Fractional domain walls from on-site softening in dipolar bosons

We study dipolar bosons in a 1D optical lattice and identify a region in parameter space—strong coupling but relatively weak on-site repulsion—hosting a series of stable charge-density-wave (CDW) states whose low-energy excitations, built from “fractional domain walls,” have remarkable similarities to those of non-Abelian fractional quantum Hall states. Here, a conventional domain wall between translated CDW's may be split by inserting strings of degenerate, but inequivalent, CDW states. Outside these insulating regions, we find numerous supersolids as well as a superfluid regime. The mentioned phases should be accessible experimentally and, in particular, the fractional domain walls can be created in the ground state using single-site addressing, i.e., by locally changing the chemical potential.

Figure 1

(a) How the CDW states, here for $\nu =k/2=2$, can be arranged in a so-called Bratteli diagram. Going from left to right, an elementary domain wall excitation is created in each step. A configuration corresponding to the dashed red line is shown in (b) and a configuration corresponding to the purple dotted line is shown in (c). In (b) and (c) we show only quasi-hole-like domain walls, but quasi-particle-like excitations can be represented analogously.

Figure 2

Schematic demonstration how a local change in the chemical potential can give rise to fractional domain walls, causing extended changes in the lattice configuration. By increasing or decreasing the local chemical potential on two neighboring sites, one can create domain walls [(b)–(d)] with charge $\pm q/2$, starting from the unperturbed state (a). The domain walls shown in this example are closely related [8] to the Majorana fermion excitations of the celebrated Moore-Read FQH state [23].

Figure 3

Phase diagram for $U=1.99V_1$, $V_{j>1}=0$, obtained by employing a Gutzwiller ansatz, together with perturbation theory up to third order in $t/U$. The yellow vertical lines represent the phase transitions between the different CDW states, and the diagram also displays the transitions between the insulating CDW regions, the supersolid (SS) phases and the superfluid (SF) region. The colorscale marks only the different phases.