Dressed-state Hamiltonian engineering in a strongly interacting solid-state spin ensemble

Abstract

In quantum science applications, ranging from many-body physics to quantum metrology, dipolar interactions in spin ensembles are controlled via Floquet engineering. However, this technique typically reduces the interaction strength between spins, and effectively weakens the coupling to a target sensing field, limiting the metrological sensitivity. In this work, we develop and demonstrate a method for direct tuning of the native interaction in an ensemble of nitrogen-vacancy (NV) centers in diamond. Our approach utilizes dressed-state qubit encoding under a magnetic field perpendicular to the crystal lattice orientation. This method leads to a $3.2\times$ enhancement of the dimensionless coherence parameter $JT_2$ compared to state-of-the-art Floquet engineering, and a $2.6\times$ ($8.3~$dB) enhanced sensitivity in AC magnetometry. Utilizing the extended coherence we experimentally probe spin transport at intermediate to late times. Our results provide a powerful Hamiltonian engineering tool for future studies with NV ensembles and other interacting higher-spin ($S>\frac{1}{2}$) systems.

Figures (4)

• Figure 1: Overview of the experiments. (a-b) The experiments are performed in an interacting ensemble of NV centersHughes2023 polarized optically by green laser within a confocal spot of a microscope. An external B-field perpendicular to the NV crystal lattice orientation is applied, and the qubit is encoded in the resulting dressed-states $\ket{\tilde{0}}$ and $\ket{\tilde{B}}$. Global microwave drive is used to manipulate the spins, and the spin-state of the ensemble is readout via the red fluorescence intensity collected with confocal microscopy. (c) The three configurations used in this work, including on-axis field (black), field perpendicular to one group of NVs (blue), and field simultaneously perpendicular to two groups of NVs (red). The same color label is used throughout the paper. (d) Comparison of Rabi oscillation under the three configurations. The semi-transparent blue trace represents the perpendicular field configuration without the pulsed field (see Ref. Gao2025 for pulsed field), and the solid blue trace represents the case with the pulsed field, which restores high quality readout. The beat node free oscillation in the two-groups configuration (red) indicates the same Rabi frequency shared by the two groups.
• Figure 2: Tunability of native interaction. (a) Bloch sphere illustration of the dressed-states encoding on $\ket{\tilde{0}}$ and $\ket{\tilde{B}}$. The factor 2 in the effective field $2\gamma B_\perp$ comes from quantum interference enhancement of the coupling between $\ket{0}$ and $\ket{B}\equiv\left(\ket{+1}+\ket{-1}\right)/\sqrt{2}$. As $B_\perp$ increases, the dressed-states obtains larger permanent magnetic moment ($\mu_\perp$, green), leading to stronger Ising coupling. (b) Theoretically predicted exchange (yellow) and Ising (green) parts of the interaction, featuring a transition from easy-plane to easy-axis Hamiltonian as $B_\perp$ increase. A native Hamiltonian with $\mathrm{SU}\left(2\right)$ symmetry is expected at $B_\perp = 362.4$ Gauss. (c) Disorder-order measurementMartin2023 of the infinite temperature local auto-correlator $C_{\mathrm{Local}}^{\mathrm{XX}}\equiv\overline{\langle s_i^x\left(t\right)s_i^x\left(0\right)\rangle_{T=\infty}}$ (solid square markers), in comparison with the decay of global X polarization (semi-transparent circle markers) at the $\mathrm{SU}\left(2\right)$ point. Colors indicates the three different configurations in Fig. \ref{['fig1']}(c). The $\mathrm{SU}\left(2\right)$ symmetric Hamiltonian is Floquet engineered in the on-axis field configuration (black), and is native in the other two cases. The faster decay of $C_{\mathrm{Local}}^{\mathrm{XX}}$ in the perpendicular field configurations indicates an enhanced interaction strength. The reported data are normalized against extrinsic decay, similar to Ref. Martin2023. See Supplement for raw data and effects of such normalization. (d) Comparison of the dimensionless coherence parameter $\left(J_0\rho\right) T_2$ for the three configurations, where $\rho$ is the independently characterized NV density (see Supplement). The XXZ anisotropy $\lambda$ is tuned via $B_\perp$ in the perpendicular field configurations (upper X axis), and via Floquet engineering in the on-axis field case (see Supplement for details on Floquet pulse sequences).
• Figure 3: Demonstration of sensitivity enhancements. (a) Comparison of the pros (green) and cons (red) of the three sensing scenarios: on-axis field configuration with and without Floquet engineering (DROID-60), and the two-groups perpendicular field configuration at native $\mathrm{SU}\left(2\right)$ point. The pulse sequence "cXY8" stands for XY8 concatenated with itselfKhodjasteh2005, which is a modified version of XY8 that has better robustness against coherent pulse errors (see Supplement). (b) Comparison of the sensing signal response in the three scenarios, while fixing the phase accumulation time to be 7.2 $\mu$s in all three scenarios. The reported AC signal amplitude (i.e. the horizontal axis) is the component along the respective direction of magnetic moment $\Delta\vec{\mu}$ (i.e. along the original NV axis for the on-axis field configuration, and along $\hat{B}_\perp$ for the perpendicular field configuration), for fair comparison between them. (c) Comparison of the sensitivity between the three scenarios. The solid lines indicate the theoretical sensitivity scaling expected from the measured coherence time. The volume normalized sensitivity is calculated with an estimated confocal spot diameter 500 nm and NV layer thickness 185 nm.
• Figure 4: Spin transport measurements. (a) Illustration of spin transport in an infinite temperature background, where the initial polarization of the central spin spreads to a larger region under unitary evolution. (b) The modified disorder-orderMartin2023 protocol for measuring local auto-correlator $C_{\mathrm{Local}}^{\mathrm{ZZ}}\equiv\overline{\langle s_i^z\left(t\right)s_i^z\left(0\right)\rangle_{T=\infty}}$. The disorder winding time is chosen as $\tau_\mathrm{wind}\sim 3.5T_2^\star$, and the dephasing time is chosen as $\tau^\prime = 3\tau_\mathrm{wind}$ (see Supplement for discussions). (c) Extrinsic decay in the above protocol due to imperfect disorder unwinding, for the on-axis field configuration (black) and two-groups perpendicular field configuration (red). Operationally, this data is measured under free evolution (i.e. no MW pulses in the dashed box "$H$" in panel (b)), where the strong on-site disorder $\sum_i h_i s_i^z$ freezes the transport. (d) Measured $C_{\mathrm{Local}}^{\mathrm{ZZ}}\left(t\right)$ at the $\mathrm{SU}\left(2\right)$ point in the two-groups perpendicular field configuration, with on-site disorder decoupled via concatenated XY8 sequenceKhodjasteh2005 (see Supplement). The data is normalized against extrinsic decay (see Supplement for raw data). The dark red line is an early-time stretched exponential fit, with fitting range including all data points where $C_{\mathrm{Local}}^{\mathrm{ZZ}}\geq 0.25$. The solid black line represents $t^{-3/2}$ decay, for comparison purposes. The dashed vertical line indicates extrinsic decay timescale in the on-axis field configuration (panel (c), black).