Spin Relaxation Times in Transition Metal-Based Defects Spin Qubits

In this work we discuss a method for the calculation of relaxation times (T1) in solid state qubits. Solid state quantum systems are an important platform for the implementation of qubits for quantum information processing. The main issue related to this technology is that in contrast to molecular qubits, solid state qubits are characterized by a much stronger coupling to the environment with consequent loss of coherence in the quantum mechanical state. A typical operational T1 for a spin qubit is usually around 1 ms[1].
The spin orbit has been shown to play an essential role in the spin-lattice relaxation process for defects with d orbitals and especially for transition metal defects. It is known that the spin relaxation in these systems is dominated by the spin orbit interaction, however, the details of the process are still unclear. The discovery and the electronic structure characterization of new spin defects such as Ge vacancy defects in diamond[2], defects in transition metal dichalcogenides [3] and in ZnO[4] are making these questions even more important.
Here we report a theoretical study of the relaxation time of spin qubits characterized by strong spin orbit effects. Our approach is based on perturbation theory beyond first order in the electron-phonon interaction. After discussing the method and how this can be derived from the full density matrix Lindbladian dynamics, we propose to apply it on different transition metal based spin defects.
[1] Wolfowicz, Gary, F. Joseph Heremans, Christopher P. Anderson, Shun Kanai, Hosung Seo, Adam Gali, Giulia Galli, and David D. Awschalom. “Quantum Guidelines for Solid-State Spin Defects.” Nature Reviews Materials 6, 1–20 (2021).
[2]Siyushev et al.. “Optical and microwave control of Germanium-vacancy center spins in diamond”, Phys. Rev. B 96 081201(R) (2017).
[3]Tsai, JY., Pan, J., Lin, H. et al., “Antisite defect qubits in monolayer transition metal dichalcogenides”. Nat Commun 13, 492 (2022).
[4] Paper under preparation