Dressed-State Resonant Coupling between Bright and Dark Spins in Diamond

Under ambient conditions, spin impurities in solid-state systems are found in thermally mixed states and are optically “dark”; i.e., the spin states cannot be optically controlled. Nitrogen-vacancy (NV) centers in diamond are an exception in that the electronic spin states are “bright”; i.e., they can be polarized by optical pumping, coherently manipulated with spin-resonance techniques, and read out optically, all at room temperature. Here we demonstrate a scheme to resonantly couple bright NV electronic spins to dark substitutional-nitrogen ($P1$) electronic spins by dressing their spin states with oscillating magnetic fields. This resonant coupling mechanism can be used to transfer spin polarization from NV spins to nearby dark spins and could be used to cool a mesoscopic bath of dark spins to near-zero temperature, thus providing a resource for quantum information and sensing, and aiding studies of quantum effects in many-body spin systems.

Figure 1

Schematic of dressed-state resonant coupling and energy-level diagrams. (a) Two spins with dissimilar Zeeman splittings cannot exchange energy in the lab frame. When driven resonantly (red and blue circular arrows), energy exchange becomes possible. Dressed states in the double-rotating frame are separated by the spin Rabi frequencies controlled by the respective driving fields $B_{1A,B}$. When the Rabi frequencies are matched, i.e., ${\Omega }_A={\Omega }_B$, energy conserving spin flip-flops can occur. (b) Nitrogen-vacancy (NV) and substitutional-nitrogen ($P1$) defects in diamond. Green arrows show the four possible orientations of the $P1$ hyperfine axis. (c) Ground electronic spin states of the negatively charged NV center. Degeneracy of the $|m_s=\pm 1⟩$ states is lifted by application of a static magnetic field $B_0$ aligned parallel to the NV axis. Blue arrow denotes spin transition driven in the experiment. (d) Ground electronic spin states of the $P1$ defect. For $B_0$ oriented along the $⟨111⟩$ crystal direction, the hyperfine splitting is $A_{P1}=114\mathrm{MHz}$ when the hyperfine axis is parallel to $B_0$, and $A_{P1}=90\mathrm{MHz}$ for the three other orientations. Blue arrows indicate transitions driven in the experiment.

Figure 2

Measured $P1$-bath ESR spectrum and Rabi oscillations. (a) NV optical and microwave (red) spin-echo sequence with a fixed free precession time of 350 ns is used to measure the $P1$ ESR spectrum and Rabi oscillations, for $B_0=128\mathrm{gauss}$. Coincident with the NV $\pi$ pulse a 65-ns-long rf pulse (blue) is applied to the $P1$ bath spins. (b) $P1$-bath ESR spectrum is given by measured NV spin-echo fluorescence signal and NV-$P1$ dipolar coupling as the width of the $P1$ rf pulse is kept fixed and its frequency is swept. The $|m_s=-1/2,m_I=0⟩\leftrightarrow |m_s=1/2,m_I=0⟩$ transition for all four $P1$ orientations yields the observed central NV fluorescence dip. The satellite dips are from the $|m_s=-1/2,m_I=\pm 1⟩\leftrightarrow |m_s=1/2,m_I=\pm 1⟩$ transitions of off- and on-axis $P1\mathrm{s}$. The small dip appearing on the shoulder of the central dip arises from other dark spins in the lattice [6, 31]. Solid line represents a fit to a set of five Gaussians (see the Supplemental Material [25]). (c) With the frequency of the rf signal set to the central $P1$ resonance dip, the width of the rf pulse is swept to yield $P1$-bath Rabi oscillations via the effect of NV-$P1$ dipolar coupling on NV spin-echo fluorescence measurements. When the rf pulse width is 62.5 ns, the spin-echo signal is reduced due to an effective reversal of the dipolar field of the $P1$ bath. The rapid decay of oscillations is due to decoherence caused by dipolar coupling between $P1$ spins and ensemble averaging. Solid line is a fit to a decaying sinusoid (see the Supplemental Material [25]).

Figure 3

Measured dressed-state NV-$P1$ resonant coupling. (a) NV optical and microwave spin-lock sequence, and timing of five-frequency rf pulse to drive $P1$ spin bath. After initializing NVs to the the $|m_s=0⟩$ state ($Z$ axis) with a $2\mu \mathrm{s}$ optical pumping pulse, $\pi /2$ and $3\pi /2$ microwave pulses are applied along the $X$ axis to rotate the spin to or from the equator of the Bloch sphere, and a microwave spin-locking pulse of variable duration is applied along the $Y$ axis. To bring the $P1$ bath into dressed-state resonance with the NV spins, a five-frequency rf pulse is applied during the spin-lock duration. (b) Measured decay of NV spin-lock signal as a function of spin-lock duration. When the $P1$ bath is not driven we record the blue trace. Driving the $P1$ bath simultaneously at all five ESR resonances such that the collective $P1$-bath Rabi frequency equals the NV Rabi frequency (8 MHz) gives the red trace, indicating strong NV spin depolarization caused by NV-$P1$ resonant coupling. Solid lines represent fits to decaying exponentials (see the Supplemental Material [25]).

Figure 4

Measured spectrum of NV-spin resonant coupling to $P1$ bath spins. Here $B_0=132\mathrm{gauss}$ and the NV Rabi $\mathrm{\text{frequency}}=8\mathrm{MHz}$. (a) A single-frequency rf signal, with power corresponding to $P1$ Rabi frequency of 8 MHz, is swept across the $P1$-bath resonances. When the rf frequency equals that of a $P1$-spin-bath resonance, the NV spin-lock signal is reduced. Solid line is a fit to a set of five Gaussians (see the Supplemental Material [25]). (b) NV-$P1$ dressed-state resonance spectrum is measured by monitoring the NV spin-lock signal, applying rf power at the central $P1$-bath resonance dip, and sweeping the power of the rf signal. Solid line represents a Gaussian fit (see the Supplemental Material [25]). The resonance is centered at 8.1(1) MHz and has a FWHM of 3.5(4) MHz.