Reflections on Quantum Reflectometry: Quantum and Tunneling capacitances as well as Sisyphus and Hermes resistances

TL;DR

This paper provides a comprehensive theoretical framework for quantum reflectometry, detailing how quantum and tunneling capacitances, along with Sisyphus and Hermes resistances, are rigorously defined and modified in driven-dissipative quantum systems.

Contribution

It introduces a rigorous method to incorporate quantum and tunneling capacitances and resistances into the analysis of quantum-resonator systems, accounting for their mutual dynamics.

Findings

Derived explicit formulas for quantum and tunneling capacitances.

Demonstrated how Hermes and Sisyphus resistances are affected by system dynamics.

Applied the framework to various quantum devices like Cooper-pair boxes and quantum dots.

Abstract

When a quantum electronic device is coupled to an electrical resonator, admittance changes of the quantum subsystem may be detected. The effective reactance may include capacitive and inductive terms that incorporate geometric, quantum, and tunneling components; while the effective resistance may be composed of Sisyphus and Hermes terms linked to relaxation and decoherence, respectively. Such reflectometry is usually studied when all characteristic times of the quantum system are much shorter than the resonator's period, in which case only stationary quantum states are probed. We present a rigorous description of a driven-dissipative qudit-resonator system. Our approach demonstrates how to strictly introduce quantum and tunneling capacitances as well as Hermes and Sisyphus resistances, and how these values are modified when the dynamics of the subsystems becomes mutually dependent. We present the cases of a Cooper-pair box, a single-Cooper-pair transistor, a double quantum dot, and a single-electron box. Our approach can be applied to describe any quantum system coupled to any classical resonator.