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

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.

Figure 1

Frequency dependence of the optical conductivity in the Mott phase with $f=1/2$ for the different number of layers (the case with $L=1$ was calculated in Ref. [20]). The hopping parameter was chosen with the values $J/U=0.03$ and $\eta =1$ (isotropic case) and the conductivity is plotted in ${\sigma }_Q$ unit $({\sigma }_Q$ is a quantum conductance). Figures are plotted for $n_0=1$ (the first lobe of the Mott-insulator phase).

Figure 2

Analogous parameters as in Fig. 1 but with $f=1/3$.

Figure 3

Analogous parameters as in Fig. 1 but with $f=1/4$.

Figure 4

The optical conductivity dependent on the number of layers for the special point $\omega =U$ and different values of $J/U$. We assume the isotropic case of the hopping parameter, i.e., (a)–(c) $\eta =1$ are plotted for $f=1/2,f=1/3$, and $f=1/4$, respectively. We observe the insulator behavior for $L=2,3,6$ and for $L=1,2,4,8$ numbers of layers for $f=1/3$ and $f=1/4$, respectively. In the case of the single-layer system see Ref. [20]. Conductivity is plotted in ${\sigma }_Q$ unit and for $n_0=1$.

Figure 5

Frequency dependence $\omega$ of: (a), (d), (g), (j) the single-particle density of states (DOS); (b), (e), (h), (k) the weighted single particle density of states for conductivity (DOSc); and (c), (f), (i), (l) the quasiparticle density of states (DOSq). Plots are made for (a)–(c) $f=0$; (d)–(f) $f=1/2$; (g)–(i) $f=1/3$; and (j)–(l) $f=1/4$. For DOSq with $n_0=1$ in (c), (f), (i), (l) we use $J/U=0.042,0.057,0.057,0.055$, respectively.

Figure 6

Distribution of $2\eta cos{k}_z$ argument of the sum in Eq. (7) for $\omega =U,\eta =1$ (red circles and green squares) and for different values of $L$ within density plot of DOSc, i.e., ${\rho }_q^{\alpha }(\omega /J,p)$. Red circle appears if ${\rho }_q^{\alpha }(2\eta cos{k}_z,p)=0$, green square appears if ${\rho }_q^{\alpha }(2\eta cos{k}_z,p)\ne 0$. (a) corresponds to $f=1/2$, (b) $f=1/3$, and (c) $f=1/4$. (b) and (c) explicitly show the vanishing components of the sum in Eq. (7) for the number of layers $L=2,3,6$ with $f=1/3$ and for $L=2,4,8$ with $f=1/4$ (dashed white lines).

Figure 7

The anisotropy dependence of the optical conductivity for the point $\omega =U$ and the special number of layers for which OC is robust with respect to the insulator state (see Fig. 4). Here we take $J/U=0.05$. Conductivity is plotted in ${\sigma }_Q$ unit and for $n_0=1$.