Characterization of Spin-Thermal Environment Interaction Leading to Nuclear Quadrupolar Spin Relaxation

The control of spin dynamics at the nanoscale is crucial for quantum technologies based on spin qubits. Quadrupolar nuclei with spin > ½ facilitates creation of N-qubit systems, the representation of many qubits with one nuclear species. Additionally, nuclei with strong quadrupole moments can be used to perform QIP with NQR. However, the strong quadrupole couplings lead to faster spin relaxation and stronger dissipation due to spin-environment interaction. It is crucial to analyze the effect of local environment fluctuations on spin-environment relaxation (SER) to correctly predict the evolution of the qubits implemented by the quadrupolar spins. The prediction of quadrupolar relaxation time (T1) in alkali halides improved considerably due to the inclusion of realistic phonon density of states, over approximate phonon dispersions. However, the predicted T1 is still off by an order of magnitude compared to measured data. Here, we extend the formulation by incorporating the full dispersion relations of thermal phonons to describe T1. Our study provides a framework to characterize the thermal noise affecting the nuclei spin qubits. We anticipate that this work will lead to tailoring the relaxation time by controlling phononic environment of the spin qubits.