Control of an Environmental Spin Defect beyond the Coherence Limit of a Central Spin

Electronic spin defects in the environment of an optically active spin can be used to increase the size and hence the performance of solid-state quantum registers, especially for applications in quantum metrology and quantum communication. Previous works on multiqubit electronic spin registers in the environment of a nitrogen-vacancy (NV) center in diamond have only included spins directly coupled to the NV. As this direct coupling is limited by the central spin coherence time, it significantly restricts the maximum attainable size of the register. To address this problem, we present a scalable approach to increase the size of electronic spin registers. Our approach exploits a weakly coupled probe spin together with double-resonance control sequences to mediate the transfer of spin polarization between the central NV spin and an environmental spin that is not directly coupled to it. We experimentally realize this approach to demonstrate the detection and coherent control of an unknown electronic spin outside the coherence limit of a central NV. Our work paves the way for engineering larger quantum spin registers with the potential to advance nanoscale sensing, enable correlated noise spectroscopy for error correction, and facilitate the realization of spin-chain quantum wires for quantum communication.

Popular Summary

Solid-state quantum registers consisting of individually controllable electronic spins serve as a leading platform for quantum technologies in the area of quantum sensing. The nitrogen-vacancy (NV) center in diamond is one such paramagnetic defect that provides an optically addressable spin, which can be harnessed for sensing of magnetic fields, with performance exceeding what is possible with classical devices. This performance can be further increased by constructing a larger network of spins (or a register) consisting of environmental defects surrounding an NV center. However, these electronic spin registers have so far been limited to a few first-layer spins, which are directly interacting with the central NV center via the magnetic-dipolar interaction. This severely limits the maximum attainable size of the register. We present a scalable approach to construct larger spin registers and experimentally demonstrate the control of an environmental spin not directly coupled to a central NV.

Our system consists of a chain of three spins starting with the NV, and we harness a first-layer spin as a probing and mediator spin to detect and control a second-layer spin. As opposed to the NV, the environmental spins cannot be polarized and measured with light, so we transfer polarization across the spin chain via the dipolar interaction. We incorporate this into a novel control protocol, which allows us to map out the Hamiltonian terms of the spin chain and achieve initialization, control, and readout of the second-layer spin. By harnessing an environmental spin beyond the limit of a central NV, we pave the way to engineering larger registers that will help to advance applications in sensing with quantum advantage, such as single-molecule imaging and noise characterization in quantum devices.

Figure 1

Controlling a dark spin in the second layer to increase the coherence volume and the quantum register size. Our system consists of a central optically addressable spin, the NV, and two dark electronic spins, labeled X and Y, forming a spin chain in the configuration NV-X-Y. (a) A first-stage SEDOR sequence enables the detection of a first-layer electronic spin defect X within the coherence limit of the NV (red shading). The SEDOR sequence is comprised of a spin echo on the probing spin with a recoupling $\pi$ pulse on the target spin. The darker (lighter) shading indicates rotations around $y$ ($x$) on the Bloch sphere. The NV is polarized and measured via laser illumination (green pulse). (b) A second-stage SEDOR sequence uses X as a probe to detect and characterize a second-layer spin Y, which exists outside the coherence limit of the NV. X is initialized and read out via the NV using HHCP, which consists of simultaneously spin locking two dipolar-coupled spins at matched Rabi frequencies. (c) Left: Y is initialized by performing sequential HHCP gates across the spin chain. Resonant microwave pulses are applied to implement unitary control operations on the second-layer spin, e.g., to sense static fields in this extended detection volume by using a $\theta$ pulse at a known Rabi frequency. Right: the state of Y is mapped back to the state of the NV with sequential HHCP gates and is then read out through the NV fluorescence. R(Y) represents a unitary rotation of the Y spin on the Bloch sphere.

Figure 2

The identification of ${\omega }_0^i$ and $d^{ij}$ for the NV-X-Y spin chain using SEDOR. (a) An illustration of the three-spin system, where the shaded region corresponds to the coherence limit of the probing spin (red for the NV and blue for X). (b) SEDOR-ESR on the NV reveals the resonance frequencies and hyperfine splitting of the first-layer spin X, with $A=26.5(3)$ MHz. No resonance is detected at the Y frequency [see (e)], confirming no coupling between the NV and Y. The $y$ axis is $⟨{\sigma }_z^{\mathrm{NV}}⟩$, with an added baseline correction to normalize for decoherence during the recoupling time of the sequence. (c) SEDOR-Ramsey(NV,X) plotted as diamonds shows coherent oscillations mediated by the dipolar coupling between the NV and X spins. The spin echo on the NV, plotted as squares, indicates the coherence time for the NV, with $T_2^{\mathrm{NV}}=50(10)\text{μ}\mathrm{s}$. (d) A fast Fourier transform (FFT) of the SEDOR-Ramsey(NV,X) signal features a single dominant peak at the dipolar coupling strength of $d=67(14)$ kHz, confirming that X is a nondegenerate spin. (e) SEDOR-ESR on X reveals the resonance frequencies and hyperfine splitting of the second-layer spin Y, with $A=33.5(3)$ MHz. (f),(g) SEDOR-Ramsey(X,Y) shows coherent oscillations between the two coupled spins and the FFT confirms that Y is a nondegenerate spin with coupling strength $d=20(4)$ kHz. The data in (e) and (f) are renormalized from $⟨{\sigma }_z^{\mathrm{NV}}⟩$ according to the calibration measurement in Appendix pp3. The insets in (b) and (e) show a SEDOR-ESR pulse sequence comprised of a spin echo on the probing spin (NV,X) at fixed evolution time and a recoupling $\pi$ pulse with swept frequency. The insets in (c) and (f) show a SEDOR-Ramsey pulse sequence comprised of a spin echo on the probing spin (NV,X) at the swept recoupling time and a recoupling $\pi$ pulse on resonance with the target spin (X,Y). See Appendix pp2 for the empirical fitting functions and best-fit parameters.

Figure 3

A demonstration of universal control of the second-layer spin Y. (a) Creating polarization transfer between X and Y via HHCP. The polarization signal $⟨{\sigma }_z^{\mathrm{X}}⟩$ reaches a minimum near the $i$swap time of $1/(2d^{\text{X,Y}})$ to initialize Y via cascaded polarization transfer. The signal is normalized by the method in Appendix pp3, with an additional offset such that the maximum fit value equals 1 (for further details, see Appendix pp2). The inset is an FFT showing that the frequency of polarization transfer is at the expected dipolar coupling strength, $d^{\text{X,Y}}$. (b) Achieving unitary control of Y by driving Rabi oscillations. Y is initialized and read out by applying sequential $i$swap gates along the chain, with the HHCP(X,Y) gate calibrated from the signal in (a). We apply a microwave (MW) pulse of swept duration on resonance with the Y electronic spin transition. The $y$-axis scale is the NV contrast and creates a mapping of the Y spin state for readout. Illustrations within the plot show the polarization of the spin chain, indicated by their shading and orientation. (c) Measuring the depolarization time under optical illumination for Y, with $T_1^{\mathrm{laser}}=120(20)\text{μ}\mathrm{s}$. Over this time scale, Y can act as a memory qubit to enable repetitive readout. (a)–(c) Quantum circuits below plots: the green I and M blocks represent laser pulses to initialize and measure the NV, the $i\mathrm{S}$ blocks represent $i$swap gates between two spins, and the R($\theta$) block represents a pulse of length $L=\theta /{\mathrm{\Omega }}_0^{\mathrm{Y}}$, where ${\mathrm{\Omega }}_0^{\mathrm{Y}}=0.5$ MHz .

Figure 4

The $⟨{\sigma }_z^{\mathrm{NV}}⟩$ mapping to $⟨{\sigma }_z^{\mathrm{X}}⟩$ by calibrating control errors during state preparation and measurement (SPAM). Above, we apply HHCP initialization and readout blocks on X and sweep the phase of the second $\pi /2$ pulse during the initialization to evolve the X spin state over a range of $3\pi$ radians. Both X hyperfine transitions are driven.

Figure 5

Repetition of the same calibration experiment shown in Fig. 4 but using twice the driving strength to achieve an optimal round-trip swap efficiency of 74%.

Figure 6

Performing the SEDOR-ESR(NV,X) experiment (introduced in Sec. 2a) showing two additional spin defects in the first layer, labeled as ${\mathrm{X}}_2$ and ${\mathrm{X}}_3$. The expected ${\mathrm{X}}_1$ resonance frequencies at this field strength are included as a reference.