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arXiv:1712.09129 · Physical Review Research

Steady state thermodynamics of two qubits strongly coupled to bosonic environments

Ketan Goyal, Ryoichi Kawai

Published Oct 11, 2019• 25 citations
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Abstract

The authors show that a quantum system does not always relax to a Gibbs state. This occurs when the coupling between the system and the environment is strong. The paper explores the consequence of this strong coupling in the context of decoherence.
DOI
10.1103/physrevresearch.1.033018

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We investigate the dynamics of a two-qubit open quantum system, in particular the two-qubit spin-boson model in the strong coupling regime, coupled to two thermal bosonic baths under non-Markovian and non-equilibrium conditions. Two complementary approaches, the Hierarchical Equations of Motion (HEOM) and Reaction Coordinate Mapping (RCM), are employed to examine various coupling regimes between the qubits and their respective baths. The dynamical features of the model and the impact of the tunneling amplitude on quantum coherence of the system are probed using the l1l_1l1​-norm of coherence. The model is further shown to have non-Markovian evolution. The nontrivial task of calculating entropy production in the strong-coupling regime is performed using auxiliary density operators in HEOM. Motivated by the realization of a quantum thermal device in the strong-coupling regime, the non-equilibrium steady-state behavior of the system is investigated. Furthermore, the relationship between the heat and spin currents and the tunneling amplitude is probed.
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Quantum mechanical entanglement can exist in noisy open quantum systems at high temperature. A simple mechanism, where system particles are randomly reset to some standard initial state, can counteract the deteriorating effect of decoherence, resulting in an entangled steady state far from thermodynamical equilibrium. We present models for both gas-type systems and for strongly coupled systems. We point out in which way the entanglement resulting from such a reset mechanism is different from the entanglement that one can find in thermal states. We develop master equations to describe the system and its interaction with an environment, study toy models with two particles (qubits), where the master equation can often be solved analytically, and finally examine larger systems with possibly fluctuating particle numbers. We find that in gas-type systems, the reset mechanism can produce an entangled steady state for an arbitrary temperature of the environment, while this is not true in strongly coupled systems. But even then the temperature range where one can find entangled steady states is typically much higher with the reset mechanism.