Quantum Interference of Single Photons from Remote Nitrogen-Vacancy Centers in Diamond

We demonstrate quantum interference between indistinguishable photons emitted by two nitrogen-vacancy centers in distinct diamond samples separated by two meters. Macroscopic solid immersion lenses are used to enhance photon collection efficiency. Quantum interference is verified by measuring a value of the second-order cross-correlation function $g^{(2)}(0)=0.35\pm 0.04<0.5$. In addition, optical transition frequencies of two separated nitrogen-vacancy centers are tuned into resonance with each other by applying external electric fields. An extension of the present approach to generate entanglement of remote solid-state qubits is discussed.

Figure 1

Schematic of the apparatus. Two diamond SILs containing multiple NV centers are housed in continuous helium flow cryostats 2 m apart. Each SIL is addressed by a separate confocal microscopy setup, which includes a path for excitation at 532 nm, a collection path for the phonon sideband (PSB), and a collection path for the zero-phonon line (ZPL). The three optical paths are superimposed using dichroic mirrors. The ZPL collection path passes through a half-wave plate (HWP) and an additional band-pass filter (633–647 nm) before being coupled into a polarization-maintaining single-mode $50:50$ fiber beam splitter. The two beam splitter output arms are connected to a pair of avalanche photodiodes (APDs), completing the Hanbury Brown–Twiss detection setup. An excitation laser at 637 nm is connected in place of the ZPL APD 2 to acquire the photoluminescence excitation spectra. Electrodes for electric field tuning are installed in one cryostat. The inset shows a simplified level structure, including resonant excitation and emission into the ZPL at 637 nm, redshifted emission into the ground state PSB, and nonresonant excitation into the excited state PSB at 532 nm.

Figure 2

Electric field tuning of optical transitions. (a) Four $\mathrm{Cr}/\mathrm{Au}$ gates deposited on silicon. The central gap has a diameter of $150\mu \mathrm{m}$. In this experiment, only one of the gate voltages was swept while the others were kept grounded. (b) PLE spectra for different applied gate voltages. The gate voltage $V_{\mathrm{app}}$ is varied from $-30$ to 50 V for NV1, which creates an electric field of up to $0.5\mathrm{MV}/\mathrm{m}$ at NV1. The $|0⟩\leftrightarrow |E_x⟩$ transition of NV1 (blue) is tuned across the $|0⟩\leftrightarrow |E_x⟩$ transition of NV2 (red). For different $V_{\mathrm{app}}$, PLE spectra are offset by $20\mathrm{kCts}/\mathrm{s}$ for clarity. (c) Linewidth measurement under electric field tuning. On resonance, the measured FWHM linewidths are $85\pm 2\mathrm{MHz}$ for NV1 (blue) and $217\pm 4\mathrm{MHz}$ for NV2 (red). The detuning of the optical transitions in two samples is $25\pm 2\mathrm{MHz}$. (d) Linewidth measurement for the NV centers used for the HOM measurement. The measured linewidths are $88\pm 3\mathrm{MHz}$ (green) and $106\pm 4\mathrm{MHz}$ (orange), and the detuning is $93\pm 15\mathrm{MHz}$ without electric field tuning.

Figure 3

(a), (b) Single-emitter second-order autocorrelation functions $g_{\mathrm{PSB}}^{(2)}(\tau )$ of the PSB emission, inferred for the two NV centers used for the HOM measurement. The FWHM of the central antibunching features are $7.5\pm 0.1\mathrm{ns}$ for (a) and $9.5\pm 0.2\mathrm{ns}$ for (b). (c), (d) Demonstration of HOM interference from remote NV centers in the (c) distinguishable case and (d) indistinguishable case. The dashed lines indicate the limit expected from independent distinguishable single-photon sources at $\tau =0$. Solid lines are a fit to the data based on the model described in the text. For the distinguishable case (c), we find that the FWHM of the central antibunching feature is $9.2\pm 0.4\mathrm{ns}$ and $g_{\perp }^{(2)}(0)=0.54\pm 0.04$. For the indistinguishable case (d), we find that the FWHM of the central antibunching feature is $5.6\pm 0.3\mathrm{ns}$ and $g_{\parallel }^{(2)}(0)=0.35\pm 0.04$. Error bars are estimated based on shot noise.