Low Temperature Studies of the Excited-State Structure of Negatively Charged Nitrogen-Vacancy Color Centers in Diamond

We report a study of the ${}^{3}E$ excited-state structure of single negatively charged nitrogen-vacancy (NV) defects in diamond, combining resonant excitation at cryogenic temperatures and optically detected magnetic resonance. A theoretical model is developed and shows excellent agreement with experimental observations. In addition, we show that the two orbital branches associated with the ${}^{3}E$ excited state are averaged when operating at room temperature. This study leads to an improved physical understanding of the NV defect electronic structure, which is invaluable for the development of diamond-based quantum information processing.

Figure 1

(a) Energy-level diagram of a single NV defect. (b) Excitation spectrum of a single NV defect presenting six resonances, which correspond to optical transitions linking identical spin sublevels. Solid line is data fitting using Lorentzian functions. Energy splittings between each excited-state spin sublevels for this NV center are written in blue (dark gray) in (a) (not in scale). (c) Pulse sequence used to measure single-electron spin Rabi oscillations (see main text). (d) and (e) Rabi nutations measured using resonant optical transitions for the spin readout in the upper branch $E_x$ (d) and in the lower branch $E_y$ (e). A $\pi$ phase shift of the Rabi nutation allows to discriminate for each orbital branch between optical transitions linking $S_z$ or $S_{x,y}$ spin sublevels.

Figure 2

Schematic diagram of the excited-state energy levels including spin-orbit interaction, spin-spin interaction and transverse local strain. Note that 1 GPa external stress gives approximately ${10}^3\mathrm{GHz}$ splitting [24].

Figure 3

(a) Excitation spectra recorded for different single NV defects denoted NV1, NV2 and NV3. (b) Excited-state energy structure as a function of the transverse strain ${\delta }_{\perp }$ for 27 single NV defects. Solid lines correspond to the calculation without any free parameter and the inset is a zoom on the lower branch for a strain corresponding to an avoided crossing between $|E_y,S_z⟩$ and $|E_y,S_x⟩$ spin sublevels. At this avoided crossing, the solid lines exchange colors for the purpose of clarity. (c) Energy-level scheme of the lower branch for the defect NV3, showing three spin-conserving transitions (solid arrows) and two spin-flip transitions (dashed arrows), appearing when the states $|E_y,S_z⟩$ and $|E_y,S_x⟩$ are crossing. (d) Energy-level scheme of the upper branch for the defect NV2. The energy splitting between the states $|E_x,S_z⟩$ and $|E_x,S_y⟩$ is equal to 2.88 GHz, leading to a repumping effect of the $|S_z⟩\to |E_x,S_z⟩$ optical transition.

Figure 4

(a) ODMR spectra of a single NV color center recorded at $T=260\mathrm{K}$ and at $T=6\mathrm{K}$. (b) Contrast of the excited-state ESR as a function of temperature. The contrast is normalized to the integral of the ground state ESR at 2.88 GHz. (c) Energy splitting between the averaged energy of $S_z$ and $S_{x,y}$ sublevels of the two orbital branches as a function of strain. Data points are inferred using the measurements depicted in Fig. 3b. The black dashed line corresponds to $D_{\mathrm{es}}=1.42\mathrm{GHz}$.