Vibronic States and Their Effect on the Temperature and Strain Dependence of Silicon-Vacancy Qubits in 4$\textit{H}$-SiC
Silicon-vacancy qubits in silicon carbide ( Si C ) are emerging tools in quantum-technology applications due to their excellent optical and spin properties. In this paper, we explore the effect of temperature and strain on these properties by focusing on the two silicon-vacancy qubits, V1 and V2, in 4$\textit{H}$-SiC. We apply density-functional theory beyond the Born-Oppenheimer approximation to describe the temperature-dependent mixing of electronic excited states assisted by phonons. We obtain a polaronic gap of around 5 and 22 meV for the V1 and V2 centers, respectively, which results in a significant difference in the temperature-dependent dephasing and zero-field splitting of the excited states, which explains recent experimental findings. Finally, we also compute how crystal deformations affect the zero-phonon line of these emitters. Our predictions are important ingredients in any quantum applications of these qubits sensitive to these effects.