Optomechanical Quantum Control of a Nitrogen-Vacancy Center in Diamond

We demonstrate optomechanical quantum control of the internal electronic states of a diamond nitrogen-vacancy (NV) center in the resolved-sideband regime by coupling the NV to both optical fields and surface acoustic waves via a phonon-assisted optical transition and by taking advantage of the strong excited-state electron-phonon coupling of a NV center. Optomechanically driven Rabi oscillations as well as quantum interferences between the optomechanical sideband and the direct dipole-optical transitions are realized. These studies open the door to using resolved-sideband optomechanical coupling for quantum control of both the atomlike internal states and the motional states of a coupled NV-nanomechanical system, leading to the development of a solid-state analog of trapped ions.

Figure 1

(a) A NV center located near the diamond surface coupling to a laser field and a propagating SAW that extends from the thin ZnO layer to about one acoustic wavelength ($\approx 6\mu \mathrm{m}$) beneath the diamond surface. (b) Schematic of the sample illustrating the use of IDTs fabricated on the piezoelectric ZnO layer to generate and detect SAWs. (c) Energy level diagram illustrating the blue and red sideband transitions for the optomechanical interactions. The carrier transition is between the $m_s=0$ ground state and the $E_y$ excited state of the NV. (d) The excitation spectrum of the carrier transition, where NV fluorescence is measured as the laser frequency is tuned across the dipole transition (the acoustic field is off). The blue line is a Lorentzian fit.

Figure 2

(a) Excitation spectrum with the NV driven by both the optical and acoustic fields and with ${\omega }_m=900\mathrm{MHz}$. The incident laser power is $P_0=0.4\mu \mathrm{W}$ and the rf input power is $P_{\text{rf}}=0.2\mathrm{W}$. The blue line is a fit to Lorentzians. (b) Measured frequency splitting between the carrier and the sideband resonances as a function of ${\omega }_m$. For the red line, the frequency $\text{splitting}={\omega }_m$. (c),(d) Amplitudes of the sideband resonances with increasing $P_0$ and $P_{\text{rf}}$. Red lines are linear least-squares fits. (e) Excitation spectra of the NV obtained for three different $P_0$ and with $P_{\text{rf}}=0.1\mathrm{W}$. The amplitude is normalized to the peak amplitude of the carrier resonance obtained with $P_0=0.1\mu \mathrm{W}$. Green lines are fits to Lorentzians. (f) Linewidths of the carrier (black squares) and red sideband (red circles) resonance as a function of $P_0$, with $P_{\text{rf}}=0.1\mathrm{W}$. Black line is the calculated power broadening. Red line is a liner fit to guide the eye.

Figure 3

(a) Two pathways corresponding to the direct dipole transition and the red sideband transition, for the excitation of state $E_y$. The figure also denotes the frequencies and phases of the optical and acoustic waves. (b) NV fluorescence as a function of detuning between ${\omega }_1$ and ${\omega }_2+{\omega }_m$. Carrier excitation power $P_{01}=0.4\mu \mathrm{W}$. Sideband excitation power $P_{02}=2\mu \mathrm{W}$. $P_{\text{rf}}=0.2\mathrm{W}$. (c) NV Fluorescence as a function of ${\phi }_m$, with ${\omega }_1-({\omega }_2+{\omega }_m)=0$, showing the interference between the two pathways. The red line is a sinusoidal oscillation with a period of $2\pi$.

Figure 4

(a) Pulse sequence used for the Rabi oscillation experiment. (b) NV fluorescence as a function of acoustic pulse duration. Rabi oscillations (offset for clarity) are shown with estimated ${\mathrm{\Omega }}_0/2\pi =290\mathrm{MHz}$ and for three different rf driving powers for an IDT with ${\omega }_m=940\mathrm{MHz}$. Solid lines are numerical fits to damped sinusoidal oscillations. Inset: Rabi frequencies obtained as a function of the rf power. Red line shows a linear least-squares fit.