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Journal of Modern Optics

Exact time-evolution of the dispersive Jaynes–Cummings model: the effect of initial correlation and master equation approach

Masashi Ban

Published Mar 14, 2011• 5 citations
Publisher

Abstract

Time-evolution of the dispersive Jaynes–Cummings model interacting with a bosonic reservoir is considered in the presence of an initial correlation between the cavity field and reservoir. When there is at most one excitation in the whole system, the exact time-evolution can be obtained. The effects of the initial correlation on the decoherence of the two-level system and cavity field are investigated. Furthermore, the validity of the time-convolutionless quantum master equation in the second-order approximation with respect to the system-reservoir interaction is examined by means of the exact solution.

DOI
10.1080/09500340.2011.563326

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Time-evolution of the dispersive Jaynes–Cummings model interacting with a bosonic reservoir is considered in the presence of an initial correlation between the cavity field and reservoir. When there is at most one excitation in the whole system, the exact time-evolution can be obtained. The effects of the initial correlation on the decoherence of the two-level system and cavity field are investigated. Furthermore, the validity of the time-convolutionless quantum master equation in the second-order approximation with respect to the system-reservoir interaction is examined by means of the exact solution.
A master equation for the Jaynes-Cummings (JC) system interacting with a bosonic reservoir through a conserved quantity is derived analytically without any approximation.The derivation is valid for any initial JC state that has no correlation with the initial reservoir at any temperature and yields a Gorini-Kossakowski-Lindblad-Sudarshan-type master equation with time-dependent coefficients.Several physical quantities of the open JC system are examined and the validity or limit of some of the standard approximations used to derive the master equation is discussed on the basis of the exact results obtained here.
Decoherence of the dispersive Jaynes–Cummings model which is placed in a lossy cavity is studied by means of the time-convolutionless non-Markovian quantum master equation. The effect of the interaction between a two-level atom and photon field on the damping operator of the quantum master equation is made clear by calculating the decay of coherence and entanglement of the relevant system. It is shown that although the interaction effect on the damping operator is small when the cavity loss has the Markovian property, it becomes significantly large when the cavity loss is subject to the non-Markovian process. Furthermore, the quantum channel of the two-level atom derived by the dispersive Jaynes–Cummings model is investigated. The decay of entanglement of the two two-level atoms is examined to show the importance of the interaction effect on the damping operator.
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.
We consider the dynamics of an atom–field system in a cavity described by means of the Jaynes–Cummings model in the dispersive limit, assuming that the electromagnetic field is interacting with a squeezed, or phase-sensitive, reservoir. After obtaining the solution of the master equation in terms of Wigner functions, we do an analysis of the system evolution and its asymptotical behaviour in terms of the so-called Mandel Q parameter and the linear entropies of the total system and the reduced system, associated with field and atom.
Abstract The quantum master equation is considered for an open system initially correlated with a thermal reservoir, where the initial correlation is created by an initial preparation of a relevant system. Perturbative expansion formulas for quantum master equations are systematically derived with respect to a system-reservoir interaction. The result is applied to the dispersive JC model and the spin-boson model. In the second order approximation, the generalized Bloch equations for a spin system are found. It is shown that the effect of the initial correlation between the spin and the thermal reservoir is equivalent to an effective external field applied to the spin system.