Superfluid response of bosonic fluids in composite optical potentials: angular dependence and Leggett's bounds

Abstract

We study the superfluid response of a dilute bosonic fluid in the presence of two-dimensional composite potentials (such as triangular, Kagomé and quasiperiodic potentials, or superlattices), which may be obtained for example by superposing multiple laser beams. We first find a sufficient condition for the external potential to yield a fully isotropic superfluid response. Then, we derive analytical expressions for Leggett's upper and lower bounds to the superfluid fraction (valid in the perturbative regime) that allow us to find the optimal direction along which each bound should be measured. Finally, we solve the problem numerically, and we confirm our analytical findings.

Figures (4)

• Figure 1: Composite optical potentials. Left: Typical momentum structure. The example shows a case with two shells ($M=2$), with the inner and outer shells generating square and triangular/hexagonal lattices, respectively ($N_1=4,\, N_2=6$). Right: Resulting potential in real space.
• Figure 2: Ground state and superfluid response in composite potentials. Top and bottom rows correspond respectively to a BEC (modeled by the GPE, with interaction strength $gN=14400\hbar^2/m$) in a Kagomé potential and a five-fold quasicrystal (see definitions in Table \ref{['tab:lattice_configs']}). From left to right, the panels show: the external potential $V(\mathbf{r})$, the ground state density, the momentum density (circles indicate peaks in the Fourier transform of the external potential, with yellow peaks being four times stronger than the red ones), and the superfluid fraction [dashed lines correspond to the perturbative results, Eqs. (\ref{['fs_pert']},\ref{['pert_upper']},\ref{['pert_lower']})].
• Figure 3: Angular dependence of Leggett's bounds in a five-fold quasicrystal. The plot shows the Leggett's bounds computed along different directions, for $V_1/gn \approx 0.9$ [compare with bottom-right panel of Fig. \ref{['fig:isotropic_fs']}]. The dashed red line corresponds to the numerically-extracted superfluid fraction, while the orange and green lines are its upper and lower Leggett's bounds, respectively. The black spots visible in the background indicate the Fourier peaks of the quasicrystal (in arbitrary units, and smoothed for visibility).
• Figure 4: Spectrum of a potential generated by interfering beams The blue dots show the location of the Fourier peaks of a potential of the form $V(\mathbf{r}) \propto \left|\sum_{j=1}^{N}e^{i\mathbf{k}_j\cdot \mathbf{r}}\right|^2$, generated by $N$ interfering beams with wavevectors ${\bf k}_j$ arranged as regular $N$-gons (red dots, with $N=3,4,5$ from left to right).