Phase-space distributions of Bose-Einstein condensates in an optical lattice: Optimal shaping and reconstruction

TL;DR

This paper demonstrates how quantum optimal control can shape and reconstruct complex phase-space states of Bose-Einstein condensates in optical lattices, enhancing quantum simulation capabilities.

Contribution

It introduces a method for optimal modulation of optical lattices to prepare and reconstruct non-trivial quantum states in phase space.

Findings

Successful preparation of translated and squeezed Gaussian states.

Complete reconstruction of non-trivial states via maximum likelihood tomography.

Enhanced dynamical tunneling signals using optimized Floquet-state superpositions.

Abstract

We apply quantum optimal control to shape the phase-space distribution of Bose-Einstein condensates in a one-dimensional optical lattice. By a time-dependent modulation of the lattice position, determined from optimal control theory, we prepare, in the phase space of each lattice site, translated and squeezed Gaussian states, and superpositions of Gaussian states. Complete reconstruction of these non-trivial states is performed through a maximum likelihood state tomography. As a practical application of our method to quantum simulations, we initialize the atomic wavefunction in an optimal Floquet-state superposition to enhance dynamical tunneling signals.