Long-time relaxation of a finite spin bath linearly coupled to a qubit

Abstract

We discuss the long-time relaxation of a qubit linearly coupled to a finite bath of $N$ spins (two-level systems, TLSs), with the interaction Hamiltonian in rotating wave approximation. We focus on the regime $N\gg 1$, assuming that the qubit-bath coupling is weak, that the range of spin frequencies is sufficiently broad, and that all the spins are initialized in the ground state. Despite the model being perfectly integrable, we make two interesting observations about the effective system relaxation. First, as one would expect, the qubit relaxes exponentially towards its zero-temperature state at a well characterized rate. Second, the bath spins, even when mutually coupled, do not relax towards a thermal distribution, but rather form a Lorentzian distribution peaked at the frequency of the initially excited qubit. This behavior is captured by an analytical approximation that makes use of the property $N\gg 1$ to treat the TLS frequencies as a continuum and is confirmed by our numerical simulations.

arXiv commentInvited contribution to the Lindblad memorial volume, to be published in Open Systems and Information Dynamics

References in corpus (19)

• Many body localization and thermalization in quantum statistical mechanics
• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• Circuit Quantum Electrodynamics
• The foundations of statistical mechanics from entanglement: Individual states vs. averages
• Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
• Open Quantum Systems. An Introduction
• Canonical Typicality
• Eigenstate Thermalization Hypothesis
• Thermalization and prethermalization in isolated quantum systems: a theoretical overview
• Markovian Master Equations: A Critical Study
• Typical fast thermalization processes in closed many-body systems
• Quantum master equation for a system influencing its environment
• Quantum systems correlated with a finite bath: nonequilibrium dynamics and thermodynamics
• Statistical mechanics of an integrable system
• Open quantum systems coupled to finite baths: A hierarchy of master equations
• Decays of unstable quantum systems
• A simple model for a minimal environment: the two-atom Tavis-Cummings model revisited
• Thermalization without chaos in harmonic systems
• Deviations from reversible dynamics in a qubit-oscillator system coupled to a very small environment

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