Quadrature interferometry for nonequilibrium ultracold atoms in optical lattices

摘要

We develop an interferometric technique formaking time-resolved measurements of field-quadrature operatorsnfor nonequilibrium ultracold bosons in optical lattices. The technique exploits the internal state structure ofnmagnetic atoms to create two subsystems of atoms in different spin states and lattice sites. A Feshbach resonancenturns off atom-atom interactions in one spin subsystem, making it a well-characterized reference state,while atomsnin the other subsystem undergo nonequilibrium dynamics for a variable hold time. Interfering the subsystemsnvia a second beam-splitting operation, time-resolved quadrature measurements on the interacting atoms arenobtained by detecting relative spin populations. The technique can provide quadrature measurements for anvariety of Hamiltonians and lattice geometries (e.g., cubic, honeycomb, superlattices), including systems withntunneling, spin-orbit couplings using artificial gauge fields, and higher-band effects. Analyzing the special casenof a deep lattice with negligible tunneling, we obtain the time evolution of both quadrature observables andntheir fluctuations. As a second application, we show that the interferometer can be used to measure atom-atomninteraction strengths with super-Heisenberg scaling ¯nn−3/2 in the mean number of atoms per lattice site, andnstandard quantum limit scaling Mn−1/2 in the number of lattice sites. In our analysis, we require M u0002 1 and fornrealistic systems ¯n is small, and therefore the scaling in total atom number N = ¯nM is below the Heisenbergnlimit; nevertheless, measurements testing the scaling behaviors for interaction-based quantum metrologies shouldnbe possible in this system.