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Physical review. B./Physical review. B

Experimental determination of energy-level structures of diamond silicon-vacancy centers in off-axis magnetic fields

Shu-Hao Wu, Xinzhu Li, Ian Gallagher, Lexington Mandachi, Benjamin J. Lawrie, Hailin Wang

Published Apr 21, 2025• 2 citations
Publisher

Abstract

We report the development of an experimental approach to efficiently determine the energy level structure of an individual silicon vacancy (SiV) center in a magnetic field along an arbitrary direction. This approach uses two coupling rates (one each for the ground and the excited states) to characterize the combined effects of static strain and dynamic Jahn-Teller coupling and exploits the fact that orbital Zeeman effects vanish when the magnetic field is normal to the SiV axis. With an analytical expression for the energy level structure of the SiV under a transverse magnetic field, the two coupling rates can be directly derived from two measurements: one on the frequency separation between two spin-conserved transitions and the other on the coherent population trapping resonance of the SiV ground spin states. A detailed comparison between the numerical calculation and the experimental result on the dependence of the spin-conserved splitting on both the amplitude and direction of the magnetic field further reveals unequal orbital magnetic coupling for the ground and excited states, indicating that unequal orbital quenching factors are needed for an accurate description of the SiV energy level structure in a magnetic field.

DOI
10.1103/physrevb.111.155426

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Physical review. B./Physical review. B•Jan 14, 2025•4 citations
We report the development of an experimental approach to efficiently determine the energy level structure of an individual silicon vacancy (SiV) center in a magnetic field along an arbitrary direction. This approach uses two coupling rates (one each for the ground and the excited states) to characterize the combined effects of static strain and dynamic Jahn-Teller coupling and exploits the fact that orbital Zeeman effects vanish when the magnetic field is normal to the SiV axis. With an analytical expression for the energy level structure of the SiV under a transverse magnetic field, the two coupling rates can be directly derived from two measurements: one on the frequency separation between two spin-conserved transitions and the other on the coherent population trapping resonance of the SiV ground spin states. A detailed comparison between the numerical calculation and the experimental result on the dependence of the spin-conserved splitting on both the amplitude and direction of the magnetic field further reveals unequal orbital magnetic coupling for the ground and excited states, indicating that unequal orbital quenching factors are needed for an accurate description of the SiV energy level structure in a magnetic field.
We report the development of an experimental approach that can characterize the energy level structure of an individual silicon vacancy (SiV) center in a magnetic field and extract the key parameters for the energy level structure. This approach builds upon a theoretical model that includes effects of the static strain, dynamic Jahn-Teller coupling, and magnetic field and introduces two coupling rates, one each for the ground and the excited states, to characterize the combined effects of strain and Jahn-Teller coupling. With the use of an analytical expression for the energy level structure of the SiV center under a transverse magnetic field, these two coupling rates can be directly derived from the measurement of the frequency separation between two spin-conserved transitions in a photoluminescence excitation spectrum and the measurement of the coherent population trapping resonance related to the SiV ground spin states. Additional experimental studies on the dependence of the energy level structure on the magnetic field amplitude and direction further verify the theoretical model and reveal contributions from unequal orbital magnetic coupling for the ground and excited states.
The neutral silicon--vacancy (SiV0^{0}0) center in diamond combines inversion symmetry with optical emission, making it a robust quantum emitter resilient to stray electric fields. Using first-principles density-functional theory, we quantify its response to isotropic strain spanning strong compression and tensile regimes (effective hydrostatic pressures of approximately −80-80−80 to 180180180~GPa). The coexistence of doubly degenerate ege_geg​ and eue_ueu​ levels produces a structural instability captured by a quadratic product Jahn--Teller model. Under isotropic compression, the zero-phonon line blue-shifts nearly linearly while the EgE_gEg​ phonon stiffens, suppressing vibronic instabilities and reducing Jahn--Teller quenching. Consequently, the Ham-reduced excited-state spin--orbit splitting increases substantially and the dark--bright vibronic gap widens. In contrast, isotropic tensile strain enhances vibronic effects and induces symmetry breaking beyond a critical strain, with tunneling-mediated dynamical averaging at the onset. Throughout the symmetry-preserving regime, parity remains well defined, so isotropic strain alone does not activate the dark transition. Charge-transition levels indicate photostability of the emission deep into the compressive regime, and near the highest photostable deformation (∼100\sim 100∼100~GPa), the radiative lifetime increases due to a reduced transition dipole moment despite the increasing optical energy. These trends yield compact calibration relations linking optical and spin observables to isotropic strain and establish SiV0^{0}0 as a symmetry-protected, strain-tunable quantum emitter operating into the multi-megabar-equivalent regime.
The negatively charged silicon vacancy (SiV) color center in diamond has recently proven its suitability for bright and stable single photon emission. However, its electronic structure so far has remained elusive. We here explore the electronic structure by exposing single SiV defects to a magnetic field where the Zeeman effect lifts the degeneracy of magnetic sublevels. The similar responses of single centers and a SiV ensemble in a low strain reference sample prove our ability to fabricate almost perfect single SiVs, revealing the true nature of the defect's electronic properties. We model the electronic states using a group-theoretical approach yielding a good agreement with the experimental observations. Furthermore, the model correctly predicts polarization measurements on single SiV centers and explains recently discovered spin selective excitation of SiV defects.
We investigate the magnetic field dependent photophysics of individual nitrogen-vacancy (NV) color centers in diamond under cryogenic conditions. At distinct magnetic fields, we observe significant reductions in the NV photoluminescence rate, which indicate a marked decrease in the optical readout efficiency of the NV's ground state spin. We assign these dips to excited state level anticrossings, which occur at magnetic fields that strongly depend on the effective, local strain environment of the NV center. Our results offer new insights into the structure of the NVs' excited states and a new tool for their effective characterization. Using this tool, we observe strong indications for strain-dependent variations of the NV's orbital g factor, obtain new insights into NV charge state dynamics, and draw important conclusions regarding the applicability of NV centers for low-temperature quantum sensing.
We report experimental studies of coherent population trapping and spin relaxation in a temperature range between 4 K and 100 mK in a silicon vacancy (SiV) center subject to a transverse magnetic field. Near and below 1 K, phonon-induced spin dephasing becomes negligible compared with that induced by the spin bath of naturally abundant 13C atoms. The temperature dependence of the spin dephasing rates agrees with the theoretical expectation that phonon-induced spin dephasing arises primarily from orbital relaxation induced by first order electron-phonon interactions. A nearly 100-fold increase in spin lifetime is observed when the temperature is lowered from 4 K to slightly below 1 K, indicating that two-phonon spin-flip transitions play an essential role in the spin relaxation of SiV ground states.
We report experimental studies of coherent population trapping (CPT) and spin relaxation in a temperature range 4 K--100 mK in a silicon vacancy (SiV\text{Si}VSiV) center subject to a transverse magnetic field. The spin linewidth, which is determined by spin dephasing, is extracted from power dependent CPT linewidths. Near and below 1 K, phonon-induced spin dephasing becomes negligible compared with that induced by the spin bath of naturally abundant 13C^{13}\mathrm{C}13C atoms. The temperature dependence of the spin dephasing rates agrees with the theoretical expectation that phonon-induced spin dephasing arises primarily from orbital relaxation induced by first order electron-phonon interactions. A nearly 100-fold increase in spin lifetime is observed when the temperature is lowered from 4 K to slightly below 1 K, indicating that two-phonon spin-flip transitions play an essential role in the spin relaxation of SiV\text{Si}VSiV ground states.