Infrared absorption band and vibronic structure of the nitrogen-vacancy center in diamond

Negatively charged nitrogen-vacancy (NV${}^{-}$) color centers in diamond have generated much interest for use in quantum technology. Despite the progress made in developing their applications, many questions about the basic properties of NV${}^{-}$ centers remain unresolved. Understanding these properties can validate theoretical models of NV${}^{-}$, improve their use in applications, and support their development into competitive quantum devices. In particular, knowledge of the phonon modes of the ${}^1{A}_1$ electronic state is key for understanding the optical pumping process. Using pump-probe spectroscopy, we measured the phonon sideband of the ${}^{1}E\to {}^1{A}_1$ electronic transition in the NV${}^{-}$ center. From this we calculated the ${}^{1}E\to {}^1{A}_1$ one-phonon absorption spectrum and found it to differ from that of the ${}^{3}E\to {}^3{A}_2$ transition, a result which is not anticipated by previous group-theoretical models of the NV${}^{-}$ electronic states. We identified a high-energy 169-meV localized phonon mode of the ${}^1{A}_1$ level.

Figure 1

(a) The diamond lattice structure, containing an NV center. (b) The NV${}^{-}$ energy-level diagram and our pump-probe spectroscopy scheme. The states are labeled by their $C_{3v}$ representations and electron-spin multiplicities. Solid arrows are optical and microwave transitions, and dashed arrows are nonradiative transitions. The label “ISC” indicates intersystem crossing, which occurs primarily for the ${}^{3}E$ $m_s=\pm 1$ states and is responsible for optical pumping. (c) A configuration coordinate diagram for $A_1$ phonon modes showing the harmonic nuclear potential wells and phonon energy levels. The configuration for each electronic state is denoted in parentheses, and $Q_{A_1}$ is the normal nuclear coordinate. With no electronic Coulomb repulsion, the ${}^3{A}_2$, ${}^{1}E$, and ${}^1{A}_1$ levels are of the $a_1^2{e}^2$ configuration and the ${}^{3}E$ level is of the $a_1{e}^3$ configuration. With Coulomb repulsion included to first order, the ${}^{1}E$ and ${}^1{A}_1$ levels couple with the ${}^1{E}^{\prime }$ (configuration $a_1{e}^3$) and ${}^1{A}_1^{\prime }$ (configuration $e^4$) levels, respectively. This coupling is denoted by the parameters ${\kappa }_E$ and ${\kappa }_A$.

Figure 2

The experimental apparatus. The data acquisition device (DAQ) monitors the chopper wheel state and triggers a spectrum acquisition when the pump is blocked or unblocked. The computer collects “pump blocked” and “pump unblocked” transmission spectra.

Figure 3

(a) The supercontiuum absorption spectrum collected at 10 K for diamond sample B8 using 35 mW of pump-laser light. PSB fluorescence from ${}^{3}E\to {}^3{A}_2$ is present for wavelengths shorter than 840 nm and has been subtracted out. The vertical ticks indicate the expected PSB absorption energies for 71- and 169-meV phonons, which align with some of the absorption features. (b) The fluorescence spectrum of a similar diamond collected at 4 K. The vertical ticks indicate the expected PSB absorption energies for 64-meV phonons. Although the 686-, 692-, and 696-nm features are often ignored, they are vital to our comparison of the ${}^{1}E\to {}^1{A}_1$ and ${}^{3}E\to {}^3{A}_2$ PSBs, as they give rise to peaks (3)–(5) in Fig. 4.

Figure 4

The one-phonon spectra for the ${}^{1}E\to {}^1{A}_1$ and ${}^{3}E\to {}^3{A}_2$ transitions, extracted from Fig. 3. The above spectra are normalized to have equal areas, and the ${}^3{A}_2$ curve is vertically offset for clarity. In each spectrum we see five peaks, labeled (1)–(5), though the ${}^1{A}_1$ peaks are shifted to higher energies (see Table ).