Preserving coherent spin and squeezed spin states of a spin-1 Bose-Einstein condensate with rotary echoes

TL;DR

This paper demonstrates that rotary echo sequences can significantly extend the coherence of both coherent and squeezed spin states in a spin-1 Bose-Einstein condensate, enabling enhanced quantum measurements beyond the standard quantum limit.

Contribution

The study introduces a continuous driving protocol using rotary echoes to preserve spin coherence and squeezing in a spin-1 condensate under magnetic noise, with analytical and numerical validation.

Findings

Spin coherence is maintained longer with rotary echoes under specific conditions.

Both spin average and squeezing are simultaneously stabilized.

The method enables quantum measurements beyond the standard quantum limit.

Abstract

A challenge in precision measurement with squeezed spin state arises from the spin dephasing due to stray magnetic fields. To suppress such environmental noises, we employ a continuous driving protocol, rotary echo, to enhance the spin coherence of a spin-1 Bose-Einstein condensate in stray magnetic fields. Our analytical and numerical results show that the coherent and the squeezed spin states are preserved for a significantly long time, compared to the free induction decay time, if the condition $h\tau = m\pi$ is met with $h$ the pulse amplitude and $\tau$ pulse width. In particular, both the spin average and the spin squeezing, including the direction and the amplitude, are simultaneously fixed for a squeezed spin state. Our results point out a practical way to implement quantum measurements based on a spin-1 condensate beyond the standard quantum limit.