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Journal of the Physical Society of Japan

Relaxation and Decoherence of Two Strongly Coupled Spin 1/2 Particles

Mio Murao

Published Aug 15, 1997• 4 citations
Publisher

Abstract

A quantum statistical model for the relaxation of two strongly coupled spin 1/2 particles toward thermal equilibrium is formulated microscopically using a master equation. Raman-type dissipation mechanisms are introduced in addition to the usual bilinear coupling between the coupled system and the reservoir. The effects of two different rotating wave approximations to derive the master equation are investigated. Decoherence is considered as a process toward thermal equilibrium for the dissipative system and is studied by observing the phase and energy relaxation.

DOI
10.1143/jpsj.66.2314

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A quantum statistical model for the relaxation of two strongly coupled spin 1/2 particles toward thermal equilibrium is formulated microscopically using a master equation. Raman-type dissipation mechanisms are introduced in addition to the usual bilinear coupling between the coupled system and the reservoir. The effects of two different rotating wave approximations to derive the master equation are investigated. Decoherence is considered as a process toward thermal equilibrium for the dissipative system and is studied by observing the phase and energy relaxation.
The decoherence of two initially entangled qubits in non-Markovian reservoirs has been investigated exactly without Born-Markovian approximation or rotating-wave approximation (RWA). The nonperturbative quantum master equation is derived and its exact solution is obtained. The decoherence behavior of two qubits, initially entangled in Bell states, has been investigated in the weak coupling regime and strong coupling regime. The results show that the counter-rotating wave terms have obvious influence on the decoherence behavior in the non-Markovian regime.
We analyze a system of two coupled cavities, where one of them is leaky, namely, is interacting with the environment. We derive the master equation for the system, and show that the relaxation term, in the case of strongly coupled cavities, is not simply the standard one, which is obtained by neglecting the interaction between the two cavities, when calculating the effect of the bath. The relaxation term is calculated here by first diagonalizing the Hamiltonian of the coupled modes of the cavities, and then it is properly evaluated by eliminating the degrees of freedom of the reservoir, maintaining only the energy-conserving terms. Only by following this prescription one can guarantee that the coupled system approaches thermal equilibrium. We study both the steady-state solutions of the master equation, and the time evolution of the system from given initial conditions.
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A phase relaxation process of interacting two qubits is studied by means of the quantum master equation, where each qubit is influenced by an independent thermal reservoir. The damping operator of the quantum master equation consists of two parts; one includes the effects of the interaction between the qubits and the other does not. It is shown that the interaction significantly affects the phase relaxation process. The decoherence of entanglement is investigated for the two qubits initially prepared in the XXX state.
We study open quantum systems where the coupling between the system and its environment is of a quantum nondmolition (QND) type. Such a system undergoes decoherence without dissipation of energy. We obtain the master equation for the evolution of such a system under the influence of a squeezed thermal bath. From the master equation it can be seen explicitly that the process involves decoherence without any dissipation. We work out the decoherence causing term in the high and zero temperature limits and show that they match with known results in the different temperature regimes for the case of a thermal bath. We also make a comparison between the quantum statistical properties of QND and non-QND (i.e., involving decoherence as well as dissipation) types of evolution.