Abstract
We present a procedure that makes use of group theory to analyze and predict the main properties of the negatively charged nitrogen-vacancy (NV) center in diamond. We focus on the relatively low temperature limit where both the spin–spin and spin–orbit effects are important to consider. We demonstrate that group theory may be used to clarify several aspects of the NV structure, such as ordering of the singlets in the (e2) electronic configuration and the spin–spin and spin–orbit interactions in the (ae) electronic configuration. We also discuss how the optical selection rules and the response of the center to electric field can be used for spin–photon entanglement schemes. Our general formalism is applicable to a broad class of local defects in solids. The present results have important implications for applications in quantum information science and nanomagnetometry.
Export citation and abstract BibTeX RIS
GENERAL SCIENTIFIC SUMMARY Introduction and background. Nitrogen-vacancy (NV) centres have emerged as promising candidates for a number of applications, ranging from high spatial resolution imaging to quantum computation. At low temperatures, the optical transitions of the NV centre become very narrow and can be coherently manipulated, allowing for spin–photon entanglement generation for quantum communication and all optical control. A detailed understanding of the properties of this defect is critical for many of these applications.
Main results. Here we present a formalism based on standard group theory combined with ab initio calculations. We consider the perturbations that lower the symmetry of the point defect, such as strain and electric field. Our analysis shows that (i) the ordering of the triplet and singlet states in the ground state configuration of NV centres is 3A2, ψ1E, ψ1A1 and that the distance between them is of the order of the exchange term of the electron–electron Coulomb energy; (ii) the non-axial spin–orbit interaction does not mix the eigenstates of the centre in a given multiplet but electron spin–spin interaction is responsible for the spin state mixing of the excited state; and (iii) external electric fields can be used to tune the polarization properties of optical transitions and the wavelength of emitted photons via the inverse piezoelectric effect which explains the Stark effect in NV centres.
Wider implications. Our paper provides the foundation for coherent interaction between electronic spins and photons in solid state. The formalism can be applied to any point defect in solid-state physics that is suitable for the desired application.
Figure. Left: energy diagram of the unperturbed nitrogen-vacancy centre in diamond. Note that each electronic configuration can contain triplets (left column) as well as singlets (right column), which have been drawn in separated columns for clarity. Red arrows indicate allowed optical transitions via electric dipole moment interactions. The circular arrows between the states E1,2 and Ex,y represent the mixing due to spin–spin interaction (ae configuration, 3E state). Dashed lines indicate possible non-radiate processes assisted by spin–orbit interaction. In the ground state (e2 configuration, 3A2 state), the distance between singlets and triplets is equal to the exchange energy of Coulomb interaction (2J). The horizontal dashed blue line represents the orbital energy of the ground state (without including spin–spin interaction). Right: spin–photon entanglement generation. When the NV centre is prepared in the excited state A2(3E), the electron can decay to the ground state 3A2 ms = 1 (ms = −1) by emitting a right (left) circularly polarized photon.