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Journal of the Physical Society of Japan

Dynamics of a Dissipative Jaynes-Cummings Model

Mio Murao, Fumiaki Shibata

Published Jul 15, 1995• 10 citations
Publisher

Abstract

A new type of the dissipative Jaynes-Cummings model is presented. Interaction between a composite relevant system and a reservoir is introduced to modulate the coupling constant in the relevant system. A quantal master equation is obtained with use of the time convolutionless (TCL) projection operator formalism and is expanded in terms of eigenstates of the composite relevant system. The resulting basic equations become solvable and can be used irrespective of the interaction strength between the relevant subsystems. Moreover, these equations give the correct equilibrium values in each subspace. Several explicit numerical calculations are done.

DOI
10.1143/jpsj.64.2394

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A new type of the dissipative Jaynes-Cummings model is presented. Interaction between a composite relevant system and a reservoir is introduced to modulate the coupling constant in the relevant system. A quantal master equation is obtained with use of the time convolutionless (TCL) projection operator formalism and is expanded in terms of eigenstates of the composite relevant system. The resulting basic equations become solvable and can be used irrespective of the interaction strength between the relevant subsystems. Moreover, these equations give the correct equilibrium values in each subspace. Several explicit numerical calculations are done.
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.
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.
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.
The master equation currently used to describe a two level atom interacting with a single mode field damped by contact with a thermal reservoir (the damped Jaynes-Cummings model) is shown not to have, as its steady state solution, the expected canonical density operator prescribed by the general principles of statistical mechanics for a system in thermal equilibrium. A modified master equation is derived here which satisfies this requirement. Except for a reservoir at zero temperature, this master equation differs from that which is currently used in that the damping terms contain contributions due to the atom-field interaction.
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.
We present a simple exactly solvable extension of of the Jaynes-Cummings model by adding dissipation. This is done such that the total number of excitations is conserved. The Liouville operator in the resulting master equation can be reduced to blocks of 4×44\times 44×4 matrices.