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

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 $|F=1,m_F=0⟩\to |F=2,m_F=0⟩$ hyperfine transition is in qualitative agreement with a numerical model based on coupled Bloch equations of motion for energy dependent spin vectors.

arXiv comment7 pages, 2 figures

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