Photon-resolved Floquet theory keeps track of the photon exchange of a quantum system with a coherent driving field. It thus complements the standard full-counting statistics that counts the number of photons exchanged with incoherent photon modes giving rise to dissipation. In this paper, we introduce a unifying framework describing both situations. We develop methods suitable for an analytical evaluation of low-order cumulants of photonic probability distributions. Within this framework we analyze the two-mode Jaynes-Cummings model to demonstrate that the photon-resolved Floquet theory and the standard full-counting statistics make consistent statistical predictions. Interestingly, we find that the photon-flux fluctuations diverge for vanishing dissipation, which can be related to an entanglement effect between the driven matter system and the driving field. To substantiate our results, we use our framework to describe efficient photon up-conversion in an ac-driven lambda system, that is characterized by a high signal-to-noise ratio. Because the framework is nonperturbative and predicts fluctuations, it paves the way toward nonperturbative spectroscopy, which will assist to improve metrological methods. Published by the American Physical Society 2024
Photon-resolved Floquet theory keeps track of the photon exchange of a quantum system with a coherent driving field. It thus complements the standard full-counting statistics that counts the number of photons exchanged with incoherent photon modes giving rise to dissipation. In this paper, we introduce a unifying framework describing both situations. We develop methods suitable for an analytical evaluation of low-order cumulants of photonic probability distributions. Within this framework we analyze the two-mode Jaynes-Cummings model to demonstrate that the photon-resolved Floquet theory and the standard full-counting statistics make consistent statistical predictions. Interestingly, we find that the photon-flux fluctuations diverge for vanishing dissipation, which can be related to an entanglement effect between the driven matter system and the driving field. To substantiate our results, we use our framework to describe efficient photon up-conversion in an ac-driven lambda system, that is characterized by a high signal-to-noise ratio. Because the framework is nonperturbative and predicts fluctuations, it paves the way toward nonperturbative spectroscopy, which will assist to improve metrological methods. Published by the American Physical Society 2024
Floquet theory and other established semiclassical approaches are widely used methods to predict the state of externally driven quantum systems, yet they do not allow the prediction of the state of the photonic driving field. To overcome this shortcoming, the photon-resolved Floquet theory (PRFT) was developed recently [], which deploys concepts from full-counting statistics to predict the statistics of the photon flux between several coherent driving modes. In this paper, we study in detail the scaling properties of the PRFT in the semi-classical regime. We find that there is an ambiguity in the definition of the moment-generating function, such that different versions of this function produce the same photonic probability distribution in the semiclassical limit, and generate the same leading-order terms of the moments and cumulants. Using this ambiguity, we establish a simple expression for the Kraus operators, which describe the decoherence dynamics of the driven quantum system appearing as a consequence of the light-matter interaction. The PRFT will pave the way for improved quantum sensing methods, e.g., for spectroscopic quantum sensing protocols, reflectometry in semiconductor nanostructures, and other applications, where the detailed knowledge of the photonic probability distribution is necessary. Published by the American Physical Society 2024
Periodically driven quantum systems can exhibit a plethora of intriguing nonequilibrium phenomena that can be analyzed using Floquet theory. Naturally, Floquet theory is employed to describe the dynamics of atoms interacting with intense laser fields. However, this semiclassical analysis cannot account for quantum-optical phenomena that rely on the quantized nature of light. In this paper, we take a significant step to go beyond the semiclassical description of atom-photon coupled systems by unifying Floquet theory with quantum optics using the framework of full-counting statistics. This is achieved by introducing counting fields that keep track of the photonic dynamics. This formalism, which we dub “photon-resolved Floquet theory” (PRFT), is based on two-point tomographic measurements, instead of the two-point projective measurements used in standard full-counting statistics. Strikingly, the PRFT predicts the generation of macroscopic light-matter entanglement when atoms interact with multimode electromagnetic fields, thereby leading to complete decoherence of the atomic subsystem in the basis of the Floquet states. This decoherence occurs rapidly in the optical-frequency regime, but is negligible in the radio-frequency regime. Our results thus pave the way for the design of efficient quantum memories and quantum operations. Finally, employing the PRFT, we propose a quantum-communication protocol that can significantly outperform the state-of-art few-photon protocols by two orders of magnitude or better. The PRFT potentially leads to insights in various Floquet settings including spectroscopy, thermodynamics, quantum metrology, and quantum simulations. Published by the American Physical Society 2024
Spectroscopic methods play a vital role in quantum sensing, which uses the quantized nature of atoms or molecules to reach astonishing precision for sensing of, e.g., electric or magnetic fields. In the theoretical treatment, one typically invokes semiclassical methods to describe the light-matter interaction between quantum emitters, e.g., atoms or molecules, and a strong coherent laser field. However, these semiclassical approaches struggle to predict the stochastic measurement fluctuations beyond the mean value, necessary to estimate the sensitivity of spectroscopic quantum sensing protocols. Here, we develop a theoretical framework based on the recently developed photon-resolved Floquet theory (PRFT), which is capable of predicting the measurement statistics describing higher-order cumulants of coherent quantum states of light. The PRFT constructs flow equations for the cumulants of the photonic measurement statistics utilizing only the semiclassical dynamics of the matter system. We apply the PRFT to spectroscopic quantum sensing using dissipative two-level and four-level systems (describing electric-field sensing with Rydberg atoms), and demonstrate how to calculate the Fisher information of the measurement statistics with respect to various system parameters. In doing so, we demonstrate that the PRFT is a flexible tool allowing for improving the sensitivity of spectroscopic quantum sensing devices by several orders of magnitude.
We study driven and open quantum systems described by a time-periodic Lindblad master equation. In closed systems, the stroboscopic dynamics can always be described by an effective time-independent Floquet Hamiltonian; this idea is the basis of Floquet engineering. However, in the presence of dissipation, the existence of an effective time-independent Floquet Lindbladian is not guaranteed due to the non-unitary nature of the evolution. Using Floquet theory, we construct a well-defined time-independent Floquet Lindbladian in an extended Sambe-Liouville space, transforming the initial time-dependent problem to a static and non-Hermitian eigenvalue problem. For harmonic driving, we introduce a matrix continued fraction method to nonperturbatively resum multiphoton processes and construct an effective Floquet Lindbladian acting only on the physical Liouville space. Compared to other high-frequency expansions, this method has the advantage of providing the whole infinite series expansion at once. Using a resolvent formalism, we show how to obtain a spectral Floquet representation of correlation functions of an open quantum system. As an application, we consider a dissipating two-level system in a linearly polarized field and calculate its resonance fluorescence spectrum. Furthermore, we consider a parametrically driven quantum dot with pump and loss for which we calculate its spectral function and current-voltage characteristics.
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.
Continuously measured quantum systems are characterized by an output current, in the form of a stochastic and correlated time series, which conveys crucial information about the underlying quantum system. The many tools used to describe current fluctuations are scattered across different communities: quantum opticians often use stochastic master equations, while a prevalent approach in condensed-matter physics is provided by full counting statistics. These, however, are simply different sides of the same coin. Our goal with this tutorial is to provide a unified toolkit for describing current fluctuations. This not only provides novel insights, by bringing together different fields in physics, but also yields various analytical and numerical tools for computing quantities of interest. We illustrate our results with various pedagogical examples and connect them with topical fields of research, such as waiting-time statistics, quantum metrology, thermodynamic uncertainty relations, quantum point contacts, and Maxwell’s demons. Published by the American Physical Society 2024