Path Integral Framework for Characterizing and Controlling Decoherence Induced by Nonstationary Environments on a Quantum Probe

Reliable processing of quantum information is a milestone to achieve for the deployment of quantum technologies. Uncontrolled, out-of-equilibrium sources of decoherence need to be characterized in detail for designing the control of quantum devices to mitigate the loss of quantum information. However, quantum sensing of such environments is still a challenge due to their nonstationary nature that in general can generate complex high-order correlations. We introduce a path integral framework to characterize nonstationary environmental fluctuations by a quantum probe. We find the solution for the decoherence decay of nonstationary, generalized Gaussian processes that induce pure dephasing. This dephasing when expressed in a suitable basis, based on the nonstationary noise eigenmodes, is defined by the overlap of a generalized noise spectral density and a filter function that depends on the control fields. This result thus extends the validity of the similar general expression for the dephasing of open quantum systems coupled to stationary noise processes to out-of-equilibrium environments. We show physical insights for a broad subclass of nonstationary noise processes that are local in time, in the sense that the noise correlation functions contain memory based on constraints of the derivatives of the fluctuating noise paths. Spectral and non-Markovian properties are discussed together with implementations of the framework to treat paradigmatic environments that are out of equilibrium, e.g., due to a quench and a pulsed noise. We show that our results provide tools for probing the spectral and time-correlation properties, and for mitigating decoherence effects of out-of-equilibrium-nonstationary-environments. Reliable processing of quantum information is a milestone to achieve for the deployment of quantum technologies. Uncontrolled, out-of-equilibrium sources of decoherence need to be characterized in detail for designing the control of quantum devices to mitigate the loss of quantum information. However, quantum sensing of such environments is still a challenge due to their nonstationary nature that in general can generate complex high-order correlations. We introduce a path integral framework to characterize nonstationary environmental fluctuations by a quantum probe. We find the solution for the decoherence decay of nonstationary, generalized Gaussian processes that induce pure dephasing. This dephasing when expressed in a suitable basis, based on the nonstationary noise eigenmodes, is defined by the overlap of a generalized noise spectral density and a filter function that depends on the control fields. This result thus extends the validity of the similar general expression for the dephasing of open quantum systems coupled to stationary noise processes to out-of-equilibrium environments. We show physical insights for a broad subclass of nonstationary noise processes that are local in time, in the sense that the noise correlation functions contain memory based on constraints of the derivatives of the fluctuating noise paths. Spectral and non-Markovian properties are discussed together with implementations of the framework to treat paradigmatic environments that are out of equilibrium, e.g., due to a quench and a pulsed noise. We show that our results provide tools for probing the spectral and time-correlation properties, and for mitigating decoherence effects of out-of-equilibrium-nonstationary-environments.