Magneto-optical properties of the neutral silicon-vacancy center in diamond under extreme isotropic strain fields

The neutral silicon--vacancy SiV$⁰$ 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 to 180 GPa). The coexistence of doubly degenerate e_g and e_u 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 E_g 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 $sim 100$ 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 as a symmetry-protected, strain-tunable quantum emitter operating into the multi-megabar-equivalent regime.