Anatomy of Fluorescence: Quantum trajectory statistics from continuously measuring spontaneous emission

TL;DR

This paper analyzes the quantum trajectories of a superconducting qubit under continuous fluorescence measurement, deriving most likely paths and correlations, and validating results with simulations, applicable to general diffusive quantum systems.

Contribution

It introduces a stochastic path integral approach to analyze continuous quantum measurement trajectories, providing analytical tools and generalization to diffusive quantum systems.

Findings

Close agreement between theoretical predictions and Monte Carlo simulations.

Derivation of most likely paths between boundary states.

Generalization of analysis to arbitrary diffusive quantum systems.

Abstract

We investigate the continuous quantum measurement of a superconducting qubit undergoing fluorescence. The fluorescence of the qubit is detected via a phase-preserving heterodyne measurement, giving the fluorescence quadrature signals as two continuous qubit readout results. By using the stochastic path integral approach to the measurement physics, we derive most likely paths between boundary conditions on the state, and compute approximate time correlation functions between all stochastic variables via diagrammatic perturbation theory. We focus on paths that increase in energy during the continuous measurement. Our results are compared to Monte Carlo numerical simulation of the trajectories, and we find close agreement between direct simulation and theory. We generalize this analysis to arbitrary diffusive quantum systems that are continuously monitored.