Violation of a Temporal Bell Inequality for Single Spins in a Diamond Defect Center

Quantum nonlocality has been experimentally investigated by testing different forms of Bell’s inequality, yet a loophole-free realization has not been achieved up to now. Much less explored are temporal Bell inequalities, which are not subject to the locality assumption, but impose a constraint on the system’s time correlations. In this Letter, we report on the experimental violation of a temporal Bell’s inequality using a nitrogen-vacancy (NV) defect in diamond and provide a novel quantitative test of quantum coherence. Such a test requires strong control over the system, and we present a new technique to initialize the electronic state of the NV with high fidelity, a necessary requirement also for reliable quantum information processing and/or the implementation of protocols for quantum metrology.

Figure 1

(a) Energy level scheme of the ${\mathrm{NV}}^{-}$ defect in a small magnetic field. Optical transitions occur between ground state (GS) and excited state (ES) (vertical arrows), dotted lines (gray) indicate radiationless decays. Line thickness corresponds to transition rates. (b) Histogram of many subsequent QND measurements of the nitrogen nuclear spin. Low fluorescence level indicates that the MW $\pi$ pulse was successful, i.e., that the nuclear spin state is $m_I=+1$. (c) Magnification of the $m_S=0$, $-1$ levels including hyperfine pitting due to the ${}^{14}N$ nuclear spin (states are denoted as $|m_S,m_I⟩$). The dotted arrow illustrates the nuclear spin selective MW $\pi$ pulse, the dashed arrow the nuclear spin transition driven by rf pulses.

Figure 2

(a) Time trace of the fluorescence of the NV under cw illumination with 600 nm, $0.4\mu \mathrm{W}$ laser light. The state fit (${\mathrm{NV}}^{-}$, ${\mathrm{NV}}^0$) shows the most likely fluorescence level. The lifetime of ${\mathrm{NV}}^{-}$ during orange illumination is around 600 ms. (b) Histogram of measurement results showing the distribution of counted photons during orange illumination for the inset sequence: the first pulse (green laser) “resets” the NV and the second pulse (8 ms orange laser) measures the charge state.

Figure 3

(a) Measurement sequence (cf. text). (b) Rabi oscillation of the nuclear spin, introduced by rf pulses of varying length $\tau$ (time axis), the solid line shows a cos fit. The large dots indicate points measured with higher accuracy. (c) Result of the temporal Bell inequality (1). The solid line is obtained by calculating the inequality for the fit curve of (b), the dotted black line is for comparison and shows the “ideal” case (error-free measurement of Rabi oscillation). The large dot corresponds to the two large dots in (b).