Probing the Limits of Dispersive Quantum Thermometry with a Nonlinear Mach-Zehnder-Based Quantum Simulator

Abstract: Temperature estimation, known as thermometry, is a critical sensing task for physical systems operating in the quantum regime. Indeed, thermal fluctuations can significantly degrade quantum coherence. Therefore, accurately determining the system's operating temperature is a crucial first step toward distinguishing thermal noise from other sources of decoherence. In this work, we estimate the unknown temperature of a collection of identical and independent two-level atoms dispersively probed by a single-mode quantized electromagnetic field. In contrast to previous works, we present an analytical sensing analysis demonstrating that the joint atom-field evolution -- without any assumptions or approximations -- can achieve, at best, the standard quantum limit of precision concerning the number of field excitations. To investigate our analysis further, we propose and implement a quantum thermometer based on a nonlinear Mach-Zehnder interferometer, which we realize through quantum digital simulation. Our simulation is highly flexible regarding atomic state preparation, allowing the initialization of atomic ensembles with positive and effective negative temperatures. This makes our platform a promising and versatile testbed for benchmarking thermometric capabilities in current quantum simulators.