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Journal of Optics B Quantum and Semiclassical Optics

The Pancharatnam phase of a two-level atom in the presence of another two-level atom in a cavity

Mahmoud Abdel‐Aty

Published Jul 2, 2003• 19 citations
Publisher

Abstract

In this paper we consider a Hamiltonian modelling a pair of two-level atoms within a perfect cavity for the case of a two-photon transition. Under the exact resonance condition and in the presence of both the Stark shift and phase shift an exact solution to the Schrödinger equation is obtained. Employing this solution gives an analytical expression for the temporal evolution of the Pancharatnam phase when a second atom is allowed to interact with the cavity mode and becomes entangled with the first atom. Numerical investigations are carried out for the phenomena of collapses and revivals for different Stark shift values, the distance between the two atoms and the phase shift. It has been shown that the Pancharatnam phase is affected by the Stark shift and the distance between the two atoms when a nonlinear two-photon process is involved

DOI
10.1088/1464-4266/5/4/304

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In this paper we consider a Hamiltonian modelling a pair of two-level atoms within a perfect cavity for the case of a two-photon transition. Under the exact resonance condition and in the presence of both the Stark shift and phase shift an exact solution to the Schrödinger equation is obtained. Employing this solution gives an analytical expression for the temporal evolution of the Pancharatnam phase when a second atom is allowed to interact with the cavity mode and becomes entangled with the first atom. Numerical investigations are carried out for the phenomena of collapses and revivals for different Stark shift values, the distance between the two atoms and the phase shift. It has been shown that the Pancharatnam phase is affected by the Stark shift and the distance between the two atoms when a nonlinear two-photon process is involved
An exact solution of the time-dependent master equation that describes the evolution of two two-level qubits (ions or atoms) within a perfect cavity for the case of multiphoton transition and in the presence of both the Stark shift and phase shift is obtained. Employing this solution, the significant features of the entanglement when a second qubit is allowed to interact with cavity mode and becomes entangled with the first qubit are investigated in the context of the measure defined by negative eigenvalues for the partial transposition of the density operator. The effects of Stark shift, distance between the two qubits, and an instantaneous phase shift experienced by the second qubit on the entanglement and probability amplitudes are indicated. It has been shown that the entanglement as well as the intensity are markedly affected by different parameters when the nonlinear two-photon process is involved. Moreover, the quasiprobability distribution function is investigated before and after the sudden phase shift experienced by the second qubit. We believe that this may throw some light on the question of the entanglement of multi-qubit systems.
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, we investigated the dynamics of atomic entanglement in a quantum system consisting of two identical two-level atoms (qubits) resonantly interacting with a mode of a thermal cavity field through degenerate two-photon transitions, in the presence of a Stark energy level shift. An analytical expression is obtained for the atom entanglement (negativity) parameter for separable and entangled initial states of atoms. The influence of the Stark shift on the degree of atom-atom entanglement is considered. It is established that the Stark shift leads to a significant increase in the degree of atom entanglement in the case of separable initial states of atoms and to stabilization of atomic entanglement in the case of entangled initial states of atoms.
The problem of a two-level atom interacting with single mode cavity field is considered, however, the optical cavity is filled with new structure of a generalized nonlinear Stark shift via Ξ configuration. One starts with a three-level trapped atom interacting with the quantized field of center of mass motion thus a Hamiltonian for one-phonon process with nonlinearities is derived. Through the elimination of the intermediate level by using the adiabatic elimination method, we generate a new structure of effective Hamiltonian for a two-level atom with a nonlinear Stark shift. The temporal evolution of the atomic inversion is studied, we introduce that in the presence of the Stark shift parameter the atom leaves in a maximal entangled sate. We use the von Neuman entropy to measure the degree of entanglement between the atom and the field. After adding the nonlinear Stark shift the system never reaches the pure state. Also we study the Q-function for obtaining more information in phase space for this system. These aspects are sensitive to changes in the Stark shift parameter. The results shows that the effect of the nonlinearity in the Stark shift changes the quasiperiod of the field entropy and hence the entanglement between the particle and the field.
In this paper, we study the interaction between a two-level atom and a three types of nonlinear interaction of two modes, two as a degenerate two photon and the third of the converter form. The solution to the Schrodinger equation is obtained exactly under a certain specific condition. By using this solution we discuss numerically the atomic inversion, the degree of entanglement through the atomic Wehrl entropy, the geometric phase entropy for chosen values of the detuning and coupling parameters. Statistical properties of the investigated system is discussed by the evolution of the Mandel parameter.
In this paper, we present some properties through two two-level atoms interacting with a two-mode quantized cavity field. We study this system in the presence of detuning parameter, Kerr nonlinearity, Stark shift, relative phase and intensity-dependent atoms-field coupling. Also, the coupling parameter is modulated to be time dependent. The exact solution of this model is given by using the Schrődinger equation when the atoms and the field are initially prepared in superposition states and coherent states, respectively. We employed the results to calculate some aspects such as linear entropy, total atomic inversion and cross-correlation function.