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We investigate the continuous quantum measurement of a superconducting qubitundergoing fluorescence. The fluorescence of the qubit is detected via aphase-preserving heterodyne measurement, giving the fluorescence quadraturesignals as two continuous qubit readout results. By using the stochastic pathintegral approach to the measurement physics, we derive most likely pathsbetween boundary conditions on the state, and compute approximate timecorrelation functions between all stochastic variables via diagrammaticperturbation theory. We focus on paths that increase in energy during thecontinuous measurement. Our results are compared to Monte Carlo numericalsimulation of the trajectories, and we find close agreement between directsimulation and theory. We generalize this analysis to arbitrary diffusivequantum systems that are continuously monitored.

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