Adiabatic Control of the Phase Memory Relaxation in the Anticrossing Region

Abstract

In the vicinity of the anticrossing region of the spin sublevels, the effective magnetic moment of the electron spin is reduced, resulting in an increase in the lifetime of the spin coherence. Based on this phenomenon, the modified electron spin echo protocol is proposed to extend the coherence relaxation time. It includes the Hahn echo sequence with the additional detuning of the magnetic field applied during the intervals between two pulses and between the refocusing pulse and the echo. The simplest system with anticrossing sublevels is an ion whose electron spin is strongly coupled to its own nucleus. To realize the proposed protocol, a narrow anticrossing region is required. The promising candidate to realize the proposed protocol is the crystal [Ho(W₅O₁₈)₂]⁹⁻, whose spin transitions have been studied in the recent paper (Kundu et al. Commun Phys 6:38 (2023)). Near the clock transition, the spin evolution of the electron–nuclear spin system is described by a fictitious spin 1/2, but with the magnetic properties dictated by the properties of the ion. The numerical study shows that the spin coherence is not destroyed by the magnetic field detuning, but it reduces the phase relaxation. In addition, the use of the unequal detuning pulses results in a phase shift of the spin echo, which can be used to discriminate between the target signal and the unwanted echo contributions.