Quadrature interferometry for nonequilbrium ultracold atoms in optical lattices

We propose an interaction-based interferometric technique for making time-resolved measurements of quadrature operators of nonequilibrium ultracold atoms in optical lattices. The technique creates two subsystems of magnetic atoms in different spin states and lattice sites--the arms of the interferometer. A Feshbach resonance turns off atom-atom interactions in one spin subsystem, making it a well-characterized reference state, while atoms in the other subsystem undergo nonequilibrium many-body dynamics for a variable hold time. The nonequilibrium evolution can involve a variety of Hamiltonians, including systems with tunneling and spin-orbit couplings using artificial gauge fields. Interfering the subsystems via a second beam-splitting operation, time-resolved quadrature measurements are directly obtained by detecting relative spin populations. Analyzing a simple application of the interferometer, we obtain analytic predictions for quadratures for deep optical lattices with negligible tunneling. As a second, distinct application, we show that atom-atom interaction strengths can in principle be determined with super-Heisenberg scaling $n^{-3/2}$ in the mean number of atoms per lattice site $n$, making it possible to test the physics of interaction-based quantum metrology.