Collective many-body dynamics in a solid-state quantum sensor controlled through nanoscale magnetic gradients

TL;DR

The work addresses the challenge of achieving coherent collective dynamics in positionally disordered solid-state spins by coupling spatially varying magnetic field gradients with Floquet-engineered SU(2)-symmetric dipolar interactions. This combination enables the creation and control of nanoscale spin spirals whose evolution exhibits disorder-resilient, nonlinear dynamics akin to one-axis twisting, with large twisting amplitudes and slow relaxation at the SU(2) point. By imaging the spin textures and tuning the spiral wavevector, orientation, and interaction anisotropy, the authors demonstrate a pathway to interaction-enhanced metrology and nanoscale imaging under ambient conditions. The results establish a versatile platform for nanoscale quantum sensing with potential for significant magnetic sensitivity gains and quantum-enhanced measurement capabilities without requiring extreme isolation or cryogenic environments.

Abstract

Coherent collective dynamics of strongly interacting qubits are a central resource in quantum information science, with applications from quantum computing and simulation to metrology. While electronic spins interact strongly via dipolar couplings in dense solid-state ensembles, imperfections and positional disorder pose major obstacles to coherent correlated behavior, limiting their usefulness. Here, we realize collective many-body dynamics by combining time-dependent magnetic field gradients with global coherent control of dense electron spin ensembles in diamond. We control and probe the dynamics of nanometer-scale spin spirals, and, by exploiting Hamiltonian engineering that enhances the microscopic symmetry of the interactions, we observe a disorder-resilient collective spin evolution. Our results establish a pathway to interaction-enhanced quantum metrology and nanoscale imaging of materials and biological systems under ambient conditions.

Figures (10)

• Figure 1: Overview of the experimental platform. (a) Schematic illustration of the experimental system, showing a positionally disordered three-dimensional ensemble of spins interacting via anisotropic magnetic dipolar coupling (red and blue coloring) and subject to a global MW field, which engineers interactions between spins, and a magnetic field gradient $\bm{\nabla}$. Positional disorder of the spins generically leads to fast dephasing driven by closely coupled pairs (inset), preventing collective dynamics. (b) The presence of four crystallographic groups of NV centers, $\bm{\eta_{i}}$, that also leads to different effective gradient directions $\bm{\nabla_{i}}$. (c) Illustration of the bulk sample device, showing a diamond plate placed atop a two-wire chip that generates a magnetic field gradient tunable via the ratio of currents on the two wires. Green laser illumination is used for spin initialization, red fluorescence indicates spin-state-dependent readout from a confocal spot. (d) Illustration of the nanobeam device, showing a piece of a diamond (black beam) with a dense ensemble of NV centers placed atop a microcoil that generates an inhomogeneous magnetic field $\bm B_{0}$. (e) Local magnetic field extracted from ESR measurements for the bulk sample, taken between microcoil wires (pink arrow in C) for currents running in each wire. Solid lines show simple quadratic fits used to determine the magnetic field gradient. (f) ESR measurements along the nanobeam (pink arrow in D) for two different NV groups. Solid lines show finite-element simulations of the spatially varying magnetic field, projected onto the quantization axes of NV groups 1 and 3. The measurements were performed at one-tenth of the maximum gradient strength used in this work.
• Figure 2: Probing dynamics of conical spin spirals. (a) Schematic of the measurement protocol, consisting of three stages: spin state preparation (winding), quench under a Floquet-engineered Hamiltonian, and readout/imaging of the spin spiral in unwinding stage. (b) Benchmarking of the winding and unwinding protocol, omitting quench, demonstrating robust and reversible preparation and readout of spin spirals. Markers indicate measured points, solid line is a simple gaussian fit. (c) Imaging of a prepared nanoscale spin texture. Measured $\hat{x}$ (red) and $\hat{y}$ (blue) components of the spin spiral showing spin texture wound at the target pitch $\bm Q$. (d) Initial spin states used to probe many-body dynamics, shown on the Bloch sphere. Preparation of antipodal states (pairwise colored) enables cancellation of spurious global rotations, isolating the genuine many-body dynamics of the spin spiral gao_signal_2025. (e) Measurement of many-body dynamics when no spiral is wound, reported in unit of Bloch sphere radius. Top panel contains data for a native dipolar interaction, while the bottom panel corresponds to the engineered SU(2) Hamiltonian. Without a spiral no time-dependent signal is observed. Data is taken with the bulk sample device throughout the paper, unless explicitly stated otherwise. (f) Measurement of the spin spiral precession dynamics for a native dipolar Hamiltonian. (g) Measurement of the spin spiral dynamics for a Floquet engineered SU(2) Hamiltonian taken over longer quench timescale.
• Figure 3: Tuning dipolar spin dynamics via geometric and microscopic Hamiltonian anisotropy. (a) Measurement of spin spiral dynamics for $\bm{Q} \parallel \bm{\eta}$. (b) Opposite-sign, slower spiral precession measured for $\bm{Q} \perp \bm{\eta}$. (c) Semiclassical mechanism generating spiral precession due to exchange mean fields at the SU(2) point. The central spin (black) experiences an effective mean field from nearby spins. The transverse components of this field lead to spin precession. (Bottom panel) For a spiral starting from an initial state on the lower hemisphere of the Bloch sphere, the direction of the mean field and the sign of the precession are reversed. (d) Illustration of the dipolar interaction, spatially modulated at the pitch of the spiral for a simplified case where quantization axis is parallel to gradient direction, $\delta \chi_{\bm Q \parallel \bm \eta}(\bm r)$. (e) Corresponding spatial modulation of the dipolar interaction for the case where the quantization axis is perpendicular to the gradient direction, $\delta \chi_{\bm Q \perp \bm \eta}(\bm r)$, sourcing an exchange field of opposite sign. (f) Measured precession frequency as a function of geometric anisotropy $\boldsymbol{\hat{Q}} \cdot \boldsymbol{\hat{\eta}}$ for $Q = 2\pi/(0.242~$µ m), showing tunable strength and sign of the exchange field. Solid line is the dipolar anisotropy $\mathcal{A}_{\hat{\bm\eta}}(\hat{\bm Q})\propto 3(\hat{\bm Q}\cdot \hat{\bm \eta})^2-1$ theoretically expected, see SI. (g) Normalized precession amplitude as a function of interaction anisotropy in the engineered XXZ Hamiltonian. Experimental data are shown as markers; solid line represents theory prediction.
• Figure 4: Magnetic imaging of microscopic polarization driving spiral dynamics. (a) Spin polarization geometry in bulk diamond: disc-shaped region set by NV layer thickness (axial) and optical pumping (transverse). Gradient directions for data in (C) (blue) and imaging in (D) (green) are indicated. (b) Analogous geometry in the nanobeam device. (c) (Top) Origin of non-monotonic precession amplitude: saturation wavevector $Q_{*}$ is inversely related to polarization extent $R_{*}$. (Bottom) Measured spiral precession frequency $\omega$ versus wavevector $Q$ in bulk diamond. Vertical line: $Q = 2\pi/(0.185~$µ m). Solid lines are theory predictions. (d) FMI taken across the bulk sample, used to extract NV layer thickness (185 nm). Inset: raw data versus $Q'$, with fit assuming a rectangular profile. (e) Maximum normalized precession amplitude measured versus $Q$ for NV group 1 in the nanobeam device. Vertical dashed line: $Q = 2\pi/(0.3~$µ m). Theory: dashed line—ideal spiral; solid line—with measured spiral winding loss (see SI). (Inset) Amplitude measured versus $Q$ for shorter optical pumping times, showing saturation shift consistent with larger polarization extent. (f) FMI along the nanobeam short axis, revealing nanoscale polarization variations from nanophotonic interference. Experimental data are shown as markers; solid line represents nanophotonics model predictions. (g) Theory cross-sections of NV polarization in the nanobeam for increasing pump times. Spatial structure arises from optical interference of the green pump light.
• Figure 5: Collective nonlinearity in a disordered, three-dimensional dipolar spin system. (a) Measured dynamics of spin spirals prepared at cone angle $\theta$ and precessing by angle $\phi$. Most transparent point marks maximum quench time $t=289.44$ µs. Data used in b–d was collected with improved drive/gradient homogeneity at $Q = 2\pi/(0.242~$µ m), shown by the thin red line in (g),(h). (b) Measured spiral precession angle $\phi$ versus quench time for a range of initial cone angles $\theta$. Solid lines are linear fits used to extract $\omega$. (c) Extracted precession rate versus cone angle $\theta$. The fitted cosine dependence (solid line) is characteristic of OAT dynamics. (d) Measurement of precession amplitude versus cone angle $\theta$ (markers). Purple line: numerical simulations multiplied by measured decoherence (Fig. S1(b)). Dashed orange: naive model $\propto\sin(\theta)\cos(\theta)$. (e) Illustration of a pair of strongly coupled spins. In the Ising case, local interactions and quantum fluctuations lead to fluctuating $\hat{z}$-field (vertical dashed line), causing random precession (curved arrows) and fast dephasing, whereas for a long-wavelength spiral evolving under an SU(2) Hamiltonian, nearby spins contribute a field nearly aligned (red dashed line) with the target spin, preventing local dephasing. (f) Decay curves for SU(2) conical spiral with $\theta = 45^{\circ}$ at varying wavevectors. Solid lines are fits to stretched exponential decay. (g) Precession frequency $\omega$ and decay rate $\gamma$ measured as functions of the spiral wavevector $Q$ for SU(2) interaction. The horizontal dashed line marks the extrinsic decay rate; solid lines denote theoretical predictions. (h) Quality factor $\omega/\gamma$ computed from (g). The horizontal dashed line indicates the theoretical maximum for a two-dimensional Ising model of dilute, positionally-disordered spins with unity spin polarization, while an orange marker indicates the measured quality factor for native interactions.