Coherent Population Trapping of a Single Nuclear Spin Under Ambient Conditions

We demonstrate coherent population trapping of a single nuclear spin in a room-temperature solid. To this end, we exploit a three-level system with a $\mathrm{\Lambda }$ configuration in the microwave domain, which consists of nuclear spin states addressed through their hyperfine coupling to the electron spin of a single nitrogen-vacancy defect in diamond. Moreover, the $\mathrm{\Lambda }$-scheme relaxation is externally controlled through incoherent optical pumping and separated in time from consecutive coherent microwave excitations. Such a scheme allows us (i) to monitor the sequential accumulation of population into the dark state and (ii) to reach a novel regime of coherent population trapping dynamics for which periodic arrays of dark resonances can be observed, owing to multiple constructive interferences. This Letter offers new prospects for quantum state preparation, information storage in hybrid quantum systems, and metrology.

Figure 1

Spin system. (a) A single NV defect is coupled with a ${}^{13}\mathrm{C}$ nuclear spin via hyperfine interaction. The energy level structure shows the nuclear spin eigenstates in the $m_s=0$ ($|0_e⟩$) and $m_s=-1$ ($|-1_e⟩$) electron spin manifolds. The arrows indicate electron spin resonance (ESR) transitions. (b) ESR spectrum of the spin system recorded at a magnetic field $B=850\mathrm{G}$ by sweeping the frequency of a microwave field while monitoring the spin-dependent photoluminescence (PL) intensity of the NV defect. Here the nuclear spin mixing parameter is $\theta \approx 1.14\mathrm{rad}$ [26]. The red solid line is data fitting with four Gaussian functions.

Figure 2

Coherent population trapping of a single nuclear spin. (a) $\mathrm{\Lambda }$ scheme configuration. Relaxation from the excited state is triggered by optical pumping with a green laser. (b) CPT pulse sequence. Two selective MW $\pi$ pulses of duration $T_{\mathrm{MW}}=6\mu \mathrm{s}$ are followed by a 300-ns-long green laser pulse, with a power corresponding to the saturation of the NV defect optical transition. These parameters ensure spectral selectivity of an isolated $\mathrm{\Lambda }$ scheme and enable optimizing the electronic spin read-out contrast [27, 28]. (c) CPT dip observed in the ESR spectrum while setting ${\delta }_1=0$. For each sweep, the CPT sequence is repeated $N\approx 2000$ times before incrementing ${\delta }_2$. (d) ESR spectra recorded for various two-photon resonance conditions. The red solid lines are data fitting with two inverted Gaussian functions. All experiments are performed under ambient conditions with a magnetic field $B=850\mathrm{G}$ applied along the NV axis.

Figure 3

Step-by-step dark-state pumping. (a) Probability ${\mathcal{P}}_{|D⟩}$ to find the nuclear spin in the dark state as a function of the number $N$ of CPT steps. The experiment is performed with ${\mathrm{\Omega }}_1\approx {\mathrm{\Omega }}_2$ using resonant microwave $\pi$ pulses. The solid line is data fitting with a rate equation model, leading to a characteristic number of steps $N_s$ of the exponential growth $N_s=1.4\pm 0.3$. (b) Analysis of the dark-state composition at the steady state ($N=20$) as the function of the Rabi frequencies ratio $r={\mathrm{\Omega }}_1/{\mathrm{\Omega }}_2$. The solid line is data fitting with the function $r^2/(1+r^2)$ weighted by the imperfect CPT contrast [26].

Figure 4

Observation of multiple dark resonances. (a) The total duration of the CPT sequence $T_{\text{seq}}$ is modified by varying the waiting time between coherent MW excitations and relaxation induced by optical pumping. (b) ESR spectra recorded in the same way as in Fig. 2 while increasing $T_{\text{seq}}$ (from top to bottom). The red solid lines are Gaussian fits used to extract the periodicity and the width of the CPT dips. (c) Pulsed MW excitations described as frequency combs driving the $\mathrm{\Lambda }$ scheme. (d) Frequency of the dark resonance array ${\mathrm{\Delta }}^{-1}$ as a function of $T_{\text{seq}}$. The red solid line corresponds to ${\mathrm{\Delta }}^{-1}=T_{\text{seq}}$. (e) Full width at half maximum of the central CPT dip as a function of $T_{\text{seq}}$. The red solid line is data fitting with the function $[N_s{T}_{\text{seq}}{]}^{-1}$, leading to $N_s=1.8\pm 0.1$.