometer (polarimeter) for simultaneous homodyne detection of both the Stokes parameters of light and the polarization phase operators and their fluctuations as well. Using an anisotropic (spatioperiodic) Kerr-like nonlinear medium associated with the polarization interferometer we could generate and also observe the polarization-squeezed phase states of light. The fluctuations in the phase difference between two orthogonally polarized modes for these non-classical states are less than the fluctuations for light in coherent state.     

Phase properties of coherent phase and generalized geometric states

Abstract

We examine some properties of a class of partial phase states of a single field mode. The quasiprobability distribution function and the phase properties of both the generalized geometric and even geometric states are investigated. The relation between the coherent phase states and the SU(1, 1) coherent states is sought.     

Two-dimensional solitons in a Kerr cavity

Abstract

We study the existence and nature of soliton-like localized states in a passive cavity containing a Kerr medium driven by a plane-wave input field. As the background intensity is increased, these structures are always created in pairs, for topological reasons. The smaller ‘soliton’ is always unstable, while in two transverse dimensions the larger ‘soliton’ usually collapses to a singularity or decays.