Observation of measurement-induced localization phenomena in a solid-state spin system

AI summary

Overview

Research area: Quantum many-body physics, specifically measurement-induced phase transitions (MIPT) and measurement-induced localization in solid-state spin systems, using nuclear spins in diamond.

Technical level: Advanced. The paper assumes familiarity with entanglement entropy, mutual information, dipolar Hamiltonians, the quantum Zeno and anti-Zeno effects, and Lindblad master equations, although the experimental logic is stated clearly enough to follow with a graduate-level background.

Scope: A single experimental report of measurement-induced suppression of thermalization in a ¹³C nuclear spin network coupled to a nitrogen-vacancy (NV) center in diamond, supported by numerical Lindblad simulations on eight spins.

What This Paper Is About

A quantum many-body system normally scrambles its local information and thermalizes, but theory predicts that frequent measurements can arrest this process and drive the system into a localized phase. Observing this cleanly is hard because environmental noise destroys the well-defined quantum trajectories the effect depends on. The authors use the exceptionally well-isolated ¹³C nuclear spins surrounding an NV center in diamond, measuring their autocorrelation decay while applying either projective measurements on one spin or global weak measurements on the whole network, and show that increasing measurement frequency substantially prolongs the spin autocorrelation time.

Key Contributions

1. A solid-state platform for measurement-induced localization. Rather than random gate sequences as in earlier circuit-model MIPT experiments, the system evolves under its intrinsic magnetic dipolar Hamiltonian, with measurements inserted at intervals, in a lattice that shields the spins from band electrons and lattice vibrations.

2. Two independent measurement protocols produce the same effect. Projective measurements on a single target ¹³C spin and global weak measurements on the whole network both prolong the spin autocorrelation time, with the global weak measurement implemented simply by a 300-ns laser pulse that dephases the nuclear spins through the hyperfine coupling.

3. A bridge from an unmeasurable quantity to a measurable one. Because mutual information cannot be measured on this platform, the authors compute a mutual-information crossover numerically and show that the onset of experimental autocorrelation-time enhancement falls within that crossover region, making a prolonged T₁ an experimental signature of the localized regime.

4. Quantitative validation with a Lindblad model. Simulations containing no phenomenological nuclear decoherence reproduce the unmonitored decay, the measurement-induced prolongation, the anti-Zeno effect and the T₁ shortening from m_S = 0 polarization, giving a consistent single-framework description of the data.

Main Findings

• Baseline thermalization is slow and stretched. The unmonitored autocorrelation function of a single ¹³C spin is well described by a stretched exponential with a characteristic time of 77.9(2.6) ms and a stretching exponent of 0.539(16); the origin of that particular exponent is stated as an open question, possibly linked to many-body glassy dynamics.

• Projective measurements prolong autocorrelation. Increasing the frequency of projective measurements on the target spin better disentangles it from the surrounding nuclear spin bath, extending its spin autocorrelation time up to 1.06 s.

• Two relaxation timescales appear at low frequency. Curves taken at low measurement frequencies are better fitted by a double exponential, indicating a fast component from local equilibration among a few strongly coupled neighbors and a slower component from the rest of the network.

• Too-frequent measurement backfires. Excessively frequent measurements accelerate relaxation through the anti-Zeno effect of single spins, traced to the transverse hyperfine coupling A_⊥ between the target spin and the NV center, which adds off-diagonal terms so that periodic NV re-initialization causes single-spin relaxation independent of many-body dynamics. The paper notes this can be mitigated by increasing the external magnetic field, which suppresses the off-diagonal terms quadratically.

• Weak measurement at a tunable strength. For spins with appreciable longitudinal coupling A_∥ = Azz, one laser pulse acts as a global weak measurement with strength γ_global ≈ 0.1f, tunable via the laser repetition frequency f. The spin network is defined operationally as spins with A∥/(2π) ≳ 1 kHz, comprising ∼100 spins.

• Mutual information shows a non-monotonic crossover. For a strongly coupled spin pair, mutual information grows with measurement strength in the weakly monitored regime, peaks at a critical value γ*, and falls when measurement dominates; γ > γ* is used as a rough criterion for the localized regime, with the crossover converted into an equivalent repetition frequency f*.

• The onset of enhancement coincides with the crossover. The onset of T₁ enhancement falls within the crossover region extracted from the mutual-information simulation, establishing a direct link between the observed localization and the MIPT localized regime. The T₁ decrease due to the anti-Zeno effect occurs at orders-of-magnitude higher frequencies and does not affect the existence of the localized regime.

• Small low-frequency dip explained. The minor decrease of T₁ at low frequencies is attributed to increased laser-induced polarization of the |m_S = 0⟩ state, which produces a disorder-free Hamiltonian under which nuclear spins tend to thermalize.

• Simulations agree qualitatively, with one gap. The simulations reproduce the decay curve, the measurement-induced prolongation and the anti-Zeno-related effects, but fail to generate the double-exponential behavior seen experimentally, possibly because of the limited spin number.

Methodology in Plain English

The sample is a bulk diamond with a natural abundance of ¹³C (≈1.1%), nitrogen concentration below 5 parts per billion, irradiated with 10-MeV electrons to a dose of approximately 1.0 kGy so that vacancies pair with nitrogen to form NV centers. A solid immersion lens is fabricated around the chosen NV center to raise its count rate to about 600 kcounts/s.

The NV electron spin serves as the control and readout handle for the surrounding ¹³C nuclei. The nuclear state is repetitively copied onto the NV electron with a C_nNOT_e gate and then read optically: a green laser pulse initializes the NV into |m_S = 0⟩, and the collected fluorescence distinguishes the nuclear state. For the projective-measurement experiment, a single C_nNOT_e gate entangles the target nuclear spin with the electron, and the following laser pulse re-initializes the electron, which destroys the target spin's entanglement with the rest of the network and thus constitutes an effective projective measurement. Each projective measurement in Fig. 1(c) uses 1100 repetitions of that gate-plus-laser block, with the left panel showing data from 5000 measurements and the histogram from 55000 measurements.

For the weak-measurement experiment, the sequence of projective measurements is replaced by single 300-ns laser pulses, each of which drives NV sublevel transitions and dephases the nuclear spins through the A_zzS_zI_z hyperfine term. The autocorrelation function ⟨σ_z(0)σ_z(t)⟩ is extracted from repeated cycles, with a correction to handle imbalanced readout counts between the |↑⟩ and |↓⟩ cases. A charge-state readout with a 594-nm laser post-selects |NV⁻⟩ events so that only unmonitored thermalization contributes to the baseline curve. Data in the frequency range [0.1 kHz, 0.5 kHz] for projective measurements, and [0.1 kHz, 4 kHz] for global weak measurements, are fitted with double exponentials; the rest with single exponentials.

For theory, the mutual information I_A,B = S_A + S_B − SA∪B is computed for individual spins A and B in the steady state, averaged over the time window in which the entanglement entropy saturates, for system sizes Nspin = 6, 8 and 10. The autocorrelation dynamics are simulated with the Lindblad master equation including only the NV center and eight strongly interacting ¹³C spins, whose coupling parameters A∥ and A⊥ were measured experimentally via dynamical decoupling; no phenomenological nuclear relaxation or decoherence channels were added, so all non-unitarity in the simulation comes from NV dynamics. A separate time step at each laser pulse makes larger simulations computationally intractable.

Why This Matters

The work extends measurement-induced physics from engineered circuit models to a physical many-body Hamiltonian in a solid-state device, and it offers a practical experimental proxy — autocorrelation time — for a localized regime whose defining quantity, entanglement entropy, remains out of reach on this platform. The simulations reproduce the data without any added dissipation, which is direct evidence that the diamond nuclear spin environment is unusually well isolated compared with superconducting circuits, trapped ions and cold atoms.

Potential applications and relevance (these follow from the platform's capabilities rather than being claims made in the paper):

• Quantum sensing and metrology: long nuclear spin relaxation times and mid-circuit measurement capability support nuclear-spin-based memories and registers read out through a single NV center.
• Quantum information processing: demonstration of mid-circuit measurement with measurement rates fast relative to intrinsic dynamics is a prerequisite for measurement-based protocols and feedback on spin qubits.
• Benchmarking and validation of open quantum system models: a solid-state testbed where Lindblad simulations with no fitted dissipation match experiment provides a calibration ground for many-body open-system theory.
• Disorder and localization studies: preparing the NV in |m_S = ±1⟩ generates site-dependent disorder for the ¹³C spins, connecting many-body localization and measurement-induced criticality in one device.

Industry relevance: diamond NV platforms are already used commercially in nanoscale magnetometry and biosensing; the demonstrated control and readout fidelity for nuclear registers is relevant to groups building spin-based quantum processors and precision sensors.

Future Directions

• Direct entanglement observation. The authors state that direct measurement of entanglement entropy or mutual information is beyond their current platform, and that they intend to investigate entanglement structures and transition behaviors as circuit-based MIPT experiments have done.
• A postselection-free protocol. Spacetime duality mapping and cross-entropy benchmarking, used in circuit experiments to avoid postselection overhead, are stated not to be directly applicable to a system governed by a physical Hamiltonian, leaving this an open methodological problem.
• Larger-scale simulation. Simulations were limited to eight ¹³C spins by the cost of stepping the Lindblad equation at every laser pulse; the failure to reproduce double-exponential behavior may stem from this limitation.
• Disorder-driven physics and noise mitigation. Exploring MIPT in a disordered monitored system via the |m_S = ±1⟩ sublevels, exploiting long-range dipolar interactions for entanglement phases beyond short-range models, and increasing the magnetic field to suppress the anti-Zeno effect are all identified as next steps.

Target Audience

Quantum many-body and open-quantum-system researchers, especially those working on measurement-induced phase transitions and the quantum Zeno and anti-Zeno effects; experimentalists in NV-center and solid-state spin physics interested in many-body dynamics and mid-circuit measurement; and graduate students or advanced readers seeking a concrete experimental counterpart to circuit-model MIPT proposals. Readers focused on applied device engineering will find the platform capabilities relevant but the physics motivation primary.

Authors’ abstract

Quantum measurement can profoundly impact the dynamics of many-body systems, for instance, inducing phase transitions from volume-law chaotic phases to area-law localized phases. While chaotic phases emerge naturally in generic many-body systems, the experimental realization of a fully localized phase driven by measurement remains challenging, primarily owing to the stringent requirement of near-perfect isolation of the system from environmental dissipation. Here we experimentally observe measurement-induced localization phenomena in an interacting $^{13}\mathrm{C}$ nuclear spin system in diamond. In contrast to previous circuit-model-based experiments, our well-isolated system evolves under a physical many-body Hamiltonian with measurements intervening at intervals. By implementing either projective measurements on a single spin or global weak measurements on the entire system, we observe substantially prolonged spin autocorrelation times as the measurement frequency increases. Our results, combined with numerical simulations, provide evidence that quantum measurement can drive a many-body system into a localized regime, and lay the groundwork for future experimental investigations into measurement-induced many-body dynamics and related entanglement phenomena.