Dynamical robustness of the conductivity of ultracold bosons confined in layered structures

Abstract

We study dynamical conductivity of strongly correlated bosons loaded in an optical lattice with restricted geometry in which gauge fields are present. We show that dynamics influenced by the uniform synthetic magnetic field combined with layered lattice structures changes into rich insulator-metallic behavior in the strongly correlated regime. Especially, the amplitude of optical conductivity for a given frequency is a nonmonotonous function of the number of layers $L$. In particular, conductivity for frequency corresponding to on-site interaction energy can abruptly vanish for a special number of applied layers. Moreover, such an insulating behavior is stable in the whole range of parameters in the Mott phase. This robustness arises from the complex gaplike behavior or from Dirac-like physics reflected in the quasiparticle energy spectra. Furthermore we show that a large interlayer tunneling anisotropy destabilizes the absence of conducting state. We also investigate the critical conductivity on the Mott-insulator--superfluid phase boundary and show the correspondence between the number of Hofstadter subbands and the number of layers. The obtained results also reveal that the value of critical conductivity gradually goes to zero when a three-dimensional system is approached. The experimental setup for generation of layered optical lattices is also proposed.