Semi-Empirical Haken-Strobl Model for Molecular Spin Qubits

Understanding the physical processes that determine the relaxation $T_{1}$ and dephasing $T_2$ times of molecular spin qubits is critical for envisioned applications in quantum metrology and information processing. Recent spin-echo $T_1$ measurements of solid-state molecular spin qubits have stimulated the development of quantum mechanical models for predicting intrinsic spin qubit timescales using first-principles electronic structure methods. We develop an alternative semi-empirical approach to construct Redfield quantum master equations for molecular spin qubits using a stochastic Haken-Strobl model for a central spin with a fluctuating gyromagnetic tensor due to spin-lattice interaction and a fluctuating local magnetic field due to interactions with other lattice spins. Using a vanadium-based spin qubit as a case study, we compute qubit population and decoherence timescales as a function of temperature and magnetic field using a bath spectral density parametrized with a small number of $T_{1}$ measurements. The theory quantitatively agrees with experimental data over a range of conditions beyond those used to parametrize the model, demonstrating the generalization potential of the method. The ability of the model to describe the temperature dependence of the ratio $T_2/T_1$ is discussed and possible applications for designing novel molecule-based quantum magnetometers are suggested.