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, bothfor 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.
We apply quantum trajectory techniques to analyze a realistic set-up of a superconducting qubit coupled to a heat bath formed by a resistor, a system that yields explicit expressionsof the relevant transition rates to be used in the analysis. We discuss the main characteristics of the jump trajectories and relate them to the expected outcomes („clicks“) of a fluorescence measurement using the resistor as a nanocalorimeter. As the main practical outcome we present a model that predicts the time-domain response of a realistic calorimeter subject to single microwave photons, incorporating the intrinsic noise due to the fundamental thermal fluctuations of the absorber and finite bandwidth of a thermometer.
In miniaturising electrical devices down to nanoscales, heat transfer has turned into a serious obstacle but also potential resource for future developments, both for conventional andquantum computing architectures. Controlling heat transport in superconducting circuits has thus received increasing attention in engineering microwave environments for circuit quantum electrodynamics (cQED) and circuit quantum thermodynamics experiments (cQTD). While theoretical proposals for cQTD devices are numerous, the experimental situation is much less advanced. There exist only relatively few experimental realisations, mostly due to the difficulties in developing the hybrid devices and in interfacing these often technologically contrasting components. Here we show a realisation of a quantum heat rectifier, a thermal equivalent to the electronic diode, utilising a superconducting transmon qubit coupled to two strongly unequal resonators terminated by mesoscopic heat baths. Our work is the experimental realisation of the spin-boson rectifier proposed by Segal and Nitzan.
Characterizing superconducting microwave resonators with highly dissipative elements is a technical challenge, but a requirement for implementing and understanding the operation ofhybrid quantum devices involving dissipative elements, e.g. for thermal engineering and detection. We present experiments on λ/4 superconducting niobium coplanar waveguide (CPW) resonators, shunted at the antinode by a dissipative copper microstrip via aluminium leads, yielding a quality factor unresolvable from the typical microwave environment. By measuring the transmission both above and below this transition, we are able to isolate the resonance. We then experimentally verify this method with copper microstrips of increasing thicknesses, from 50 nm to 150 nm, and measure quality factors in the range of 10∼67 in a consistent way.