Single-Shot Readout of Multiple Nuclear Spin Qubits in Diamond under Ambient Conditions

We use the electronic spin of a single nitrogen-vacancy defect in diamond to observe the real-time evolution of neighboring single nuclear spins under ambient conditions. Using a diamond sample with a natural abundance of ${}^{13}\mathrm{C}$ isotopes, we first demonstrate high fidelity initialization and single-shot readout of an individual ${}^{13}\mathrm{C}$ nuclear spin. By including the intrinsic ${}^{14}\mathrm{N}$ nuclear spin of the nitrogen-vacancy defect in the quantum register, we then report the simultaneous observation of quantum jumps linked to both nuclear spin species, providing an efficient initialization of the two qubits. These results open up new avenues for diamond-based quantum information processing including active feedback in quantum error correction protocols and tests of quantum correlations with solid-state single spins at room temperature.

Figure 1

(a) Energy-level diagram of the NV defect as a function of the strength of a static magnetic field $B$ applied along the NV defect axis. Level anticrossings in the ground state (GSLAC) and in the excited state (ESLAC) are highlighted. (b) Hyperfine structure of the $m_s=0$ and $m_s=-1$ electron spin manifolds for a NV defect coupled with its intrinsic ${}^{14}\mathrm{N}$ nuclear spin ($m_{I^{(\mathrm{N})}}$) and with a nearby single ${}^{13}\mathrm{C}$ nuclear spin ($\uparrow$ or $\downarrow$). The hyperfine sublevels are denoted as $|m_{I^{(\mathrm{N})}},\uparrow (\downarrow )⟩$. Blue arrows indicate the microwave (MW) transitions used for single-shot readout measurements. (c) Optically detected ESR spectrum recorded for a magnetic field $B\approx 2000\mathrm{G}$. (d) FID signal of the NV defect electron spin recorded at the ESLAC ($B\approx 510\mathrm{G}$) showing a coherence time $T_2^{*}=2.9\pm 0.1\mu \mathrm{s}$. (e) Fourier transform of the FID signal.

Figure 2

(a) Logic diagram of the single-shot readout scheme and corresponding experimental sequence. The duration of the $\pi$-pulses is set to $4\mu \mathrm{s}$. The 300-ns laser pulse is used both for spin-state read-out and to achieve an efficient preparation of the NV defect electron spin in the $m_s=0$ sublevel ($|0{⟩}_e$) at each repetition of the sequence. (b) PL time trace showing quantum jumps of the ${}^{13}\mathrm{C}$ nuclear spin state. The solid line is a fit with a two states hidden Markov model from which the relaxation time $T_1$ of the nuclear spin state is extracted. (c) Normalized nuclear-spin dependent photon counting distributions ${\mathcal{S}}_{\uparrow (\downarrow )}$. The solid lines are data fitting with the formula given in Ref. 23. (d) Single-shot readout fidelity ${\mathcal{F}}_{\uparrow (\downarrow )}$ as a function of the readout threshold. The initialization thresholds ${\mathcal{N}}_{i,\downarrow }$,${\mathcal{N}}_{i,\uparrow }$ and the optimized discrimination threshold ${\mathcal{N}}_{r,\mathrm{opt}}$ are indicated with dashed lines. The solid lines are extracted from the fits in (c). We note that the initialization fidelity in state $|\downarrow ⟩$ ($|\uparrow ⟩$) is given by ${\mathcal{F}}_{\downarrow }({\mathcal{N}}_{i,\downarrow })$ [${\mathcal{F}}_{\uparrow }({\mathcal{N}}_{i,\uparrow })$].

Figure 3

Nuclear spin relaxation time $T_1$ as a function of the magnetic field strength for the bright state (red) and the dark state (blue). The solid lines are data fitting with a simple model including nuclear spin flips induced by the transverse component of the hyperfine tensor and electron-nuclear spin flip flops at the GSLAC and ESLAC [23].

Figure 4

(a) Experimental sequence. (b), (c) PL time trace recorded by continuously repeating the sequence for a magnetic field $B=5280\mathrm{G}$. Each data point corresponds to approximatively 3000 repetitions of the readout sequence (20 ms). Quantum jumps linked to (b) the weakly coupled ${}^{13}\mathrm{C}$ nuclear spin and to (c) the intrinsic ${}^{14}\mathrm{N}$ nuclear spin can be distinguished. (d) Normalized nuclear-spin dependent photon counting distributions measured with the initialization thresholds set to ${\mathcal{N}}_{i,\mathrm{dark}}=110$ counts and ${\mathcal{N}}_{i,\mathrm{bright}}=160$ counts. The projective readout fidelity is optimized for a discrimination threshold ${\mathcal{N}}_{r,\mathrm{opt}}=135$ counts.