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.
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.
Knowing a quantum system's environment is critical for its practical use as a quantum device. Qubit sensors can reconstruct the noise spectral density of a classical bath, provided long enough coherence time. Here, we present a protocol that can unravel the characteristics of a more complex environment, comprising both unknown coherently coupled quantum systems, and a larger quantum bath that can be modeled as a classical stochastic field. We exploit the rich environment of a nitrogen-vacancy center in diamond, tuning the environment behavior with a bias magnetic field, to experimentally demonstrate our method. We show how to reconstruct the noise spectral density even when limited by relatively short coherence times, and identify the local spin environment. Importantly, we demonstrate that the reconstructed model can have predictive power, describing the spin qubit dynamics under control sequences not used for noise spectroscopy, a feature critical for building robust quantum devices. At lower bias fields, where the effects of the quantum nature of the bath are more pronounced, we find that more than a single classical noise model are needed to properly describe the spin coherence under different controls, due to the back action of the qubit onto the bath.
Quantum sensing protocols that exploit the dephasing of a probe qubit are powerful and ubiquitous methods for interrogating an unknown environment. They have a variety of applications, ranging from noise mitigation in quantum processors, to the study of correlated electron states. Here, we discuss a simple strategy for enhancing these methods, based on the fact that they often give rise to an inadvertent quench of the probed system: there is an effective sudden change in the environmental Hamiltonian at the start of the sensing protocol. These quenches are extremely sensitive to the initial environmental state, and lead to observable changes in the sensor qubit evolution. We show how these new features give access to environmental response properties. This enables methods for direct measurement of bath temperature, and for detecting non-thermal equilibrium states. We also discuss how to deliberately control and modulate this quench physics, which enables reconstruction of the bath spectral function. Extensions to non-Gaussian quantum baths are also discussed, as is the application of our ideas to a range of sensing platforms (e.g., nitrogen-vacancy (NV) centers in diamond, semiconductor quantum dots, and superconducting circuits).
Many-body dynamics constitutes a promising approach for creating correlations between quantum particles which can be used for applications in sensing and metrology. However, utilizing this potential for substantial gains in practical settings is a challenging task with only a very few applications realized to date. Here, we demonstrate an approach to nanoscale magnetic sensing enabled by strongly interacting electronic spins in a room temperature solid. By coherently controlling collective many-body dynamics of a dipolar ensemble of ∼104 nitrogen-vacancy (NV) centres in diamond with pulsed magnetic field gradients, we demonstrate practical metrological gain up to 7.9(2)dB for magnetic signal detection and 8.8(3)dB for magnetic noise sensing, fully accounting for experimental overheads. Finally, we combine these methods to demonstrate a momentum-space-resolved sensing modality that enables detection of spatially correlated magnetic noise at continuously tunable length scales down to 50 nanometers. These observations open the door toward practical applications of interaction-enhanced quantum sensors for nanoscale biological imaging and material characterization.
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.
We employ a quantum computer to simulate the effect of spin impurities on nitrogen-vacancy (NV) centers in diamond. As these defects operate as nanoscale quantum sensors, modeling quantum noise is crucial to identify limitations in precision. The analysis is performed by means of quantum state tomography on two transmon qubits, representing respectively the NV center and a single spin impurity, modeling either a nuclear spin or an additional NV center. We demonstrate a versatile platform to simulate benchmark protocols such as Ramsey or Hahn-echo. Although we focus on a two-spin system, the same approach opens the door to using quantum processors as scalable simulators of many-spin environments, intractable in classical simulation due to the rapid exponential growth of the Hilbert space. The results reveal the effect different spin-sensor coupling regimes have on coherence, helping to identify detection schemes that maximize the sensitivity under the effect of impurities. Moreover, the role of entanglement generation is analyzed using the Peres-Horodecki criterion and CHSH inequalities. Although no violation of the latter is observed, the presence of entanglement is confirmed.
Quantum probes offer a powerful platform for exploring environmental dynamics, particularly through their sensitivity to decoherence processes. In this work, we investigate the emergence of critical behavior in the estimation of the environmental memory time , modeled as an Ornstein–Uhlenbeck process characterized by a Lorentzian spectral density. Using dynamically controlled qubit-based sensors—realized experimentally via solid-state Nuclear Magnetic Resonance (NMR) and supported by numerical simulations—we implement tailored filter functions to interrogate the environmental noise spectrum and extract from its spectral width. Our results reveal a sharp transition in estimation performance between short-memory (SM) and long-memory (LM) regimes, reflected in a non-monotonic estimation error that resembles a phase transition. This behavior is accompanied by an avoided-crossing-like structure in the estimated parameter space, indicative of two competing solutions near the critical point. These features underscore the interplay between control, decoherence, and inference in open quantum systems. Beyond their fundamental significance, these critical phenomena offer a practical diagnostic tool for identifying dynamical regimes and optimizing quantum sensing protocols. By exploiting this criticality, our findings pave the way for adaptive control strategies aimed at enhancing precision in quantum parameter estimation—particularly in complex or structured environments such as spin networks, diffusive media, and quantum materials.