The optimal frequency window for Floquet engineering in optical lattices

Abstract

The concept of Floquet engineering is to subject a quantum system to time-periodic driving in such a way that it acquires interesting novel properties. It has successfully been employed in atomic quantum gases in driven optical lattices. Typically, Floquet engineering is based on two approximations. On the one hand, it is assuming that resonant excitations to high-lying states above some energy gap are suppressed for sufficiently low driving frequencies, so that the system can be described within some low-energy subspace (e.g. spanned by the lowest Bloch band of a lattice). On the other hand, the driving frequency is also assumed to still be large compared to the typical energy scale of this low-energy subspace, so that it does not resonantly create excitations within this space. Eventually, on some time scale \(\tau\), deviations from these approximations will make themselves felt as unwanted heating. Floquet engineering, thus, requires a window of driving frequencies, where both types of heating processes are suppressed on the experimentally relevant time scale. In this paper, we theoretically investigate the existence of such an optimal frequency window, using the example of interacting bosons in a shaken optical lattice. We find that the maximum value of \(\tau\), measured in the experimentally relevant unit of the tunneling time, increases with the lattice depth.