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arXiv:2412.21026 · Nature Communications

Observation of metastability in open quantum dynamics of a solid-state system

Junxiang Zhang, Yuan-De Jin, Chu-Dan Qiu, Wen-Long Ma, Gang‐Qin Liu

Published Nov 6, 2025• 2 citations
arXivHTMLPDF

Abstract

Abstract Metastability is a ubiquitous phenomenon in non-equilibrium physics and classical stochastic dynamics. It arises when the system dynamics settles in long-lived states before eventually decaying to true equilibria. Remarkably, it has been predicted that quantum metastability can also occur in continuous-time and discrete-time open quantum dynamics. However, the direct experimental observation of metastability in open quantum systems has remained elusive. Here, we experimentally observe metastability in the discrete-time evolution of a single nuclear spin in diamond, realized by sequential Ramsey interferometry measurements of a nearby nitrogen-vacancy electron spin. We demonstrate that the metastable polarization of the nuclear spin emerges at around 60,000∼250,000 sequential measurements, enabling high-fidelity single-shot readout of the nuclear spin. Our results represent a concrete step towards uncovering non-equilibrium physics in open quantum dynamics, which is practically relevant for the utilization of metastable information for various quantum information processing tasks.

DOI
10.1038/s41467-025-64772-6

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Abstract Metastability is a ubiquitous phenomenon in non-equilibrium physics and classical stochastic dynamics. It arises when the system dynamics settles in long-lived states before eventually decaying to true equilibria. Remarkably, it has been predicted that quantum metastability can also occur in continuous-time and discrete-time open quantum dynamics. However, the direct experimental observation of metastability in open quantum systems has remained elusive. Here, we experimentally observe metastability in the discrete-time evolution of a single nuclear spin in diamond, realized by sequential Ramsey interferometry measurements of a nearby nitrogen-vacancy electron spin. We demonstrate that the metastable polarization of the nuclear spin emerges at around 60,000∼250,000 sequential measurements, enabling high-fidelity single-shot readout of the nuclear spin. Our results represent a concrete step towards uncovering non-equilibrium physics in open quantum dynamics, which is practically relevant for the utilization of metastable information for various quantum information processing tasks.
Metastability in open system dynamics describes the phenomena of initial relaxation to long-lived metastable states before decaying to the asymptotic stable states. It has been found in continuous-time stochastic dynamics of both classical and quantum systems. However, many cases of open quantum system dynamics are intrinsically discrete, and the evolution within each discrete time interval is described by an arbitrary quantum channel, which often cannot be generated by continuous-time master equations. Here we develop a general theory of metastability in discrete-time open quantum dynamics, described by sequential repetitive quantum channels. We apply the general metastability theory to a typical class of quantum channels on a target system, induced by an ancilla qubit with a pure-dephasing coupling to the target system and under Ramsey sequences. Interesting metastable behaviors are predicted and numerically demonstrated by decomposing the average dynamics of sequential quantum channels into stochastic trajectories. We also present examples of applications in quantum state and dynamics engineering of a target quantum system with an ancilla qubit.
We use the electronic spin of a single nitrogen-vacancy defect in diamond to observe the real-time evolution of neighboring single nuclear spins under ambient conditions. Using a diamond sample with a natural abundance of (13)C isotopes, we first demonstrate high fidelity initialization and single-shot readout of an individual (13)C nuclear spin. By including the intrinsic (14)N nuclear spin of the nitrogen-vacancy defect in the quantum register, we then report the simultaneous observation of quantum jumps linked to both nuclear spin species, providing an efficient initialization of the two qubits. These results open up new avenues for diamond-based quantum information processing including active feedback in quantum error correction protocols and tests of quantum correlations with solid-state single spins at room temperature.
Nuclear spins in certain solids couple weakly to their environment, making them attractive candidates for quantum information processing and inertial sensing. When coupled to the spin of an optically active electron, nuclear spins can be rapidly polarized, controlled, and read via lasers and radio-frequency (rf) fields. Possessing typical coherence times of several milliseconds at room temperature, nuclear spins hosted by a nitrogen-vacancy center in diamond are thus intriguing systems to observe how classical physical rotation at quantum timescales affects a quantum system. In this work, we demonstrate optical nuclear-spin polarization and rapid quantum control of nuclear spins in a diamond physically rotating at 1kHz1\phantom{\rule{0.16em}{0ex}}\mathrm{kHz}1kHz, faster than the nuclear-spin coherence time. Free from the need to maintain strict field alignment, we are able to measure and control nuclear spins in the presence of a large, time-varying magnetic field that makes an angle of more than ${100}^{\ensuremath{\circ}}$ to the nitrogen-lattice vacancy axis. The field induces spin mixing between the electron and nuclear states of the qubits, decoupling them from oscillating rf fields. We are able to demonstrate that coherent spin state control is possible at any point of the rotation. We combine continuous dynamical decoupling with feed-forward control to eliminate decoherence induced by imperfect mechanical rotation. Our work liberates a previously inaccessible degree of freedom of the NV nuclear spin, unlocking new approaches to quantum control and rotation sensing.
We present a general theory of classical metastability in open quantum systems. Metastability is a consequence of a large separation in timescales in the dynamics, leading to the existence of a regime when states of the system appear stationary, before eventual relaxation toward a true stationary state at much larger times. In this work, we focus on the emergence of classical metastability, i.e., when metastable states of an open quantum system with separation of timescales can be approximated as probabilistic mixtures of a finite number of states. We find that a number of classical features follow from this approximation, for the manifold of metastable states, long-time dynamics between them, and symmetries of the dynamics. Namely, those states are approximately disjoint and thus play the role of metastable phases, the relaxation toward the stationary state is approximated by a classical stochastic dynamics between them, and weak symmetries correspond to their permutations. Importantly, the classical dynamics is observed not only on average but also at the level of individual quantum trajectories: We show that time coarse-grained continuous measurement records can be viewed as noisy classical trajectories, while their statistics can be approximated by that of the classical dynamics. Among others, this explains how first-order dynamical phase transitions arise from metastability. Finally, to verify the presence of classical metastability in a given open quantum system, we develop an efficient numerical approach that delivers the set of metastable phases together with the effective classical dynamics. Since the proximity to a first-order dissipative phase transition manifests as metastability, the theory and tools introduced in this work can be used to investigate such transitions---which occur in the large size limit---through the metastable behavior of many-body systems of moderate sizes accessible to numerics.
In this work, we introduce an information-theoretic approach for considering changes in dynamics of finitely dimensional open quantum systems governed by master equations. This experimentally motivated approach arises from considering how the averages of system observables change with time and quantifies how non-stationary the system is during a given time regime. By drawing an analogy with the exponential decay, we are able to further investigate regimes when such changes are negligible according to the logarithmic scale of time, and thus the system is approximately stationary. While this is always the case within the initial and final regimes of the dynamics, with the system respectively approximated by its initial and asymptotic states, we show that a distinct regime of approximate stationarity may arise. In turn, we establish a quantitative description of the phenomenon of metastability in open quantum systems. The initial relaxation occurring before the corresponding metastable regime and of the long-time dynamics taking place afterwards are also characterised. Furthermore, we explain how metastability relates to the separation in the real part of the master equation spectrum and connect our approach to the spectral theory of metastability, clarifying when the latter follows. All of our general results directly translate to Markovian dynamics of classical stochastic systems.
Projective measurement of single electron and nuclear spins has evolved from a gedanken experiment to a problem relevant for applications in atomic-scale technologies like quantum computing. Although several approaches allow for detection of a spin of single atoms and molecules, multiple repetitions of the experiment that are usually required for achieving a detectable signal obscure the intrinsic quantum nature of the spin's behavior. We demonstrated single-shot, projective measurement of a single nuclear spin in diamond using a quantum nondemolition measurement scheme, which allows real-time observation of an individual nuclear spin's state in a room-temperature solid. Such an ideal measurement is crucial for realization of, for example, quantum error correction protocols in a quantum register.