Methods for developing new kinds of inertial sensors with optical cavities and optical lattices

There is currently major interest in developing novel quantum sensors that utilize interparticle entanglement or other quantum features to sense with a quantum advantage. Optical cavities, operating in both the dispersive and dissipative regimes, provide a pristine environment to mediate nonlinear interactions between atoms, leading to spin squeezing and entanglement. In collaboration with the Thompson and Rey groups at JILA, we analyze squeezing between momentum states in a matter-wave experiment in a vertical cavity. Here, the influence of gravity allows one to isolate two momentum states from the rest of the momentum manifold, and by driving the cavity with an external laser, one can achieve either one-axis twisting or two-axis countertwisting (TACT) even in the presence of collective decoherence. Other atom interferometry systems that we study involve atoms in three- dimensional optical lattices controlled by machine-learned protocols. Quantum sensors can also be developed for higher dimensional systems where quantum enhanced multiparameter estimation for vector or tensorial sensing becomes possible. While these systems can lead to highly entangled states, the extra complication can make examining the metrological usefulness of the generated states difficult. To this end, we develop a computationally efficient algorithm that determines the unitary evolution that a quantum state is most sensitive to, allowing one to unravel the optimal metrological use of state in complex systems where intuition from simple canonical squeezing examples breaks down.