Quantum phases of bosonic chiral molecules in helicity lattices

We reveal the existence of polarizing quantum phases for the enantiomers of cold, interacting chiral molecules in an optical helicity lattice by means of an extended Bose-Hubbard model. These recently proposed lattices have sites with alternating helicity which exert a discriminatory force on chiral molecules with different handedness. In our study of the phase diagram we find that a strong dipolar repulsion between molecules results in the separation of left and right enantiomers.

Figure 1

Left: Illustration of a conventional optical lattice. Oscillating electric fields induce a periodic potential for atoms (represented as yellow circles). We show an homogeneous lattice potential $V=V_0[{sin}^2\left(kx\right)+{sin}^2\left(ky\right)]$, where $k$ depends on the laser's wavelength [10]. Right: Illustration of a square helicity lattice. Red and blue regions correspond to sites with opposite helicity densities $h$ [9] which induce a discriminatory force on enantiomers [6].

Figure 2

Illustrations of a representative set of quantum phases. Red and blue squares correspond left and right sites, respectively. Solid squares correspond to superfluid sites, cross-hatched squares correspond to insulator sites, and open squares correspond to unoccupied sites. The lattices in the second row correspond to equivalent degenerate phases by exchanging left with right sites.

Figure 3

Phase diagrams for $V=V_{LR}$ and ${\mu }_L={\mu }_R$ as a function of the chemical potential $\mu /U$ and hopping $t/U$.

Figure 4

Average occupations $n$ (blue solid lines), $|n_L-n_R|$ (dashed orange lines), and $|n_A-n_B|$ (dotted green lines) for $V=V_{LR}=0.2U$ as a function of $\mu /U$. We show results for $t=0$ (upper panel) and $t=0.02U$ (bottom panel).

Figure 5

Phase diagrams for $V\ne V_{LR}$ and ${\mu }_L={\mu }_R$ as a function of the chemical potential $\mu /U$ and hopping $t/U$.

Figure 6

Ground-state occupations $\langle n_{\chi }\rangle$ [(a), (b)] and condensate fractions ${\mathrm{\Omega }}_{c,\chi }$ and polarizations $\mathrm{\Delta }{n}_{\text{h.l.}}$ [(c), (d)] obtained from ED for $V=V_{LR}=0.2U$. We consider five enantiomers of each handedness in (a) and (c), and three in (b) and (d).