Analysing quantum large deviations using classical (unravelled) stochastic processes

An important class of non-equilibrium quantum systems can be described by Markovian models, using the Lindblad formalism.  For example, one can consider an atom with a few quantum states, absorbing energy from a laser, and emitting photons into its environment.  In this case, the sequences of emitted photons are random; their behaviour can be captured by a stochastic process for the system wavefunction (or a pure-state density matrix).  Such stochastic processes can be analysed by the methods of classical probability : I will present a level-2.5 description of their large deviations [1,2].  This provides a detailed description of the joint fluctuations of the system and the emitted photons.  Examples include quantum reset processes, for which this method yields an uncertainty relation between the mean and variance of the photon counts [1].  The method can be extended to systems under continuous (weak) measurement, using the theory of quantum state diffusion [2].

[1] F Carollo, RL Jack, and JP Garrahan, Phys. Rev. Lett. 122, 130605 (2019)
[2] F Carollo, JP Garrahan, and RL Jack, arXiv:2101.04138