Quadrature interferometry for nonequilibrium ultracold atoms in optical lattices
Philip Johnson, Eite Tiesinga
We develop an interferometric technique for measuring quadrature operators of nonequilibrium states of ultracold atoms in optical lattices. The technique exploits the internal state structure of magnetic atoms to create two subsystems of 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. This evolution can involve many Hamiltonia, from single-band Bose-Hubbard to sytems with spin-orbit coupling, and lattice geometries, from simple-cubic to honeycomb. Interfering the subsystems via a second beam-splitting operation, time-resolved quadrature measurements are directly obtained by detecting relative spin populations. Analyzing the interferometer for the Bose-Hubbard Hamiltonian in a deep lattice, we predict the time evolution of both quadrature observables and their fluctuations, which can show both squeezing and antisqueezing. The system also makes possible investigations of interaction-based quantum metrology, where many-body dynamics are exploited to charaterize a system and its parameters. In particular, we show that the interferometer can be used to measure atom-atom interaction strengths with super-Heisenberg scaling $\barn}^-3/2}$ in the mean number of atoms per lattice site, and standard quantum limit (SQL) scaling $M^-1/2}$ in the number of lattice sites. In our analysis, we require $M\gg1,$ nevertheless, for realistic lattice systems our interferometer suggests up to an order of magnitude improvement in precision over the SQL
and Tiesinga, E.
Quadrature interferometry for nonequilibrium ultracold atoms in optical lattices, Physical Review Letters, [online], https://doi.org/10.1103/PhysRevA.87.013423, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=912677
(Accessed December 9, 2023)