Quantum metrology and simulation: squeezed matterwave interferometer and cavity-mediated momentum exchange interaction*

Collective cavity-QED systems have been powerful tools for generating large amounts entanglement involving the internal degrees of freedom of laser-cooled atomic ensembles. By coupling the internal states to the external degrees of freedom, we utimize the cavity-mediated interactions via internal states to generate entanglement between atoms of their momentum states. We then sucessfully inject the squeezed state into a matter-wave interferometer, and for the first time, achive a directly observed phase resolution below the standard quantum limit. By decoupling the internal state from the external states, the interaction between the matter-wave and the high finesse cavity can also induce a momentum exchange interaction where the atoms exchange their momentum states without involving the internal degrees of freedom. With the momentum exchange interaction, we obseve both the well-known one-axis twisting dynamics and the many-body energy gap that protect the coherence of the system. Through enginnering the interaction between matter-wave and cavity, our works could potentially find application in improving quantum sensing with matter-wave as well as providing a new platform for quantum simulation.