Photon-resolved Floquet theory I: Full-Counting statistics of the driving field in Floquet systems

TL;DR

This paper advances photon-resolved Floquet theory by analyzing its scaling in the semiclassical regime, revealing ambiguities in the moment-generating function and deriving Kraus operators for decoherence, with implications for quantum sensing.

Contribution

It provides a detailed analysis of the photon-resolved Floquet theory's scaling properties and introduces a simplified expression for Kraus operators related to light-matter decoherence.

Findings

Ambiguity in the moment-generating function in the semiclassical limit.

Different versions of the moment-generating function yield the same photonic distribution.

Derived a simple expression for Kraus operators describing decoherence.

Abstract

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 to predict the state of the photonic driving field. To overcome this shortcoming, the photon-resolved Floquet theory (PRFT) has been developed recently [Phys. Rev. Research 6, 013116], 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 semiclassical regime. We find that there is an ambiguity in the definition of the moment-generating function, such that different versions of the moment-generating 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.