Vibronic states and their effect on the temperature and strain dependence of silicon-vacancy qubits in 4H silicon carbide

Silicon-vacancy qubits in silicon carbide (SiC) 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 4H 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 polaronic gap around 5 and 22~meV for V1 and V2 centers, respectively, that results in significant difference in the temperature dependent dephasing and zero-field splitting of the excited states, which explains recent experimental findings. 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.