Asymptotic Large Deviations of Counting Statistics in Open Quantum Systems

TL;DR

This paper develops a semi-Markov process approach to analyze large deviations in counting statistics for various open quantum systems, revealing relationships between rate functions and eigenvalues of non-Hermitian Hamiltonians.

Contribution

It introduces a semi-Markov method to compute large deviations in open quantum systems, including complex cases where polynomial equations are involved.

Findings

Large deviation rate functions at zero current relate to eigenvalues of a non-Hermitian Hamiltonian.

Unified formula for large current regimes across different quantum systems.

Asymptotic large deviations are obtained even for complex systems with polynomial equations.

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 $-{\rm i}\hat H$, where $\hat H$ is a non-Hermitian Hamiltonian, while at a large current, these functions possess a unified formula.