Anatomy of fluorescence: quantum trajectory statistics from continuously measuring spontaneous emission

Andrew Jordan 1 Areeya Chantasri 1 Pierre Rouchon 2, 3 Benjamin Huard 2, 4
2 QUANTIC - QUANTum Information Circuits
Inria de Paris, MINES ParisTech - École nationale supérieure des mines de Paris, ENS Paris - École normale supérieure - Paris, UPMC - Université Pierre et Marie Curie - Paris 6
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. 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.
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Andrew Jordan, Areeya Chantasri, Pierre Rouchon, Benjamin Huard. Anatomy of fluorescence: quantum trajectory statistics from continuously measuring spontaneous emission. Quantum Studies: Mathematics and Foundations, Springer, 2016, 3, pp.237 - 263. ⟨10.1007/s40509-016-0075-9⟩. ⟨hal-01403635⟩

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