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CIENCIA EN DESARROLLO

A Study of the Quantum Correlations in a Tavis-Cummings System

Duvalier Madrid-Úsuga

Published Feb 6, 2018• 0 citations
Publisher

Abstract

The quantum correlations of two qubits in a microcavity with dissipation and a single quantized mode of the electromagnetic field are studied. In order to study our physical system, the Tavis-Cummings model and the formalism of the master equation of the density operator under the Born-Markov approximations will be used. The cavity mode will be coupled with an external pulsed laser and the master equation of the density operator that describes the evolution of the system will be solved numerically. The concurrence, the quantum mutual information, and the quantum discord are determined for the system of two qubits. The correlations are studied as a function of the dimensionless quantity $\tau = gt $ when the intensity of the laser cavity coupling varies, and two initial conditions are considered in the weak coupling regime in which the dynamic evolution of these correlations was studied.

DOI
10.19053/01217488.v9.n1.2018.7232

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The quantum correlations of two qubits in a microcavity with dissipation and a single quantized mode of the electromagnetic field are studied. In order to study our physical system, the Tavis-Cummings model and the formalism of the master equation of the density operator under the Born-Markov approximations will be used. The cavity mode will be coupled with an external pulsed laser and the master equation of the density operator that describes the evolution of the system will be solved numerically. The concurrence, the quantum mutual information, and the quantum discord are determined for the system of two qubits. The correlations are studied as a function of the dimensionless quantity τ=gt\tau = gt τ=gt when the intensity of the laser cavity coupling varies, and two initial conditions are considered in the weak coupling regime in which the dynamic evolution of these correlations was studied.
We investigate the quantum correlation between light and matter in bipartite quantum systems, drawing on the Jaynes–Cummings model and the Tavis–Cummings model, which are well-established in cavity quantum electrodynamics. Through the resolution of the quantum master equation, we can derive the dissipative dynamics in open systems. To assess the extent of quantum correlation, several measures are introduced: von Neumann entropy, concurrence and quantum discord. The effects of initial entanglement and dissipation intensity on quantum discord are carefully examined. Furthermore, we examined the dynamics of quantum discord within the O H + model.
Abstract We revisit the problem of the dynamics of quantum correlations in the Tavis–Cummings model. Our results show that the dynamics of entanglement and quantum discord are far from being trivial or intuitive. We find states with the same entanglement but different discord and states where the two quantifiers give opposite information about correlations at a certain time. We furthermore show that many of the dynamical features of quantum discord attributed to dissipation are already present in the exact framework and are due to the characteristic quantum nonlinearity of the model and to the choice of initial conditions. Through a comprehensive analysis of pure and mixed initial conditions, we find a fascinating range of phenomena that can be used for experimental purposes. We propose an experiment called quantum discord gates where for a given pure initial condition discord is zero or non-zero depending on the number of photons in the cavity. Given the marginal character of states with zero discord this result is not only completely counterintuitive but is also useful as a way to count photons.
We consider two two-level atoms fixed at different positions, driven by a resonant monochromatic laser field, and interacting collectively with all the modes of the quantum electromagnetic field. A Born-Markov-secular master equation is used to describe the dynamics of the two atoms. When the atoms have the same coupling with the laser field, it is shown that their steady-state density operator is approximately an XXX state and this is used to obtain simple approximate analytic expressions for steady-state quantum and classical correlations which are characterized as functions of the laser field intensity and the distance between the two atoms. Moreover, the values of both the laser field intensity and the distance between the two atoms that maximize correlations are identified.
Abstract This work delves into the nonlocal correlation dynamics of the maximum-Bell nonlocality (MBN), uncertainty-induced nonlocality (UIN), and concurrence of two two-level atoms having time-dependent atomic locations within Tavis-Cummings model. By considering a scenario where the pure two qubits resonantly interact with an even coherent cavity field through a two-photon transition, we explore the nonlocal correlation dynamics of both moving and stationary two-atom configurations under varying conditions and coupling parameters. Our findings reveal that the coherent cavity induces the successful generation of nonlocal correlations between atoms in both modes, with moving atoms exhibiting higher and symmetrical nonlocal correlations. Interestingly, dynamical maps showcase distinct behaviors for atoms at rest, exhibiting precocity at higher atom-cavity strengths. Moreover, equal coupling strength results in lower quantum correlations. The UIN measure emerges as the most robust quantum function, showing enhancements with sustained unequal coupling strengths, contrasting with the MBN and concurrence. These insights offer a nuanced understanding of nonlocal correlations in the Tavis-Cummings model, essential for advancing quantum information science and technology.
The dynamics of entanglement and quantum discord between two identical qubits strongly interacting with a common single mode leaky cavity field have been investigated beyond the rotating wave approximation (RWA) by using a recently derived Lindblad type quantum optical master equation [F. Beaudoin, J. M. Gambetta, and A. Blais, Phys. Rev. A 84, 043832 (2011)] that can describe the losses of the cavity field in a strong atom-field coupling regime. Contrary to previous investigations of the same model in the dissipative regime by using the standard Lindblad quantum optical master equation in a strong-coupling regime, the atom-field steady states are found to be cavity decay rate independent and have a very simple structure determined solely by the overlap of initial atomic state with the subradiant state which is valid for all coupling regimes. Non-RWA dynamics are found to have remarkable effects on the steady state quantum discord and entanglement that cannot be achieved under RWA conditions, for instance, they can induce steady state entanglement even for the initial states that have no overlap with the subradiant state. Moreover, the non-RWA dynamics are found to reverse the initial state dependence of steady state entanglement and quantum discord contrary to the RWA case.
Dissipative properties of a composite system interacting with an environment are studied in order to obtain insight into relaxation and decoherence phenomena. As a typical system with internal degree of freedom, a Jaynes–Cummings (JC) model is considered where a spin (qubit) interacts with a single bosonic mode. When the whole system is initially in a state of at most single excitation, the model becomes solvable for excitation number conserving Hamiltonians, even if the JC system interacts with its environment composed of harmonic oscillators. Effects of initial correlations between the system and the environment are also taken into account. Basic equations for the density matrix are solved exactly to determine dynamics of the reduced systems. Mutually related problems of initial correlations, entanglement and non-Markovian property are studied explicitly by examining the time evolution of the reduced density matrices, the concurrence and the trace distance.