Thermodynamics of Quadrature Trajectories in Open Quantum Systems

Abstract

We apply a large-deviation method to study the diffusive trajectories of the quadrature operators of light within a reservoir connected to dissipative quantum systems. We formulate the study of quadrature trajectories in terms of characteristic operators and show that in the long time limit the statistics of such trajectories obey a large-deviation principle. We take our motivation from homodyne detection schemes which allow the statistics of quadrature operator of the light field to be measured. We illustrate our approach with four examples of increasing complexity: a driven two-level system, a `blinking' three-level system, a pair of weakly-coupled two-level driven systems, and the micromaser. We discuss how quadrature operators can serve as alternative order parameters for the classification of dynamical phases, which is particularly useful in cases where the statistics of quantum jumps cannot distinguish between such phases. The formalism we introduce also allows us to analyse the properties of the light emitted by quantum jump trajectories which fluctuate far from the typical dynamics.

17 pages, 20 figures

References in corpus (6)

• The large deviation approach to statistical mechanics
• Dynamic first-order phase transition in kinetically constrained models of glasses
• Counting Statistics of Non-Markovian Quantum Stochastic Processes
• Thermodynamic formalism for dissipative quantum walks
• Decoherence as attenuation of mesoscopic echoes in a spin-chain channel
• Consistent histories for tunneling molecules subject to collisional decoherence

Cited by in corpus (32)

• Nonequilibrium Markov processes conditioned on large deviations
• Nonequilibrium microcanonical and canonical ensembles and their equivalence
• Unravelling the large deviation statistics of Markovian open quantum systems
• Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables
• Population dynamics method with a multi-canonical feedback control
• Current large deviations for driven periodic diffusions
• Symmetry and the thermodynamics of currents in open quantum systems
• Exact large-deviation statistics for a nonequilibrium quantum spin chain
• Harnessing symmetry to control quantum transport
• Dynamical phase transitions, time-integrated observables and geometry of states
• Large-deviation statistics of a diffusive quantum spin chain and the additivity principle
• Theory of classical metastability in open quantum systems
• Large deviations at level 2.5 for Markovian open quantum systems: quantum jumps and quantum state diffusion
• Time-integrated observables as order parameters for dynamical phase transitions in closed quantum systems
• Quantum trajectories of dissipative time-crystals
• Free Fermions with a Localized Source
• Intermittency and dynamical Lee-Yang zeros of open quantum systems
• Anomalous nonequilibrium current fluctuations in the Heisenberg model
• Trajectory phase transitions and dynamical Lee-Yang zeros of the Glauber-Ising chain
• Interaction signatures and non-Gaussian photon states from a strongly driven atomic ensemble coupled to a nanophotonic waveguide
• Coupled activity-current fluctuations in open quantum systems under strong symmetries
• Thermodynamics of trajectories and local fluctuation theorems for harmonic quantum networks
• Concentration Inequalities for Output Statistics of Quantum Markov Processes
• Conditional reversibility in nonequilibrium stochastic systems
• Spectral signatures of symmetry-breaking dynamical phase transitions
• Dynamical symmetries and crossovers in a three-spin system with collective dissipation
• Thermodynamics of trajectories of open quantum systems, step by step
• Dissipative failure of adiabatic quantum transport as a dynamical phase transition
• Dynamical transitions in Markovian exciton transport
• Measurement-feedback control of chiral photon emission from an atom chain into a nanofiber
• Statistical time-domain characterization of non-periodic optical clocks
• Thermodynamics of quantum-jump trajectories of open quantum systems subject to stochastic resetting