Magic density in a self-rephasing ensemble of trapped ultracold atoms

TL;DR

This paper demonstrates the existence of a 'magic density' in a trapped ultracold atom ensemble where the clock transition becomes insensitive to density fluctuations, enhancing quantum sensor stability.

Contribution

It introduces the concept of a 'magic density' in a self-rephasing bosonic ensemble, combining experimental observation with a numerical model to improve quantum sensor stability.

Findings

Identification of a 'magic density' point where density fluctuations do not affect the clock transition.

Qualitative agreement between Ramsey spectroscopy results and a coupled Bloch equations model.

Potential for enhanced stability in quantum sensors using this 'magic density' phenomenon.

Abstract

We investigate the collective spin dynamics of a self-rephasing bosonic ensemble of $^{87}$Rb trapped in a 1D vertical optical lattice. We show that the combination of the frequency shifts induced by atomic interactions and inhomogeneous dephasing, together with the spin self-rephasing mechanism leads to the existence of a `magic density': \textit{i.e} a singular operating point where the clock transition is first-order insensitive to density fluctuations. This feature is very appealing for improving the stability of quantum sensors based on trapped pseudo-spin-1/2 ensembles. Ramsey spectroscopy of the $|F=1,m_{F}=0\rangle\rightarrow|F=2,m_{F}=0\rangle$ hyperfine transition is in qualitative agreement with a numerical model based on coupled Bloch equations of motion for energy dependent spin vectors.