Thermodynamics of quantum jump trajectories in systems driven by classical fluctuations

Abstract

The large-deviation method can be used to study the measurement trajectories of open quantum systems. For optical arrangements this formalism allows to describe the long time properties of the (non-equilibrium) photon counting statistics in the context of a (equilibrium) thermodynamic approach defined in terms of dynamical phases and transitions between them in the trajectory space [J.P. Garrahan and I. Lesanovsky, Phys. Rev. Lett. 104, 160601 (2010)]. In this paper, we study the thermodynamic approach for fluorescent systems coupled to complex reservoirs that induce stochastic fluctuations in their dynamical parameters. In a fast modulation limit the thermodynamics corresponds to that of a Markovian two-level system. In a slow modulation limit, the thermodynamic properties are equivalent to those of a finite system that in an infinite-size limit is characterized by a first-order transition. The dynamical phases correspond to different intensity regimes, while the size of the system is measured by the transition rate of the bath fluctuations. As a function of a dimensionless intensive variable, the first and second derivative of the thermodynamic potential develop an abrupt change and a narrow peak respectively. Their scaling properties are consistent with a double-Gaussian probability distribution of the associated extensive variable.

12 pages, 3 figures

References in corpus (12)

• The large deviation approach to statistical mechanics
• The Quantum Jump Approach to Dissipative Dynamics in Quantum Optics
• Dynamic first-order phase transition in kinetically constrained models of glasses
• First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories
• Thermodynamics of Quantum Jump Trajectories
• Large deviations and ensembles of trajectories in stochastic models
• Rules for transition rates in nonequilibrium steady states
• Photon Statistics; Nonlinear Spectroscopy of Single Quantum Systems
• Super and Sub-Poissonian photon statistics for single molecule spectroscopy
• Open quantum system approach to single-molecule spectroscopy
• Quantum-jumps and photon-statistic in fluorescent systems coupled to classically fluctuating reservoirs
• Thermodynamics of histories for the one-dimensional contact process

Cited by in corpus (16)

• Dynamical phases and intermittency of the dissipative quantum Ising model
• Exact large-deviation statistics for a nonequilibrium quantum spin chain
• Quantum trajectory phase transitions in the micromaser
• Large-deviation statistics of a diffusive quantum spin chain and the additivity principle
• Large deviations at level 2.5 for Markovian open quantum systems: quantum jumps and quantum state diffusion
• Stochastic Quantum Zeno by Large Deviation Theory
• Large deviations of ergodic counting processes: a statistical mechanics approach
• Free Fermions with a Localized Source
• Anomalous nonequilibrium current fluctuations in the Heisenberg model
• A generic map from non-Lindblad to Lindblad master equations
• A generalized fluctuation relation for power-law distributions
• Fluctuation relations with intermittent non-Gaussian variables
• Dynamical transitions in Markovian exciton transport
• Large Deviations, Central Limit and dynamical phase transitions in the atom maser
• Dynamical phase transitions in one-dimensional hard-particle systems
• Asymptotic Large Deviations of Counting Statistics in Open Quantum Systems