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Journal of Experimental and Theoretical Physics

Nonradiative Transitions 3E → 1A1 and $$^{1}\tilde {E}$$ → 3A2 in the NV– Center in Diamond

Yu. M. Belousov

Published May 1, 2022• 0 citations
Publisher

Abstract

A mechanism is proposed for a nonradiative transition between excited energy levels of the NV– center in diamond. The nonradiative transition between the levels of the spin triplet and the singlet is possible due to the spin–orbit interaction with simultaneous excitation of vibrational (vibronic) states of the cluster and the excitation of lattice phonons and, hence, can be obtained in the second order of perturbation theory. For describing this process, the spin–vibronic interaction operator and nonzero matrix elements ensuring nonradiative transitions are obtained. It is found that the matrix elements are proportional to the overlap integrals for one-particle electron wavefunctions. It is shown that the rate of transitions 3E → 1A1 and $$^{1}\tilde {E}$$ → 3A2 are described by identical expressions. Therefore, the nonradiative transitions considered here are explained not by a multiphonon process, but by the excitation of vibronic states of atoms of the NV– center. Numerical estimates are in good agreement with experimental data.

DOI
10.1134/s1063776122030128

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Nonradiative Transitions 3E → 1A1 and 1E~^{1}\tilde {E}1E~ → 3A2 in the NV– Center in Diamond
A mechanism is proposed for a nonradiative transition between excited energy levels of the NV– center in diamond. The nonradiative transition between the levels of the spin triplet and the singlet is possible due to the spin–orbit interaction with simultaneous excitation of vibrational (vibronic) states of the cluster and the excitation of lattice phonons and, hence, can be obtained in the second order of perturbation theory. For describing this process, the spin–vibronic interaction operator and nonzero matrix elements ensuring nonradiative transitions are obtained. It is found that the matrix elements are proportional to the overlap integrals for one-particle electron wavefunctions. It is shown that the rate of transitions 3E → 1A1 and 1E~^{1}\tilde {E}1E~ → 3A2 are described by identical expressions. Therefore, the nonradiative transitions considered here are explained not by a multiphonon process, but by the excitation of vibronic states of atoms of the NV– center. Numerical estimates are in good agreement with experimental data.
The positively charged nitrogen vacancy (NV+) center in diamond has been traditionally treated as a dark state due to the experimental lack of an optical signature. Recent computational studies have shown that it is possible for the NV+ defect to have an excited state transition equivalent to that of the negatively charged (NV−) center, but no photoluminescence (PL) predictions have been reported so far. We report the first ab initio calculation showing that the NV+ center presents quantum emission, with zero phonon line at 765 nm and a non-zero transition dipole moment, approximately one quarter of the transition dipole moment of NV−. We calculate the energy levels of the multielectron states under the time-dependent density functional theory (singlet and triplet E states), and using our recently developed frequency cutoff method, we predict the full PL spectrum. Our results suggest that this state cannot be considered intrinsically “dark” and charge specific quenching mechanisms should be investigated as the cause of the lack of optical activity in experimental characterizations.
The negatively charged nitrogen-vacancy (NV(-)) center in diamond is considered to be one of the most promising solid state systems for quantum information applications. Excited states of the NV(-) center play a center role in the proposed applications. Using a combination of first-principles calculations and vibronic interaction model analysis, we establish the presence of a dynamic Jahn-Teller effect in the (3)E excited state. The calculated temperature-dependent dephasing rate for the zero phonon line as well as the splitting of the first two vibronic states are in good agreement with experiment.
The spin-selective photokinetics of a single matrix-isolated impurity molecule with a triplet-triplet optical transition, T 0–T 1, is considered and the manifestations of the photokinetics in the fluorescence excitation spectra and intensity autocorrelation functions g (2)(τ) of the molecule undergoing narrow-band optical excitation is studied to resolve the fine structure of the transition. The rates of intersystem crossings (ISCs) T 1→S→T 0 to and from a nonradiating singlet state S of the molecule and the rate of population relaxation among the ground (T 0) state sublevels can be obtained from the spectra and g (2)(τ) using the analytical expressions obtained. New experiments on an individual NV defect center in nanocrystals of diamond, where, for the first time, the fine structure of its triplet-triplet 3 A-3 E zero-phonon optical transition (~637 nm) at 1.4 K was resolved, are interpreted. It is concluded that the rate of the ISC transition from the m S =0 sublevel of the excited 3 E state to the singlet 1 A state (~1 kHz) is much slower than the rates from the m S =±1 substates, while the rates of ISC transitions to different m S substates of the ground 3 A state are close to each other (~1 Hz). As a result, only the optical transition between m S =0 sublevels in the 3 A-3 E manifold contributes strongly to the fluorescence. The experimentally observed double-exponential decay of the g (2)(τ) function is explained by the two pathways available to the center for it to leave the S state: (i) the S→ T 0(m S )=0) transition and (ii) the S→T 0(m S =±1) transitions followed by the slow spin-lattice relaxation T 0(m S =±1)→T 0(m S =0) (rate ~0.1 Hz). The work is important for studies where the NV center is used as a single photon source or for quantum information processing.
We theoretically investigate the multiphonon effects on the optical emission spectra of the negatively charged nitrogen-vacancy (NV−) center in diamond and find that the fluorescence emission spectra described by the single frequency model agree quite well with the experimental data. From a comparison between our theory and the experimental results, we also find a reduction of the anti-Stokes shift of the emission spectra at high temperature. This is contradictory to the linear hole-phonon interaction model. We resolve this contradiction by adding the quadratic hole-phonon interaction to our model. Our theoretical analyses show that this may reduce the lattice relaxation energy. As a consequence, fewer phonons are emitted in the optical transition, therefore explaining the reduction of the anti-Stokes shift at high temperature.
The nitrogen-vacancy (NV) center in diamond is of high importance in quantum information processing applications. The operation of the NV center relies on the efficient optical polarization of its electron spin. However, the full optical spin-polarization process, which involves the intersystem crossing between the shelving singlet state and the ground-state triplet, is not understood. Here we develop a detailed theory of this process which involves a combination of pseudo- and dynamic Jahn-Teller interactions together with spin-orbit interaction. Our theory provides an explanation for the asymmetry between the observed emission and absorption spectra of the singlet states. We apply density functional theory to calculate the intersystem crossing rates and the optical spectra of the singlets, and we obtain a good agreement with the experimental data. Since the NV center serves as a template for other solid-state-defect quantum bit systems, our theory provides a toolkit to study them that might help optimize their quantum bit operation.
The nitrogen-vacancy (NV) center in diamond has emerged as a versatile atom-like system, finding diverse applications at both ambient and cryogenic temperatures. At room temperature, the NV center's spin-triplet electronic ground state has a long coherence time and can be read out and initialized using nonresonant optical excitation, which has enabled a wide range of metrology and quantum information applications. At cryogenic temperatures, the NV center exhibits a variety of narrow, atom-like optical transitions, which has made the NV center a promising platform for quantum optics applications. We use coherent optical manipulation of the NV center at cryogenic temperatures to probe its internal dynamics and aspects of its interactions with its environment.\nFirst, we investigate the intersystem crossing (ISC) process, which is a spin-dependent nonradiative decay mechanism that enables the electronic spin state to be optically initialized and read out at room temperature. We measure the ISC rates from different excited states as well as the rate at which interactions with phonons redistribute population between these states. Based on these measurements, we develop a theoretical model that unifies the phonon-induced mixing and ISC mechanisms. We find that our model is in excellent agreement with experiment and that it can be used to predict unknown elements of the NV center's electronic structure.\nSecond, we investigate a novel method of using coherent optical manipulation of the NV center's electronic spin to control a nearby nuclear spin. Coherent interactions between the NV center and nearby nuclear spins have enabled the development of NV center-based, multi-qubit quantum registers, but these techniques have generally required the application of microwave or radio-frequency radiation. We demonstrate control of the nuclear spin using an all-optical Raman technique and theoretically evaluate the extent to which the intrinsic physics of the NV center limits the coherence of this Raman-based manipulation technique.