Dark States of Single Nitrogen-Vacancy Centers in Diamond Unraveled by Single Shot NMR

The nitrogen-vacancy (NV) center in diamond is supposed to be a building block for quantum computing and nanometer-scale metrology at ambient conditions. Therefore, precise knowledge of its quantum states is crucial. Here, we experimentally show that under usual operating conditions the NV exists in an equilibrium of two charge states [70% in the expected negative (${\mathrm{NV}}^{-}$) and 30% in the neutral one (${\mathrm{NV}}^0$)]. Projective quantum nondemolition measurement of the nitrogen nuclear spin enables the detection even of the additional, optically inactive state. The nuclear spin can be coherently driven also in ${\mathrm{NV}}^0$ ($T_1\approx 90\mathrm{ms}$ and $T_2\approx 6\mu \mathrm{s}$).

Figure 1

(a) Nitrogen nuclear spin Rabi oscillation (${\mathrm{NV}}^{-}$, $m_S=0$). The fidelity $F$ reduces the achievable contrast ($\to 100\%$ population) by the dark gray regions. The even smaller Rabi amplitude is because of some population that is not in the ${\mathrm{NV}}^{-}$ $m_S=0$ state (light gray region). (b) QND initialization and readout of nuclear spin state: Microwaves (mw) manipulate the electron spin, and a green laser ($L$, 532 nm) reads it out and polarizes it into $m_S=0$ [18]. A resonant rf $\pi$ pulse flips the nuclear spin. (c) NMR spectra showing transition frequencies of the ${}^{14}\mathrm{N}$ and ${}^{15}\mathrm{N}$ nuclear spin for different NV center states. The corresponding quantum numbers $m_I$ for each transition are given. Dark state NMR transitions are marked with orange arrows; other lines belong to the bright state $m_S=0$. Gray lines with stars mark expected transitions in the dark state (see text). (d) Energy level scheme of NV center nuclear spin in the dark state. NMR transitions among spin states are marked with orange lines [arrows in (c)]. Hyperfine interaction $hf$ and quadrupole splitting $Q$ are marked. The gray dashed lines mark the energy levels for a reversed hyperfine field [stars in (c)].

Figure 2

(a) NMR pulse sequence to investigate transition into the dark state. After readout and initialization, a red laser pulse (637 nm) of variable length transfers a certain amount of population into the dark state. A subsequent nuclear spin $\pi$ pulse monitors the NMR line intensities. (b) 2D plot of NMR amplitude (color coded) over rf frequency (horizontal) and red laser pulse length (vertical). Spectra for minimal and maximal laser pulse lengths are shown above and below the 2D plot. (c) Populations in the dark and bright states deduced from (b). (d) Nuclear spin Rabi oscillation in the dark state for rf fields of two different strengths (18 dB difference), showing homogeneous dephasing.

Figure 3

(a) Energy level scheme of the bright and dark states. The bright state comprises of the triple ($T$) and singlet ($S$) levels of ${\mathrm{NV}}^{-}$ [23], whereas the dark state is at least a doublet ($D$) supposedly in another charge state. The arrows symbolize transition rates, where green and red are due to the respective lasers and the black dashed arrows are decay processes. (b) The fluorescence signal of the bright state for increasing red laser duration shows an exponential decay depending on the magnetic field orientation ($\mathrm{\text{aligned}}\to \tau =120\mu \mathrm{s}$, $\mathrm{\text{misaligned}}\to \tau =184\mu \mathrm{s}$). (c) Fluorescence decrease and increase rates depending on corresponding red or green laser power for pumping into or out of the dark state, respectively. Insets show respective pulse sequences and corresponding fluorescence intensities. For fits, see the text.