Spin squeezing by geometric focusing in vacuum Rabi oscillations

Abstract

We show that vacuum Rabi oscillations can directly generate spin squeezing through geometric focusing on the Bloch sphere. Starting from a coherent spin state resonantly coupled to a cavity initially in the vacuum state, quantum fluctuations are focused by the curvature of the Bloch sphere as the collective spin approaches the atomic ground state, producing squeezing transverse to the direction of motion. The squeezing timescale is set by the collective Rabi frequency $t_s\sim 1/(g\sqrt{N})$. The optimal Wineland squeezing parameter scales as $ξ_{\rm opt}^2\propto N^{-1/3}$, which is an outcome of the competition between the geometric focusing effects and the cavity-field vacuum fluctuations. The squeezing remains robust against realistic dissipation. In the end, an application example of $^{171}$Yb is briefly discussed to show the feasibility of our protocol.