Heat bath in a quantum circuit

TL;DR

This paper explores how to realize effective heat baths in solid state quantum systems, analyzing different models like Josephson junction arrays, two-level systems, and harmonic oscillators, to understand their suitability for quantum thermalization.

Contribution

It demonstrates conditions under which a set of qubits or harmonic oscillators can serve as a proper heat bath in quantum circuits, highlighting the importance of energy distribution.

Findings

Finite Josephson junction arrays do not qualify as true dissipative environments.

A dense, wide energy distribution in two-level systems is necessary for effective thermalization.

Superconducting resonators can serve as alternative harmonic oscillator baths.

Abstract

We discuss the concept and realization of a heat bath in solid state quantum systems. First we demonstrate that, unlike a true resistor, a finite one-dimensional Josephson junction array or analogously a transmission line with non-vanishing frequency spacing does not strictly qualify as a Caldeira-Leggett type dissipative environment. We then consider a set of quantum two-level systems as a bath, which can be realized as a collection of qubits. We demonstrate that only a dense and wide distribution of energies of the two-level systems can secure long Poincare recurrence times characteristic of a proper heat bath. An alternative for this bath is a collection of harmonic oscillators, for instance in form of superconducting resonators.