Using a qubit to measure photon number statistics of a driven, thermal oscillator

TL;DR

This paper presents a theoretical method to extract photon number statistics of a driven, thermal oscillator by measuring a coupled qubit's dephasing spectrum, with implications for quantum optics and nano-electromechanical systems.

Contribution

It extends previous work by providing a detailed analysis of how a qubit's dephasing spectrum can reveal photon number statistics in a thermal, driven oscillator.

Findings

Analytic results for qubit dephasing by a thermal mode

Assessment of measurement fidelity for photon statistics

Comparison of approximation levels in dephasing analysis

Abstract

We demonstrate theoretically how photon number statistics of a driven, damped oscillator at finite temperature can be extracted by measuring the dephasing spectrum of a two-level system dispersively coupled to the oscillator; we thus extend the work of Dykman (1987) and Gambetta et al. (2006). We carefully consider the fidelity of this scheme-- to what extent does the measurement reflect the initial number statistics of the mode? We also derive analytic results for the dephasing of a qubit by a driven, thermal mode, and compare results obtained at different levels of approximation. Our results have relevance both to experiments in circuit cavity QED, as well as to nano-electromechanical systems.