Qubit decay in circuit quantum thermodynamics

We describe a qubit linearly coupled to a heat bath, either directly or via a cavity. The bath is formed of oscillators with a distribution of energies and coupling strengths, both for qubit-oscillator and oscillator-oscillator interaction. A direct numerical solution of the Schrödinger equation for the full system including up to 106 oscillators in the bath and analytic solutions are given, verifying quantum decay in short time quadratic (Zeno), long time exponential and eventually power law relaxation regimes. The main new results of the paper deal with applications and implications in quantum thermodynamics setups. We start by providing a correspondence of the oscillator bath to a resistor in a circuit. With the presented techniques we can then shed light on two topical questions of open quantum systems. First, splitting a quantum to uncoupled baths is presented as an opportunity for detection of low energy photons. Second, we address quantitatively the question of separation between a quantum system and its classical environment.