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 systems at atomic and nanoscales is crucial for the progress of quantum technologies. While numerous protocols employ quantum probes to extract information from stationary or weakly coupled environments, the challenges intensify at atomic- and nano-scales where the environment is inherently out-of-equilibrium or strongly coupled with the sensor. We here prove that the time-reversal symmetry in the quantum-sensor control dynamics is broken, when partial information is probed from an environment that is out-of-equilibrium with non stationary fluctuations or is described by quantum non-Gaussian, strongly coupled environmental correlations. We exploit this phenomenon as a quantum sensing paradigm with proof-of principle experimental quantum simulations using solid-state nuclear magnetic resonance (NMR). This introduces a signal contrast on a qubit-probe that quantifies how far the sensed environment is from equilibrium or its quantum non-Gaussian nature. Protocols are also presented to discern and filter a variety of environmental properties including stationary, non-stationary and non-Gaussian quantum noise fluctuations as a step toward sensing the ubiquitous environments of a quantum-sensor at atomic and nanoscales.