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Solution of the two-atom Tavis-Cummings model having different couplings and detunings with an application to the study of the influence of noise on quantum behaviour

G. L. Deçordi, A. Vidiella-Barranco

Published May 12, 2015• 0 citations
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Abstract

In this paper we present an exact analytical solution of the two-atom Tavis-Cummings model in which the constituent atoms are coupled with different strengths to the field and having different atom-field frequency detuning. As an application, we investigate some aspects of the dynamics of our system of interest: one of the atoms (atom 1) coupled with one mode of the cavity field. The remaining atom (atom 2) is treated as an external, noisy system (environment) which is assumed to be in a highly mixed state. We analyze properties such as linear entropy and atomic dipole squeezing of atom 1, and we show that, although in general the action of the external system (atom 2) has a destructive effect, the quantum behaviour of the system of interest may be restored if the field is sufficiently detuned from the atomic resonance of atom 2, the environment.

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In this paper we present an exact analytical solution of the two-atom Tavis-Cummings model in which the constituent atoms are coupled with different strengths to the field and having different atom-field frequency detuning. As an application, we investigate some aspects of the dynamics of our system of interest: one of the atoms (atom 1) coupled with one mode of the cavity field. The remaining atom (atom 2) is treated as an external, noisy system (environment) which is assumed to be in a highly mixed state. We analyze properties such as linear entropy and atomic dipole squeezing of atom 1, and we show that, although in general the action of the external system (atom 2) has a destructive effect, the quantum behaviour of the system of interest may be restored if the field is sufficiently detuned from the atomic resonance of atom 2, the environment.
Individual quantum systems may be interacting with surrounding environments having a small number of degrees of freedom. Here we discuss a simple toy model: a system constituted by a two-level atom (atom 1) interacting with a single mode cavity field which is (weakly) coupled to a small environment (atom 2). We investigate the influence of the minimal environment on the dynamics of the linear entropy and the atomic dipole squeezing of atom 1, as well as the entanglement between atom 1 and the field. We also obtain the full analytical solution of the two-atom Tavis–Cummings model for both arbitrary coupling strengths and frequency detunings, necessary to analyse the influence of the field-environment detuning on the evolution of the system’s quantum properties. For complementarity, we discuss the role of the degree of mixedness of the environment by analysing the time-averaged linear entropy of atom 1.
We investigate the entanglement dynamics of two atoms interacting with a single-mode cavity field within the Tavis-Cummings model in the presence of noise. The atoms are initially prepared in either pure Bell states or mixed Werner states, allowing a direct comparison of pure- and mixed-state entanglement. The cavity field is described by generalized single-mode squeezed coherent thermal states, incorporating both thermal and quantum noise effects. Atom-atom and atom-field entanglement are quantified using concurrence and negativity, respectively. We analyze entanglement sudden death and revival, and examine how Ising-type coupling, dipole-dipole interaction, Kerr nonlinearity, and detuning modify the entanglement dynamics. Our results show that thermal photons generally suppress entanglement and enhance sudden death, while squeezing counteracts these effects. The influence of nonlinearities and interatomic interactions depends sensitively on the purity of the initial atomic state, leading to qualitatively different behaviors for Bell and Werner states.
We study the properties of atoms and cavity field in the two-atom Tavis–Cummings model where the two atoms interact with each other and are also driven by an external classical field. We consider the special case that the cavity is initially in a coherent state. The atomic inversion, the average photons number and the Mandel parameter in the driven Tavis–Cummings model are given and analysed numerically. We pay special attention to the dynamical behaviour of the atoms and the cavity field modified by the external field.
The entanglement between two two-level atoms (qubits) interacting not-resonantly with a one mode of thermal field in a lossless cavity via effective degenerate two-photon transitions is investigated. Based on the exact solution for the time-dependent density matrix of the system under consideration, negativity is calculated as a measure of the entanglement of atoms. The influence of a detuning on the dynamics of entanglement of atoms for separable and entangled initial atomic states and thermal cavity state is investigated.
We study in this thesis composite quantum systems under the influence of external environments.In the first part of this work, we investigate a two qubit interacting system having one of them isolated and the other coupled to a thermal bath.We analyze the effect of the temperature of the bath on the dynamics of the two qubit system.In order to do that, we consider two different models of system-reservoir interaction: i) a "microscopic" model, in which the master equation is derived taking into account the interaction between the two subsystems (qubits), ii) a "phenomenological" approach, in which the master equation consists of a dissipative term added to the unitary evolution term.We show that in the strong coupling regime between the subsystems (qubits), the expected thermal equilibrium steady state for the two-qubit system naturally arises in the framework of the microscopic model, while in the phenomenological approach it is obtained a steady state density operator which is not correct.Furthermore, the differences are even more profound in the weak coupling regime, when the models give rise to opposite behaviors with regard to the linear entropy of qubit 1.At the context of quantum systems coupled to environments with few degrees of freedom, we solve analytically the matter-radiation interaction model known as two atom Tavis-Cummings Model.With the solutions at hand, achieved in general circumstances until the present not found in literature, in which the constituent atoms may be coupled with different strengths to the field and also have different frequency detunings, we study the effects that arise from the interaction of a small environment (atom in a statistical mixture state) with the other atom coupled to an oscillator (cavity mode).We show that nonclassical features associated to the main system may be significantly degraded by the action of the small environment, if atom 2 is resonantly coupled to the field.We also demonstrate that the nonclassical behaviour of the system may be restored if we detune the field from the transition frequency of atom 2, the environment.
An exact solution of the problem of two-atom one- and two-mode Jaynes-Cummings model with intensity- dependent coupling is presented. Asymptotic solutions for system state vectors are obtained in the approximation of large initial coherent fields. The atom-field entanglement is investigated on the basis of the reduced atomic entropy dynamics. The possibility of the system being initially in a pure disentangled state to revive into this state during the evolution process for both models is shown. Conditions and times of disentanglement are derived.