Sensing Out-of-Equilibrium and Quantum Non-Gaussian Environments via Induced Time-Reversal Symmetry Breaking on the Quantum-Probe Dynamics

Advancing quantum sensing tools for investigating atomic and nanoscale systems is crucial for the progress of quantum technologies. While many protocols use quantum probes to extract information from stationary or weakly coupled environments, challenges intensify at the atomic scale and the nanoscale, where the environment is inherently out of equilibrium and/or strongly coupled with the sensor. In this work, we demonstrate that time-reversal symmetry in the control dynamics of a quantum sensor is broken when the qubit sensor interacts with environments that are out of equilibrium (with nonstationary fluctuations), contain quantum non-Gaussian correlations, or exhibit intrinsic time-reversal symmetry breaking. Leveraging this phenomenon, we introduce a quantum sensing paradigm based on time-asymmetric dynamical control sequences, enabling the probing of the distance of an environment from equilibrium, its time-reversal symmetry-breaking behavior, or its quantum non-Gaussian nature. Additionally, we propose sensing strategies to distinguish between these different sources of symmetry breaking. We validate our approach through proof-of-principle experimental quantum simulations using solid-state nuclear magnetic resonance, where we drive the environment of a qubit sensor out of equilibrium and use our protocol to quantify the nonstationary characteristics of the generated states. Our findings highlight the potential of this framework for quantifying nonstationary behavior, designing tailored pump-probe experiments (including measurements of quantum information scrambling), and detecting quantum states that exhibit time-reversal symmetry breaking, time-crystal structures, or quantum non-Gaussian fluctuations. Overall, this work constitutes a step forward in designing quantum devices for atomic scale and nanoscale sensing, broadening their applicability to complex and dynamic quantum environments.