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Dynamics of collective decoherence and thermalization |
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| Authors: | M Merkli GP Berman IM Sigal |
| Institution: | a Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL, Canada A1C 5S7 b Theoretical Division and CNLS, MS B213, Los Alamos National Laboratory, Los Alamos, NM 87545, USA c Department of Mathematics, University of Toronto, Toronto, ON, Canada M5S 2E4 |
| Abstract: | We analyze the dynamics of N interacting spins (quantum register) collectively coupled to a thermal environment. Each spin experiences the same environment interaction, consisting of an energy conserving and an energy exchange part.We find the decay rates of the reduced density matrix elements in the energy basis. We show that if the spins do not interact among each other, then the fastest decay rates of off-diagonal matrix elements induced by the energy conserving interaction is of order N2, while that one induced by the energy exchange interaction is of the order N only. Moreover, the diagonal matrix elements approach their limiting values at a rate independent of N. For a general spin system the decay rates depend in a rather complicated (but explicit) way on the size N and the interaction between the spins.Our method is based on a dynamical quantum resonance theory valid for small, fixed values of the couplings. We do not make Markov-, Born- or weak coupling (van Hove) approximations. |
| Keywords: | Decoherence Decoherence rate Thermalization rate Reduced density matrix Open quantum system Quantum register Qubit Spin system Thermal reservoir Thermal equilibrium Quantum resonance theory Level shift operator |
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