Nonlinear Sensing With Collective States of Ultracold Atoms in Optical Lattices

Abstract : The goal of this project was to develop and evaluate methods for nonlinear sensing with collective states of ultracold atoms in optical lattices. Major results include the following: (1) We showed how to use the collapse-and-revival dynamics of interacting atoms to measure m-body interaction strengths with accuracy scaling as n(m-1/2); m = 1 corresponds to the shot-noise limit. We developed techniques for both m=2 and m=3, the latter exploiting 3-body interactions with super-Heisenberg scaling n-5/2. (2) We predicted novel spin-dependent 3- body interactions with applications to sensing external magnetic fields. (3) We proposed a method to measure gravitational accelerations (little g) in a very small region of space (e.g., lending itself to atom-chip-based approaches), with potentially long interrogation times. (4) We showed how collapse-and-revival physics can be used to probe Mott insulating and fermionic states. (5) We characterized the effective 3-, 4-, and 5-body interactions between trapped atoms, including universal, effective range, and nonuniversal physics. (6) We developed a dynamical decoupling protocol for removing the influence of 2-body interactions, leaving 3-body interactions dominant. Finally, (7) We characterized Feshbach resonances of magnetic atoms providing results for using spinor atoms to measure magnetic fields accurately.