Quantum simulation of the microscopic to macroscopic crossover using superconducting quantum impurities

• URL: http://arxiv.org/abs/2410.21941v1
• Date: Tue, 29 Oct 2024 11:01:33 GMT
• Title: Quantum simulation of the microscopic to macroscopic crossover using superconducting quantum impurities
• Authors: Amir Burshtein, Moshe Goldstein,
• Abstract summary: We look at the onset of Fermi's golden rule as a discrete microscopic bath of modes approaches the macroscopic thermodynamic limit. We show that it is necessary to keep a small but finite escape rate for each single-photon mode to obtain a finite long-time decay rate. Our formalism could be used to analyze recent experiments in superconducting circuits.
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• Abstract: Despite being a pillar of quantum mechanics, little attention has been paid to the onset of Fermi's golden rule as a discrete microscopic bath of modes approaches the macroscopic thermodynamic limit and forms a continuum. Motivated by recent experiments in circuit quantum electrodynamics, we tackle this question through the lens of single-photon decay in a finite transmission line coupled to a qubit ("quantum impurity"). We consider a single-photon state, coupled via the nonlinear impurity to several baths formed by multi-photon states with different number of photons, which are inherently discrete due to the finite size of the line. We focus on the late-time dynamics of the single-photon, and uncover the conditions under which the photon's decoherence rate approaches the decay rate predicted by Fermi's golden rule. We show that it is necessary to keep a small but finite escape rate (unrelated to the impurity) for each single-photon mode to obtain a finite long-time decay rate. We analyze the contribution of the baths formed by many-body states with different number of photons, and illustrate how the decay rate induced by some bath of $n$ photon states is enhanced by the presence of other baths of $m \neq n$ photon states, highlighting the contribution of cascade photon decay processes. Our formalism could be used to analyze recent experiments in superconducting circuits.

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