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.