First-principles Calculation of the Temperature-dependent Transition Energies in Spin Defects

Spin qubits associated with color centers are promising platforms for various quantum technologies. However, to be deployed in robust quantum devices, the variations of their intrinsic properties with the external conditions, and in particular, temperature, should be known with high precision. Unfortunately, a predictive theory on the temperature dependence of the resonance frequency of electron and nuclear spin defects in solids remains lacking. In this work, we develop a first-principles method for the temperature dependence of zero-field splitting, hyperfine interaction, and nuclear quadrupole interaction of color centers. As a testbed, we compare our ab-initio calculation results with experiments in the Nitrogen-Vacancy (NV) center finding good agreement. Interestingly, we identify the major origin of temperature dependence as a second-order effect of phonon vibration. Applying our method to various color centers, we provide theoretical predictions of the temperature effects on solid spin qubits for designing high-precision quantum sensors.