Matter-Wave Platforms for Sensing Beyond the Standard Quantum Limit

We propose spin squeezing protocols to generate metrologically useful entanglement in the presence of decoherence with matter-wave systems. We model a current vertical cavity (VC) experiment of the Thompson Lab at JILA in which a packet of ⁸⁷Rb atoms fall under the influence of gravity through the cavity mode. By choosing a suitable initial fall time before a cavity drive is turned on, two momentum states can be energetically isolated from the rest of the momentum manifold allowing for a controllable platform for a cavity-mediated nonlinear interaction by way of a two-photon transition. We first demonstrate that, under suitable parameters, a constant cavity drive leads to a one-axis twisting (OAT) interaction. We explore different parameter regimes of this interaction and discuss how to achieve an appreciable amount of inter-particle entanglement even in the presence of collective emission via cavity decay. We then demonstrate that this squeezing can be sped up by periodically modulating the intensity and frequency of the cavity drive. This leads to a two-axis countertwisting (TACT) interaction which reaches Heisenberg limit scaling faster than OAT. We show that the states created by the TACT interaction saturate the quantum Cramér-Rao bound with simple quadrature measurements. Furthermore, the TACT interaction creates the Berry-Wiseman phase state which maximizes the information gained about an unknown phase after a single measurement, and so our proposal offers a promising platform to study previous theoretical work in quantum information science in a controllable experimental spin system.