Excited-State Spectroscopy Using Single Spin Manipulation in Diamond

We use single-spin resonant spectroscopy to study the spin structure in the orbital excited state of a diamond nitrogen-vacancy ($\mathrm{N}\mathrm{\text{−}}V$) center at room temperature. The data show that the excited-state spin levels have a zero-field splitting that is approximately half of the value of the ground state levels, a $g$ factor similar to the ground state value, and a hyperfine splitting $\sim 20\times$ larger than in the ground state. In addition, the width of the resonances reflects the electronic lifetime in the excited state. We also show that the spin level splitting can significantly differ between $\mathrm{N}\mathrm{\text{−}}V$ centers, likely due to the effects of local strain, which provides a pathway to control over the spin Hamiltonian and may be useful for quantum-information processing.

Figure 1

(a) Energy diagram of electronic and spin levels for a $\mathrm{N}\mathrm{\text{−}}V$ center. Both the ground state (${}^{3}A$) and the excited state (${}^{3}E$) are spin triplets, with a zero-field splitting ($D_{\mathrm{gs}}$, $D_{\mathrm{es}}$) between the $m_S=0$ and the $m_S=\pm 1$ levels. Black arrows show the largely spin-conserving optical transitions. There is also nonradiative relaxation through ${}^{1}A$ that is not spin conserving (gray arrows indicate the dominate pathway). (b) Spatial photoluminescence map with $\mathrm{N}V1$ and $\mathrm{N}V2$ indicated. We verified that each spot corresponds to a single $\mathrm{N}\mathrm{\text{−}}V$ center using photon correlation measurements (not shown). (c) The top trace shows optically detected spin resonance at $B=57\mathrm{G}$ where $B_{\mathrm{rf}}$, laser illumination, and photon counters are all on continuously. The bottom trace is a measurement where $B_{\mathrm{rf}}$ is applied while the laser is off so that the spin is manipulated only in the ground state. (d) Surface plot of cw spin resonance as a function of magnetic field. The viewpoint is below the data so that dips in $I_{\mathrm{pl}}$ appear as peaks. The sharp features are the GS spin resonances while the broad features are resonant transitions in the ES.

Figure 2

Fits of the ES $m_S=0\leftrightarrow +1$ doublets to a double Lorentzian for (a) 67, (b) 503, and (c) 804 G. (d) Amplitudes of the $m_S=0\leftrightarrow +1$ dips vs $B$. (e) FWHM vs $B$ for $m_S=0\leftrightarrow +1$, $m_I=+1/2$. (f) Average variation of dip amplitude vs laser power. (g)–(h) Fit results for $m_S=0\leftrightarrow -1$, $m_I-1/2$ (●), $m_S=0\leftrightarrow -1$, $m_I=+1/2$ (◆), $m_S=0\leftrightarrow +1$, $m_I=+1/2$ (▴) and $m_S=0\leftrightarrow +1$, $m_I=-1/2$ (▪) at $B=57\mathrm{G}$. (g) Amplitude of the dips in $I_{\mathrm{pl}}$ vs amplitude of $B_{\mathrm{rf}}$. (h) FWHM in MHz vs amplitude of $B_{\mathrm{rf}}$.

Figure 3

Frequencies of the ES spin transitions obtained from Lorentzian fits to the spin resonance data (points) as well as fits to the eigenvalues of to Eq. (1) (dashed lines) as described in the text for the entire field range (a) and low field (b). (c) Left: diagram of the energy levels of the excited ${}^{3}E$ manifold as a function of strain along $x$ axis. Adopting the notation of 10: $A_1=|E_X,S_X⟩+|E_Y,S_Y⟩$, $A_2=|E_X,S_Y⟩-|E_Y,S_X⟩$, $E_Y^{\prime }=|E_X,S_Z⟩$, $E_X^{\prime }=|E_Y,S_Z⟩$, $E_Y=-|E_X,S_X⟩+|E_Y,S_Y⟩$, and $E_X=-|E_X,S_Y⟩-|E_Y,S_X⟩$. Right: diagram of level splitting as a function of $B$. (d) cw ESR data at $B=0.7\mathrm{G}$ for $\mathrm{N}V1$ and $\mathrm{N}V2$. The insets show the splitting of the GS transitions at 0.7 G by $\sim 9$ and 21 MHz for $\mathrm{N}V1$ and $\mathrm{N}V2$, respectively, (marked with arrows) which indicates there is strain-induced splitting between $S_X$ and $S_Y$ even in the GS orbital singlet.