Coherent population trapping and spin relaxation of a silicon vacancy center in diamond at millikelvin temperatures

We report experimental studies of coherent population trapping (CPT) and spin relaxation in a temperature range 4 K--100 mK in a silicon vacancy ($\text{Si}V$) 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 $¹³\mathrm{C}$ 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 $\text{Si}V$ ground states.