Calorimetric measurement of work for a driven harmonic oscillator

TL;DR

This paper extends calorimetric measurement techniques to a driven quantum harmonic oscillator, analyzing the validity of a two-level approximation for work statistics in different damping regimes.

Contribution

It introduces a new protocol for measuring work in a driven harmonic oscillator and compares it to the standard two-measurement approach, highlighting its regime-dependent accuracy.

Findings

The two-level approximation is valid for average work in the underdamped regime with short driving times.

In the overdamped regime, the approximation holds for all driving times.

The approximation fails for work variance and higher moments at finite temperatures.

Abstract

A calorimetric measurement has recently been proposed as a promising technique to measure thermodynamic quantities in a dissipative superconducting qubit. These measurements rely on the fact that the system is projected into energy eigenstates whenever energy is exchanged with the environment. This requirement imposes a restriction on the class of systems that can be measured in this way. Here we extend the calorimetric protocol to the measurement of a driven quantum harmonic oscillator. We employ a scheme based on the two-level approximation to define a new work quantity and show how its statistics relates to the standard two-measurement protocol. We find that for the average work the two-level approximation holds in the underdamped regime for short driving times and, in the overdamped regime, for any driving time. However, this approximation fails for the variance and higher moments of work at finite temperatures. Furthermore, we show how to relate the work statistics obtained through this scheme to the work statistics given by the two-measurement protocol.