Floquet dynamics of ultracold atoms in optical lattices with a parametrically modulated trapping potential

TL;DR

This paper explores how strong, modulated trapping potentials in ultracold atom optical lattices enable Floquet engineering of quantum states, revealing rich dynamics and potential for creating Floquet condensates that mimic classical orbits.

Contribution

It introduces a novel experimental setup with a strong, time-periodically modulated trap, and develops a Mathieu approximation to accurately construct near-resonant Floquet states in this context.

Findings

Resonant trap modulation creates nonlinear Floquet states.

Phase of trap turn-on significantly influences state populations.

Effective ground states enable Floquet condensates following classical orbits.

Abstract

Experiments with ultracold atoms in optical lattices usually involve a weak parabolic trapping potential which merely serves to confine the atoms, but otherwise remains negligible. In contrast, we suggest a different class of experiments in which the presence of a stronger trap is an essential part of the set-up. Because the trap-modified on-site energies exhibit a slowly varying level spacing, similar to that of an anharmonic oscillator, an additional time-periodic trap modulation with judiciously chosen parameters creates nonlinear resonances which enable efficient Floquet engineering. We employ a Mathieu approximation for constructing the near-resonant Floquet states in an accurate manner and demonstrate the emergence of effective ground states from the resonant trap eigenstates. Moreover, we show that the population of the Floquet states is strongly affected by the phase of a sudden turn-on of the trap modulation, which leads to significantly modified and rich dynamics. As a guideline for further studies, we argue that the deliberate population of only the resonance-induced effective ground states will allow one to realize Floquet condensates which follow classical periodic orbits, thus providing challenging future perspectives for the investigation of the quantum-classical correspondence.