Triggering single-molecule qubit spin dynamics via non-Abelian geometric phase effects

Abstract

We illustrate how macroscopic rotations can be utilised to trigger and control a spin dynamics within the ground doublet of both Kramers and non-Kramers-type molecular nanomagnets via the non-Abelian character of the time-evolution operator. For Kramers magnets, we show how this effect can be harnessed to realise single-qubit quantum gates and give the explicit example of a recently reported CoCl₂(tu)₄ single-molecule magnet (SMM). We demonstrate that gating operations could be performed on this magnet in as fast as 10 ps before the breakdown of adiabaticity, much faster than typical spin–lattice relaxation times. Based on this effect, we also suggest CoCl₂(tu)₄ as a quantum gyroscope for sensing yaw-axis rotations. For integer spin nanomagnets where non-axial crystal field interactions often lift ground state degeneracy, we show how spin dynamics from the non-Abelian geometric propagator can be recovered using non-adiabatic macroscopic rotations not-necessarily resonant with the tunnel splitting gap. Using the well-known TbPc₂ single-ion magnet as a further example, we identify an experimentally plausible non-adiabatic rotation that induces a coherent superposition of tunnelling ground states, tantamount to preparing each member of a TbPc₂ ensemble in the maximal angular momentum state |m_J = 6〉. The detection of an ensuing coherent oscillation of the macroscopic magnetisation polarised along the TbPc₂ principal magnetic axis after the completed rotation could then proceed via time-resolved magnetisation measurements.