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Journal of Modern Optics

Influence of Kerr-like medium on the dynamics of a two-mode Raman coupled model

Sudha Singh, Karuna Gilhare

Published Mar 25, 2016• 5 citations
Publisher

Abstract

We study the quantum dynamics of an effective two-level atom interacting with two modes via Raman process inside an ideal cavity in the presence of Kerr non-linearity. The cavity modes interact both with the atom as well as the Kerr-like medium. The unitary transformation method presented here, not only solves the time-dependent problem, but also provides the eigensolutions of the interacting Hamiltonian at the same time. We study the atomic-population dynamics and the dynamics of the photon statistics in the two cavity modes. The influence of the Kerr-like medium on the statistics of the field is explored and it is observed that Kerr medium introduces antibunching in mode 1 and this effect is enhanced by a stronger interaction with the non-linear medium. In the high non-linear coupling regime anticorrelated beam become correlated. Kerr medium also introduces non-classical correlation between the two modes.

DOI
10.1080/09500340.2016.1158330

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We study the quantum dynamics of an effective two-level atom interacting with two modes via Raman process inside an ideal cavity in the presence of Kerr non-linearity. The cavity modes interact both with the atom as well as the Kerr-like medium. The unitary transformation method presented here, not only solves the time-dependent problem, but also provides the eigensolutions of the interacting Hamiltonian at the same time. We study the atomic-population dynamics and the dynamics of the photon statistics in the two cavity modes. The influence of the Kerr-like medium on the statistics of the field is explored and it is observed that Kerr medium introduces antibunching in mode 1 and this effect is enhanced by a stronger interaction with the non-linear medium. In the high non-linear coupling regime anticorrelated beam become correlated. Kerr medium also introduces non-classical correlation between the two modes.
Abstract The dynamics of an effective two-level atom coupled to two-mode intensity-dependent quantized cavity fields via a ladder process in the presence of a Kerr medium has been investigated. Eigenfunctions and eigenvalues of the Hamiltonian of the interacting system have been obtained using a unitary transformation method. The cavity field statistics and non-classical properties are investigated numerically through second-order correlation functions. The effect of detuning and the Kerr medium on the non-classical features of the atom-field state has been analyzed. We find that the presence of Kerr non-linearity enhances the non-classical correlation between the correlated beams at short time intervals and increases antibunching at short time intervals.
We study the quantum dynamics of a two-atom Raman coupled model interacting with a quantized bimodal field with intensity-dependent coupling terms in a lossless cavity. The unitary transformation method used to solve the time-dependent problem also gives the eigensolutions of the interaction Hamiltonian. We study the atomic-population dynamics and dynamics of the photon statistics in the two cavity modes, and present evidence of cooperative effects in the production of antibunching and anticorrelations between the modes. We also investigate the effect of detuning on the evolution of second-order correlation functions and observe that the oscillations become more rapid for large detuning.
In this paper, we investigate the dynamics of two two-level atoms interacting with a two-mode field inside an optical cavity, in presence of a nonlinear Kerr-like medium as well as the Stark shift. We derive the exact analytical solution of the time-dependent Schrödinger equation that provides a comprehensive framework for analyzing the system's quantum properties. To characterize the nonclassical features of the radiation field, we examine photon number distribution, second-order correlation function 𝑔2⁡(0), squeezing properties, and Mandel's 𝑄𝑀 parameter. These properties reveal significant insights into the quantum statistical behaviour of the field and its deviation from classicality under different interaction regimes. In addition, we quantify the atom-atom entanglement using linear entropy which captures the mixedness of the atomic subsystem and elucidates the interplay between atom-atom interactions. The results highlight the crucial role of nonlinear interactions and the Stark shift in shaping the quantum correlations and nonclassical phenomena of the system.
In this paper, the effects of the field damping and Kerr-like medium on a system of a four-level atom in the [Formula: see text]-type interacting nonlinearly with a two-mode field are studied. Analytical solution of the system of differential equations resulting from the Schrödinger equation is obtained. The effects of detuning parameters, Kerr-like parameter, coupling function and damping rate are discussed for atomic population inversion, the second-order correlation function, Shannon information entropy, and linear entropy. Under justifiable all conditions, extreme entanglement states may appear periodically with the evolution of time. The arrival of the quantum system to a pure state can be controlled by variations of the Kerr medium and the damping parameters. The results also exhibit that the periods of strong and weak entanglement between the parts of the system are achieved during the periods of collapses and revivals of the atomic population inversion. Moreover, the photon distribution changes from non-classical to classical by increasing the damping rate.
We consider a generalized multi-photon interaction of two collectively two-level atoms with two-mode of electromagnetic field in the presence of Kerr medium and intensity-dependent coupling. We show that this atomic system possesses supersymmetric structure. We solved this system by virtue of supersymmetric unitary transformation. The supersymmetric generators of this atomic system are constructed. The diagonalization of the corresponding Hamiltonian is performed by introducing a supersymmetric unitary transformation. Accordingly, the eigenvalues and eigenfunctions of the Hamiltonian of the atomic system are obtained. The time evolution of the atom–field wave functions is derived in an exact form for two cases of the initial states of the atoms and the field modes. Some quantum effects such as the second-order correlation function, cross-correlation, purity and Husimi Q-function are investigated. The effects of the Kerr medium, detuning parameter, intensity-dependent coupling and multi-photon transition on the evolution of these quantum effects are examined. We conclude that the supersymmetric unitary transformation method is very simple and can be applied to a variety of atomic systems which possess a supersymmetric structure.
A quantum cavity filled with a nonlinear medium (Kerr like medium) and contains a 2-mode field interacting with time dependence of 2-qubit is investigated. Part of the two qubits interact in the form of an amplifier, while the other is in the form of a ladder. The constants of motion are calculated by using the Heisenberg differential equation. Moreover, the analytical solution is calculated by solving the Schrodinger differential equations. Some statistical quantities are calculated to identify the features of the proposed model. The effective of the nonlinear term on the phenomena of collapse and revival are discussed through atomic population. The amount of entanglement between the quantum subsystem, whether it is between the 2-qubit and the cavity field, or between the 2-qubit together are calculated using the linear entropy and the concurrence. The results indicated that there is a superstructure between the atomic population and the linear entropy, concurrence. The intensity of oscillations decreases for the entanglement between the field and the two qubits when the Kerr like medium of the Hamiltonian system is included. The nonclassical distribution of the quantum system decreases after taking Kerr like medium into account.