We study the fluctuations of photon currents in a non-linear optical model. These are found to exhibit very exhotic on/off switching behavior as a consequence of the quantum features of the model. We use the tools of full counting statistics to explain why this switching behavior leads to an exponential growth of fluctuations.
The parametrically pumped Kerr model describes a driven-dissipative nonlinear cavity, whose nonequilibrium phase diagram features both continuous and discontinuous quantum phase transitions. We consider the consequences of these critical phenomena for the fluctuations of the photocurrent obtained via continuous weak measurements on the cavity. Considering both direct photodetection and homodyne detection schemes, we find that the current fluctuations diverge exponentially at the discontinuous phase transition. However, we find strikingly different current fluctuations for these two detection schemes near the continuous transition, a behavior which is explained by the complementary information revealed by measurements in different bases. To obtain these results, we develop formulas to efficiently compute the diffusion coefficient---which characterizes the long-time current fluctuations---directly from the quantum master equation, thus connecting the formalisms of full counting statistics and stochastic quantum trajectories. Our findings highlight the rich features of current fluctuations near nonequilibrium phase transitions in quantum-optical systems.
Understanding nonequilibrium transport and fluctuations driven by nonclassical light in nonlinear quantum optical systems is challenging. Here, we formulate a driven quantum master equation in the rotating frame combined with full counting statistics, retaining the drive-induced frequency shifts in the system-reservoir interactions and providing a unified description of drive-assisted incoherent transitions based on the rotated system dressed-basis. Applied to a Kerr resonator and a nonlinear Jaynes-Cummings model, the approach reveals pronounced multiphoton-resonant enhancement of the drive input energy current, with significant high peaks under two-photon driving compared to the single-photon case. The two-photon resonance relations are analytically obtained. Resonance structure in the nonlinear Jaynes-Cummings model nonlinearly relies on qubit-photon couplings, with additional dressed-state branches. A low-energy-state approximation attributes the resonant current enhancement to dressed-state hybridization and efficient activation of incoherent energy exchange processes. Beyond the average current, two-photon-driving induced energy exchange picture near resonance also substantially modifies the second-order current fluctuation and higher-order current cumulant, while increasing the time-normalized signal-to-noise ratio. Adding two-photon loss introduces extra incoherent photon-pair exchange pathways and further reshapes the current and its fluctuations. We hope these results may deepen interpretation of photon driving and quantum dissipation cooperatively governing nonequilibrium energy transport and fluctuations.
Full-counting statistics (FCS) provides a systematic framework for characterising current fluctuations in quantum transport, quantum optics, and open quantum systems. We introduce QuantumFCSjl, an open-source Julia package for efficient and flexible numerical FCS calculations. The package defines currents through monitored jump operators and weights, allowing particle, electric, and heat currents to be treated within the same workflow. It implements a recursive cumulant algorithm with dense, sparse, and iterative solver backends, making it suitable for models that are challenging for direct dense methods. We demonstrate the package on photon counting in a driven-dissipative Jaynes-Cummings system near the blockade-breakdown phase transition and on heat-current fluctuations in a non-linear circuit-QED heat engine. These examples show how higher cumulants reveal intermittency between bright and dim emission, antibunching, and provide probes of thermodynamic uncertainty relations. Benchmarks against an existing FCS implementation show substantial speed-ups.
We consider current shot noise and the full counting statistics in a chain of quantum dots which exhibits a continuous nonequilibrium phase transition as a function of the tunnel couplings of the chain with the electrodes. Using a combination of analytical and numerical methods, we establish that the full counting statistics is conventional away from the phase transition, but becomes, in a well-defined sense, essentially non-Gaussian on the critical line, where the current fluctuations are controlled by the dynamic critical exponent z. We find that signatures of the critical full counting statistics persist in quantum-dot chains of finite length.