Measuring Fluorescence to Track a Quantum Emitter's State: a Theory
Measuring Fluorescence to Track a Quantum Emitter's State: A Theory Review Philippe Lewalle,1, 2, ∗ Sreenath K. Manikandan,1, 2 Cyril Elouard,1, 2 and Andrew N. Jordan1, 2, 3 1Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627, USA 2Center for Coherence and Quantum Optics, University of Rochester, Rochester, NY 14627, USA 3Institute for Quantum Studies, Chapman University, Orange, CA 92866, USA (Dated: May 29, 2020) We review the continuous monitoring of a qubit through its spontaneous emission, at an introduc- tory level. Contemporary experiments have been able to collect the fluorescence of an artificial atom in a cavity and transmission line, and then make measurements of that emission to obtain diffusive quantum trajectories in the qubit's state. We give a straightforward theoretical overview of such scenarios, using a framework based on Kraus operators derived from a Bayesian update concept; we apply this flexible framework across common types of measurements including photodetection, homodyne, and heterodyne monitoring, and illustrate its equivalence to the stochastic master equa- tion formalism throughout. Special emphasis is given to homodyne (phase{sensitive) monitoring of fluorescence. The examples we develop are used to illustrate basic methods in quantum trajectories, but also to introduce some more advanced topics of contemporary interest, including the arrow of time in quantum measurement, and trajectories following optimal measurement records derived from a variational principle. The derivations
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