Dissipatively Stabilized Quantum Sensor Based on Indirect Nuclear-Nuclear Interactions

We propose to use a dissipatively stabilized nitrogen vacancy (NV) center as a mediator of interaction between two nuclear spins that are protected from decoherence and relaxation of the NV due to the periodical resets of the NV center. Under ambient conditions this scheme achieves highly selective high-fidelity quantum gates between nuclear spins in a quantum register even at large NV-nuclear distances. Importantly, this method allows for the use of nuclear spins as a sensor rather than a memory, while the NV spin acts as an ancillary system for the initialization and readout of the sensor. The immunity to the decoherence and relaxation of the NV center leads to a tunable sharp frequency filter while allowing at the same time the continuous collection of the signal to achieve simultaneously high spectral selectivity and high signal-to-noise ratio.

Figure 1

(a) Illustration of the basic principle. An NV center mediates the coupling between two nuclear spins, while itself becoming decoupled from the dynamics, enabling long coherent interactions, e.g., for high fidelity selective quantum gates. (b) Dissipation-assisted sensing setup composed of a nuclear quantum sensor [a single ${}^{13}\mathrm{C}$ spin (green) $\sim 1\mathrm{nm}$ removed from the associated NV center (red)] and an NV implanted 3–4 nm below the diamond surface, where the target spins reside (yellow). (c) Energy level diagram. The Rabi frequency $\mathrm{\Omega }$ of the MW drive is far off resonance from the Larmor frequency of the target nucleus which is on resonance with the sensor.

Figure 2

(a) Comparison of the effective (eff) dynamics under master equation (3) and the exact numerical simulation (num) by using full Hamiltonian Eq. (2) and NV resets applied every $T_{1\rho }=t_{\text{re}}=1\mathrm{ms}$. The solid blue (dashed red) curve denotes the probability of measuring $|\downarrow ,\uparrow ⟩$ ($|\uparrow ,\downarrow ⟩$) as a function of time $t$. Choosing $[\mathrm{\Omega },{\omega }_{Li}]=(2\pi )[300,200]\mathrm{kHz}$, we achieve a near perfect coherent flip-flop between nuclear spins 1 and 2 with $(a_{{\parallel }_1},a_{{\perp }_1})=(2\pi )(1.99,2.01)$, $(a_{{\parallel }_2},a_{{\perp }_2})=(2\pi )(2.00,5.01)\mathrm{kHz}$ that are coupled via the NV spin, while the nuclear spin 3 with $(a_{{\parallel }_3},a_{{\perp }_3})=(2\pi )(2.30,2.01)\mathrm{kHz}$ is not affected. (b) The parameters are the same as in (a), with the blue line denoting the occupation probability of the state $|\downarrow ,\uparrow ⟩$ for the evolution time $T=37\mathrm{ms}$. The high selectivity is demonstrated by assuming a shift of the detuning of the second spin from the resonance condition, with $\mathrm{\Delta }\delta ={\delta }_i-{\delta }_2$.

Figure 3

(a) The effect of the NV $T_{1\rho }$ and the target spin decoherence time $T_2^T$ on the detection bandwidth. The sensor signal $S$ Eq. (5) is calculated by exact simulation for a total run time of $T=90\mathrm{ms}$ and three combinations of $T_{1\rho }$, $T_2^T$. The NV spin is reinitialized every $t_{\text{re}}=T_{1\rho }$ and we chose frequencies and couplings for the sensor and targets as $[{\omega }_{L1},\mathrm{\Omega },a_{{\perp }_1},a_{{\perp }_2}]=(2\pi )[200,400,10,1]\mathrm{kHz}$. (b) The tunable NV detuning ${\mathrm{\Delta }}_{\pm i}$ as a frequency filter—the red dotted line has identical parameters to that in (a), the purple dashed line with different MW Rabi frequency results in smaller detuning which leads to increased linewidth due to increased $A_{wo}$ and ${\mathrm{\Gamma }}_{ij}^{\text{eff}}$. (c) Assuming three ${}^{13}\mathrm{C}$ nuclear spins in a Valine molecule. The NV spin is at the origin, the sensor at $[-0.601,0.676,-0.692]\mathrm{nm}$, and targets at $[-1.260,-1.451,2.904]$, $[-1.260,-1.317,3.135]$, and $[-1.260,-1.317,2.673]\mathrm{nm}$, with the magnetic field direction $[44.7°,52.0°]$ and $T=60\mathrm{ms}$. The black solid line represents the total signal of the three spins, when the dashed lines show individual contributions. The internuclear coupling has been suppressed by means of WAHUHA [33, 36] decoupling, at the cost of a reduction factor in the dipolar coupling strength $1/\sqrt{3}$. The small amplitude oscillations on the observed signal are due to off-resonant contributions, which can be suppressed by choosing larger detunings ${\mathrm{\Delta }}_{\pm i}$, i.e., larger Rabi frequency $\mathrm{\Omega }$.