Vibrational relaxation dynamics of the nitrogen-vacancy center in diamond

We employ a combination of spectrally resolved optical pump-probe spectroscopy and excited-state ab initio molecular dynamics (ESAIMD) simulations to study the ultrafast vibrational relaxation dynamics of the ${}^{3}E$ excited state of negatively charged nitrogen vacancy ($\mathrm{N}{\mathrm{V}}^{-}$) defects. The experimental results reveal vibrational relaxation in the phonon sideband with a time constant of approximately 50 fs, in excellent agreement with the $\sim 40$-fs structural equilibration timescale predicted by ESAIMD simulations. The observed ultrafast vibrational energy relaxation implies that dynamical processes triggered by photoexcitation into the phonon sideband of the $\mathrm{N}{\mathrm{V}}^{-}$ center occur primarily in the lowest vibronic level of the ${}^{3}E$ state.

Figure 1

(a) Optical absorption spectrum of the $\mathrm{N}{\mathrm{V}}^{-}$ sample recorded at 77 K, revealing clear zero-phonon line (0PL), one-phonon line (1PL), and two-phonon line (2PL) transitions. The spectra of the pump pulses used to excite the 0PL and 1PL transitions are also shown as blue shaded; the inset illustrates the structure of the $\mathrm{N}{\mathrm{V}}^{-}$ defect within the diamond lattice, indicating the distances between vacancy and nitrogen atoms $d_{\text{N-V}}$ (green dashed line), as well as between vacancy and carbon atoms $d_{\text{C-V}}$ (gray dashed line); (b) Time-resolved, isotropic differential transmission spectra $S_{\mathrm{iso}}$ after 1PL photoexcitation (lower panel). The upper panel shows the $S_{\mathrm{iso}}$ spectrum obtained at a time delay of 1 ps (dashed black line in the lower panel), depicting ground-state bleaching on the blue side of the 0PL and stimulated emission on the red side of the 0PL.

Figure 2

(a) Schematic of monitoring the vibrational relaxation process: 1PL excitation (gray solid arrow) creates population at $v{}^{\prime }=1$ in the excited state (accompanied by GSB of the probe to the blue side of the 0PL, blue arrows) that subsequently relaxes to the vibrational ground state $v^{\prime }=0$ within the time $\tau$ (gray dashed arrow). Stimulated emission on the red side of the 0PL probe spectrum (red arrows) occurs when population has relaxed. (b) Early-time $S_{\mathrm{iso}}$ spectra obtained after 0PL excitation (left) and 1PL excitation (right). (c) Zeroth moment of $S_{\mathrm{iso}}$ for 0PL excitation (upper panel) and 1PL excitation (lower panel) of the probe on the blue side and red side of the 0PL; the time shift between the zeroth momenta of blue and red sides of 1PL excitation give the relaxation time $\tau$. (d) First moment of $S_{\mathrm{iso}}$ for 0PL excitation (gray dots) and 1PL excitation (black dots). The black line is a fit of the 1PL data to the relaxation model.

Figure 3

Simulated ESAIMD trajectories for N-V (green line) and C-V distances (gray line). At $t=0\mathrm{fs}$, an electron is promoted from the $a_1$ HOMO to the $e$ LUMO, representative of the electronic excitation of the $\mathrm{N}{\mathrm{V}}^{-}$ defect. The dashed lines indicate the calculated equilibrium distances of the ${}^{3}E$ excited state.