Asymptotic Large Deviations of Counting Statistics in Open Quantum Systems

Abstract

We use a semi-Markov process method to calculate large deviations of counting statistics for three open quantum systems, including a resonant two-level system and resonant three-level systems in the $\Lambda$- and $V$-configurations. In the first two systems, radical solutions to the scaled cumulant generating functions are obtained. Although this is impossible in the third system, since a general sixth-degree polynomial equation is present, we still obtain asymptotically large deviations of the complex system. Our results show that, in these open quantum systems, the large deviation rate functions at zero current are equal to two times the largest nonzero real parts of the eigenvalues of operator $-\mathrm{i}\hat{H}$, where $\hat{H}$ is a non-Hermitian Hamiltonian, while at a large current, these functions possess a unified formula.

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References in corpus (7)

• The large deviation approach to statistical mechanics
• Quantum thermodynamic uncertainty relation for continuous measurement
• Heat-exchange statistics in driven open quantum systems
• Stochastic thermodynamics of rapidly driven systems
• Characteristic Functions Based on Quantum Jump Trajectory
• Thermodynamics of quantum jump trajectories in systems driven by classical fluctuations
• Semi-Markov processes in open quantum systems: Connections and applications in counting statistics