Long-Time Relaxation of a Finite Spin Bath Linearly Coupled to a Qubit

Author:

Pekola Jukka P.1,Karimi Bayan12,Cattaneo Marco13,Maniscalco Sabrina123

Affiliation:

1. Pico group, QTF Centre of Excellence, Department of Applied Physics, Aalto University, P.O. Box 15100, FI-00076 Aalto, Finland

2. Helteq group, QTF Centre of Excellence, Department of Physics, University of Helsinki, P.O. Box 43, FI-00014 Helsinki, Finland

3. Algorithmiq Ltd, Kanavakatu 3C 00160 Helsinki, Finland

Abstract

We discuss the long-time relaxation of a qubit linearly coupled to a finite bath of [Formula: see text] spins (two-level systems, TLSs), with the interaction Hamiltonian in rotating wave approximation. We focus on the regime [Formula: see text], 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 behaviour is captured by an analytical approximation that makes use of the property [Formula: see text] to treat the TLS frequencies as a continuum and is confirmed by our numerical simulations.

Funder

National Natural Science Foundation of China

Publisher

World Scientific Pub Co Pte Ltd

Subject

Mathematical Physics,Statistics and Probability,Statistical and Nonlinear Physics

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