Quadrature interferometry for nonequilibrium ultracold bosons in optical lattices

TL;DR

This paper introduces a novel interferometric method for time-resolved quadrature measurements of nonequilibrium ultracold bosons in optical lattices, enabling insights into quantum dynamics and interaction strengths.

Contribution

The authors develop a new interferometric technique utilizing atomic internal states for precise quadrature measurements in ultracold lattice systems, applicable to various Hamiltonians and geometries.

Findings

Time evolution of quadrature observables and fluctuations in deep lattices.

Measurement of atom-atom interaction strengths with super-Heisenberg scaling.

Feasibility of testing quantum metrology scaling laws in ultracold atom systems.

Abstract

We develop an interferometric technique for making time-resolved measurements of field-quadrature operators for nonequilibrium ultracold bosons 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. 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 dynamics for a variable hold time. Interfering the subsystems via a second beam-splitting operation, time-resolved quadrature measurements on the interacting atoms are obtained by detecting relative spin populations. The technique can provide quadrature measurements for a variety of Hamiltonians and lattice geometries (e.g., cubic, honeycomb, superlattices), including systems with tunneling, spin-orbit couplings using artificial gauge fields, and higher-band effects. Analyzing the special case of a deep lattice with negligible tunneling, we obtain the time evolution of both quadrature observables and their fluctuations. As a second application, we show that the interferometer can be used to measure atom-atom interaction strengths with super-Heisenberg scaling n^(-3/2) in the mean number of atoms per lattice site n, and standard quantum limit scaling M^(-1/2) in the number of lattice sites M. In our analysis, we require M >> 1 and for realistic systems n is small, and therefore the scaling in total atom number N = nM is below the Heisenberg limit; nevertheless, measurements testing the scaling behaviors for interaction-based quantum metrologies should be possible in this system.