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arXiv:2406.07772

Quantum embedding study of strain and charge induced Stark effects on the NV$^{-}$ center in diamond

Gabriel I. López‐Morales, Joanna M. Zajac, Johannes Flick, Carlos A. Meriles, Cyrus E. Dreyer

Published Jun 11, 2024• 0 citations
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Abstract

The NV$^{-}$ color center in diamond has been demonstrated as a powerful nanosensor for quantum metrology due to the sensitivity of its optical and spin properties to external electric, magnetic, and strain fields. In view of these applications, we use quantum embedding to derive a many-body description of strain and charge induced Stark effects on the NV$^{-}$ center. We quantify how strain longitudinal to the axis of NV$^{-}$ shifts the excited states in energy, while strain with a component transverse to the NV$^{-}$ axis splits the degeneracies of the $^{3}E$ and $^{1}E$ states. The largest effects are for the optically relevant $^{3}E$ manifold, which splits into $E_{x}$ and $E_{y}$ with transverse strain. From these responses we extract strain susceptibilities for the $E_{x/y}$ states within the quasi-linear regime. Additionally, we study the many-body dipole matrix elements of the NV$^{-}$ and find a permanent dipole 1.64 D at zero strain, which is somewhat smaller than that obtained from recent density functional theory calculations. We also determine the transition dipole between the $E_{x}$ and $E_{y}$ and how it evolves with strain.

DOI
10.48550/arxiv.2406.07772

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The negatively charged nitrogen vacancy (NV${}^{\ensuremath{-}}$) center in diamond is a well-known color center with interesting applications in nanoscale sensing and quantum metrology, due to its high sensitivity to minute local electric, magnetic, and strain fields. Motivated by these applications of the this center, the authors employ here first-principles calculations based on quantum embedding to derive a many-body description of its excited-state dipole couplings and strain susceptibilities, which underlie the electric field and strain induced Stark effects.
We report measurements of optically detected magnetic resonance spectra of ensembles of negatively charged nitrogen-vacancy (NV) centers in diamonds in the presence of strain and DC external electric fields. The Stark shift of the spectral lines is stronger when the axial magnetic field along the NV centers quantization axis is minimized. The shift is also enhanced at avoided crossings between the hyperfine levels at an axial field of 77 uT. Since the intrinsic strain in the diamond also induces a Stark shift, we are able to calculate the magnitude and direction of the strain within the crystal. We also use the Stark effect to map the electric field in the diamond volume between patterned electrodes.
Determining Strain Components in a Diamond Waveguide from Zero-Field ODMR Spectra of NV−^{-}− Center Ensembles
The negatively charged nitrogen-vacancy (NV−^{-}−) center in diamond has shown great potential in nanoscale sensing and quantum information processing due to its rich spin physics. An efficient coupling with light, providing strong luminescence, is crucial for realizing these applications. Laser-written waveguides in diamond promote NV−^{-}− creation and improve their coupling to light but, at the same time, induce strain in the crystal. The induced strain contributes to light guiding but also affects the energy levels of NV−^{-}− centers. We probe NV−^{-}− spin states experimentally with the commonly used continuous-wave zero-field optically detected magnetic resonance (ODMR). In our waveguides, the ODMR spectra are shifted, split, and consistently asymmetric, which we attribute to the impact of local strain. To understand these features, we model ensemble ODMR signals in the presence of strain. By fitting the model results to the experimentally collected ODMR data, we determine the strain tensor components at different positions, thus determining the strain profile across the waveguide. This shows that zero-field ODMR spectroscopy can be used as a strain imaging tool. The resulting strain within the waveguide is dominated by a compressive axial component transverse to the waveguide structure, with a smaller contribution from vertical and shear strain components.
Negatively charged nitrogen-vacancy (NV) centers and other color centers in diamonds have emerged as promising platforms for quantum communication, quantum information processing, and nanoscale sensing, owing to their long spin coherence times, fast spin control, and efficient photon coupling. Deterministic placement of individual color centers into nanophotonic structures is critical for scalable device integration, and ion implantation is the most viable technique. Nanofabrication processes, including diamond etching, are essential to realize these structures but can introduce crystal strain through lattice damage. In this work, we investigate the impact of ion implantation and nanofabrication-induced strain on the electronic spin levels of NV-centers. We demonstrate that the zero-field continuous-wave optically detected magnetic resonance (CW-ODMR) spectroscopy serves as a sensitive probe of local crystal strain. We report the presence of a shear strain feature in diamond substrates arising from the ion-implantation and nanofabrication processes, as evidenced by the asymmetric splitting black observed in the zero-field CW-ODMR spectrum of NV-centers.
Electron and nuclear spins of diamond nitrogen-vacancy (NV) centers are good candidates for quantum information processing as they have long coherence time and can be initialized and read out optically. However, creating a large number of coherently coupled and individually addressable NV centers for quantum computing has been a big challenge. Here we propose methods to use high-density diamond NV centers coupled by spin-spin interaction with an average separation on the order of 10 nm for quantum computing. We propose to use a strain gradient to encode the position information of each NV center in the energy level of its excited electron orbital state, which causes a shift of its optical transition frequency. With such strain encoding, more than 100 closely-packed NV centers below optical diffraction limit can be read out individually by resonant optical excitation. A magnetic gradient will be used to shift the electron spin resonant (ESR) frequencies of NV centers. Therefore, the spin state of each NV center can be individually manipulated and different NV centers can be selectively coupled. A universal set of quantum operations for two-qubit and three-qubit system is introduced by careful design of external drives. Moreover, entangled states with multiple qubits can be created by this protocol, which is a major step towards quantum information processing with solid-state spins.
The physical properties of diamond crystals, such as color or electrical conductivity, can be controlled via impurities.In particular, when doped with nitrogen and under certain conditions, optically active nitrogen-vacany centers (NV) can be induced.The center is an outstanding quantum spin system that enables, under ambient conditions, optical initialization, readout, and coherent microwave control with applications in sensing and quantum information.Under optical and radio frequency excitation, the Zeeman splitting of the degenerate states allows the quantitative measurement of external magnetic fields with high sensitivity.This study provides a pedagogical introduction to the properties of the NV centers as well as a step-by-step process to develop and test, a simple magnetic quantum sensor based on color centers with large potential for the development of highly compact multi-sensor systems.