Tunable anisotropic superfluidity in an optical kagome superlattice

We study the phase diagram of the Bose-Hubbard model on the kagome lattice with a broken sublattice symmetry. Such a superlattice structure can naturally be created and tuned by changing the potential offset of one sublattice in the optical generation of the frustrated lattice. The superstructure gives rise to a rich quantum phase diagram, which is analyzed by combining quantum Monte Carlo simulations with the generalized effective potential Landau theory. Mott phases with noninteger filling and a characteristic order along stripes are found, which show a transition to a superfluid phase with an anisotropic superfluid density. Surprisingly, the direction of the superfluid anisotropy can be tuned by changing the particle number, the hopping strength, or the interaction. Finally, we discuss characteristic signatures of anisotropic phases in time-of-flight absorption measurements.

Figure 1

(a) Potential from Eq. (1) of the optical kagome superlattice using an enhanced LW laser in the $x$ direction with $\gamma =1.5$. Potential along cuts (dashed lines) in the (b) $a_2$ direction and (c) $a_1$ direction, respectively, showing the resulting potential offset $\mathrm{\Delta }\mu$ for sublattice A.

Figure 2

Average density $\overline{n}=(n_{\mathrm{A}}+n_{\mathrm{B}}+n_{\mathrm{C}})/3$ and density difference $\mathrm{\Delta }n=n_{\mathrm{A}}-(n_{\mathrm{B}}+n_{\mathrm{C}})/2$ vs $\mu$ from QMC with $T=U/300$ and $N=243$ sites at $t/U=0.025$ for different offsets $\mathrm{\Delta }\mu /U$.

Figure 3

Quantum phase diagram extrapolated to the thermodynamic limit obtained from QMC (blue) and multicomponent GEPLT in second order in $t/U$ (red) at (a) $\mathrm{\Delta }\mu /U=0$, (b) $\mathrm{\Delta }\mu /U=0.25$, and (c) $\mathrm{\Delta }\mu /U=0.5$. The vertical lines indicate the parameter ranges in Figs. 2 and 4 while the horizontal lines are used in Fig. 5.

Figure 4

Total superfluid density ${\rho }_{+}^{\mathrm{s}}=({\rho }_1^{\mathrm{s}}+{\rho }_2^{\mathrm{s}})/2$ and superfluid density difference ${\rho }_{-}^{\mathrm{s}}={\rho }_1^{\mathrm{s}}-{\rho }_2^{\mathrm{s}}$ vs filling $\overline{n}$ from QMC for $\beta U=1200$ and $N=243$ at $t/U=0.025$. Inset: schematic illustration of the different mechanisms for positive and negative anisotropy parameters.

Figure 5

Superfluid anisotropy parameter $I_{\pm }=({\rho }_1^{\mathrm{s}}-{\rho }_2^{\mathrm{s}})/({\rho }_1^{\mathrm{s}}+{\rho }_2^{\mathrm{s}})$ as a function of $t/U$ from QMC for $\beta U=2000$ and $N=432$ in the parameter range indicated by the horizontal lines in Fig. 3. Insets: QMC simulations of the TOF image for $t/U=0.0375, \beta U=800, N=243, \mathrm{\Delta }\mu /U=0.5$, and $\mu /U=-0.175$ (top) and $\mu /U=0.425$ (bottom).