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 been employed, for instance, for the realization of artificial magnetic fluxes in optical lattices and, typically, it is based on two approximations. First, the driving frequency is assumed to be low enough to suppress resonant excitations to high-lying states above some energy gap separating a low energy subspace from excited states. Second, the driving frequency is still assumed to be large compared to the energy scales of the low-energy subspace, so that also resonant excitations within this space are negligible. Eventually, however, deviations from both approximations will lead to unwanted heating on a time scale $\tau$. Using the example of a one-dimensional system of repulsively interacting bosons in a shaken optical lattice, we investigate the optimal frequency (window) that maximizes $\tau$. As a main result, we find that, when increasing the lattice depth, $\tau$ increases faster than the experimentally relevant time scale given by the tunneling time $\hbar/J$, so that Floquet heating becomes suppressed.

Highlights

  • The idea of Floquet engineering is to subject a quantum system to time-periodic driving in such a way that it acquires interesting properties that are difficult to achieve by other means

  • We depict the lowest-band zero-quasimomentum occupation n0(t ) in units of its initial value n0(0) at time t ≈ 40h/Js. This time is chosen to be large compared to the tunneling time h/Js, which is the relevant timescale for experiments

  • We focus on values of K/hω that are interesting for Floquet engineering

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Summary

INTRODUCTION

The idea of Floquet engineering is to subject a quantum system to time-periodic driving in such a way that it acquires interesting properties that are difficult to achieve by other means. This form of energy absoprtion (heating) can be reduced considerably by considering driving frequencies that are sufficiently large, so that absorbing an energy quantum of hω corresponds to an exponentially slow high-order process in which several elementary excitations are created at once [39,40] If this is the case, we can employ a rotating-wave approximate and describe the system by the time-averaged low-energy Hamiltonian (or compute further corrections using a high-frequency expansion [40,41,42,43,44]).

SYSTEM AND MODEL
LOW- AND HIGH-FREQUENCY APPROXIMATIONS
INTRABAND HEATING
INTRABAND AND INTERBAND HEATING
CONCLUSIONS
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