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arXiv:2506.08302 · Physical Review A

Photon-resolved Floquet theory approach to spectroscopic quantum sensing

Georg Engelhardt, Konstantin Dorfman, Zhedong Zhang

Published Nov 5, 2025• 2 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/btrr-bd3q

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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.
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
In this work, we investigate precision limitations in spectrophotometry (i.e., spectroscopic concentration measurements) imposed by chemical processes of molecules. Using the recently developed Photon-resolved Floquet theory, which generalizes Maxwell-Bloch theory for higher-order measurement statistics, we analyze a molecular model system subject to chemical reactions whose electronic and optical properties depend on the chemical state. Analysis of sensitivity bounds reveals: (i) Phase measurements are more sensitive than intensity measurements; (ii) Sensitivity exhibits three regimes: photon-shot-noise limited, chemically limited, and intermediate; (iii) Sensitivity shows a turnover as a function of reaction rate due to the interplay between coherent electronic dynamics and incoherent chemical dynamics. Our findings demonstrate that chemical properties must be considered to estimate ultimate precision limits in optical spectrophotometry.
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
In this work, we investigate precision limitations in spectrophotometry (i.e., spectroscopic concentration measurements) imposed by chemical processes of molecules. Using the recently developed photon-resolved Floquet theory, which generalizes Maxwell-Bloch theory for higher-order measurement statistics, we analyze a molecular model system subject to chemical reactions whose electronic and optical properties depend on the chemical state. Analysis of sensitivity bounds reveals: (i) Phase measurements are more sensitive than intensity measurements; (ii) sensitivity exhibits three regimes: photon-shot-noise limited, chemically limited, and intermediate; and (iii) sensitivity shows a turnover as a function of reaction rate due to the interplay between coherent electronic dynamics and incoherent chemical dynamics. Our findings demonstrate that chemical properties must be considered to estimate ultimate precision limits in optical spectrophotometry.
In this paper, we present a comprehensive investigation into the sensitivity of a Rydberg atom electric field sensor, with a specific focus on the minimum detectable field (MDF) as a key metric. The study utilizes one-mode Floquet theory to calculate the Stark shift for selected Rydberg states when exposed to a signal electric field. The results are compared to those obtained using the rotating wave approximation (RWA). To enhance the sensor's sensitivity when the frequency of the signal electric field deviates from resonance frequencies between Rydberg states, we propose incorporating an extra coupling electric field and using many-mode Floquet theory, a generalization of one-mode Floquet theory, to theoretically analyze this kind of Rydberg atom electric field sensor. The Autler-Townes effect resulting from this coupling electric field causes Rydberg states to split into dressed states, effectively increasing sensitivity by modulating the frequencies of resonance peaks. Moreover, the phenomenon of two-photon absorption in the presence of the coupling electric field is explored. We demonstrate that by appropriately adjusting the coupling electric field's amplitude or frequency, one can control the occurrence of two-photon resonances, providing additional sensitivity enhancement for the Rydberg sensor within the significantly extended off-resonance domain. The study underscores the significance of coupling fields in enhancing the sensitivity of Rydberg atom electric field sensors. These insights hold promising implications for the development of more robust and versatile electric field sensing devices, applicable in diverse fields such as precision measurements and quantum information processing.