Progress toward cryogen-free spin-photon interfaces based on nitrogen-vacancy centers and optomechanics

The implementation of quantum networks involving quantum memories and photonic channels without the need for cryogenics would be a major technological breakthrough. Nitrogen-vacancy centers have excellent spin properties even at room temperature, but phonon-induced broadening makes it challenging to coherently interface these spins with photons at noncryogenic temperatures. Inspired by recent progress in achieving high mechanical quality factors, we propose that this challenge can be overcome using spin-optomechanical transduction. We quantify the coherence of the interface by calculating the indistinguishability and single-photon purity of photons emitted from such a device and describe promising paths towards experimental implementation. Our results show that for ultrahigh mechanical quality factor frequency products, as have recently been achieved, our proposed interface could generate single photons with high indistinguishability and efficiency without cryogenic cooling, an important step towards room-temperature quantum networks.

Figure 1

Schematic of the proposed spin-optomechanical transducer emitting indistinguishable single photons. The optomechanical system consists of a trampoline membrane oscillator coupled to a high-finesse optical cavity. A magnetic tip on the membrane couples the oscillator to the dressed ground states of an NV center implanted in a diamond substrate. The cooling laser keeps the oscillator near its ground state while the control laser induces the spin-photon interaction required to extract a single telecom photon. Here $Q_{\text{m}}{f}_{\text{m}}$ denotes quality factor-frequency product.

Figure 2

(a) The NV ground-state spin triplet dressed by a microwave field with Rabi frequency ${\mathrm{\Omega }}_{\text{q}}$ and detuning ${\mathrm{\Delta }}_{\text{q}}$. (b) Dressed states $|e,d\rangle =(|+1\rangle \pm |-1\rangle )/\sqrt{2}$ provide a tunable system with ${\omega }_{\text{q}}={\mathrm{\Omega }}_{\text{q}}^2/{\mathrm{\Delta }}_{\text{q}}$ that couples to the mechanical oscillator. (c) Level diagram of the effective Raman transition. The excited spin state $|e00\rangle$ with decoherence rate ${\gamma }^{★}$ is coupled to the $\delta$-detuned state ${\widehat{b}}^{†}|d00\rangle =|d10\rangle$ by magnetic coupling rate $\lambda$; $|d10\rangle$ then couples to ${\widehat{a}}^{†}|d00\rangle =|d01\rangle$ by the optomechanical coupling rate $g_{\text{SP}}$. This indicates the absorption of a control laser photon and oscillator phonon to generate a single photon that is released by the cavity at the rate ${\kappa }_{\text{SP}}$, leaving the system in $|d00\rangle$. In the adiabatic regime, $|d10\rangle$ is bypassed due to the Raman detuning $\delta$, allowing the effective coupling rate $\mathrm{\Omega }=\lambda g_{\text{SP}}/\delta$. (d) Illustration of the single-photon wave packet with lower and upper gate times.

Figure 3

(a) Indistinguishability $I$, brightness $\beta$, and purity $g^{\left(2\right)}$, as a function of gate end time $t_u$ for $t_l=0$. (b) Improvement in the indistinguishability at the cost of brightness by decreasing total gate time $t_u^{\prime }-t_l$ for fixed $t_u^{\prime }=22\mu \mathrm{s}$. (c) Improvement in indistinguishability and purity by increasing mechanical quality factor. Single-photon quality as a function of (d) spin-dephasing rate, (e) temperature, and (f) cooling mode optomechanical coupling rate. The parameters used for all plots are $T=300$ K, $Q_{\text{m}}=5\times {10}^8$, $f_{\text{m}}=3\mathrm{MHz}$, $\delta =2\pi \times 1\mathrm{MHz}$, $\lambda =g_{\text{SP}}=2\pi \times 100\mathrm{kHz}$, ${\kappa }_{\text{SP}}=2\mathrm{\Omega }=2\pi \times 20\mathrm{kHz}$, ${\kappa }_{\text{c}}=4g_{\text{c}}=2\pi \times 600\mathrm{kHz}$, ${\gamma }^{★}=2\pi \times 0.2\mathrm{kHz}$ [8], $t_l=10\mu \mathrm{s}$, and $t_u=22\mu \mathrm{s}$ unless indicated otherwise.