Witnessing non-stationary and non-Markovian environments with a quantum sensor

Quantum sensors offer exceptional sensitivity to nanoscale magnetic fluctuations, where non-stationary effects – such as spin diffusion – and non-Markovian dynamics arising from coupling to few environmental degrees of freedom play critical roles. Because fully reconstructing the microscopic structure of realistic spin baths is often infeasible, a practical challenge is to identify the dynamical features that are actually encoded in the sensor’s decoherence signal. Here, we demonstrate how quantum sensors can operationally characterize the statistical nature of environmental noise, distinguishing between stationary and non-stationary behaviors, as well as Markovian and non-Markovian dynamics. Using nitrogen-vacancy (NV) centers in diamond as a platform, we develop a physical noise model that captures the essential dynamical features of realistic environments relevant to sensor observables – independently of the microscopic bath details – and provides analytical predictions for Ramsey decay across different regimes. These predictions are experimentally validated through controlled noise injection with tunable correlation properties. Our results showcase the capability of quantum sensors to isolate and identify key dynamical properties of complex environments, without requiring full microscopic bath reconstruction. This work clarifies the operational signatures of non-stationarity and non-Markovian behavior at the nanoscale and lays the foundation for strategies that mitigates decoherence while exploiting environmental dynamics for enhanced quantum sensing.

💡 Research Summary

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This paper presents a practical framework for classifying the statistical nature of nanoscale environmental noise using a quantum sensor, specifically a nitrogen‑vacancy (NV) center in diamond. The authors recognize that while decoherence limits quantum technologies, it also serves as a valuable signal for quantum sensing. Conventional noise‑characterization techniques typically assume stationary, Markovian noise (often modeled by an Ornstein‑Uhlenbeck process), which fails to capture the rich dynamics of realistic spin baths that exhibit memory effects (non‑Markovian) and out‑of‑equilibrium behavior (non‑stationary).

To address this gap, the authors introduce a unified stochastic model for the fluctuating magnetic field experienced by the NV qubit. The model treats the noise as a Gaussian process n(t) governed by a Langevin‑type second‑order differential equation:

  m n″ + Γ n′ + κ n = η(t),

where m (effective mass) encodes inertia, Γ is a damping coefficient, κ represents a confining potential, and η(t) is zero‑mean white Gaussian noise with strength A. When m = 0 the equation reduces to an overdamped Ornstein‑Uhlenbeck process, which is memoryless (Markovian) and stationary if initialized in equilibrium. For m ≠ 0 the inertia term introduces finite memory, yielding non‑Markovian dynamics. Moreover, the model distinguishes stationary from non‑stationary (quenched) regimes by the choice of initial conditions: equilibrium initialization leads to time‑translation‑invariant correlations, whereas a sudden quench (e.g., optical initialization of the NV) produces time‑dependent correlations.

The central observable is the Ramsey coherence signal S(t) = ⟨cos φ(t)⟩, where φ(t) = ∫₀ᵗ γ_NV ΔB_z(t′) dt′ is the accumulated phase. Because n(t) is Gaussian with zero mean, φ(t) is also Gaussian, and the signal reduces to S(t) = exp