Pair-Supersolid Phase in a Bilayer System of Dipolar Lattice Bosons

The competition between tunneling and interactions in bosonic lattice models generates a whole variety of different quantum phases. While, in the presence of a single species interacting via on site interaction, the phase diagram presents only superfluid or Mott insulating phases, for long-range interactions or multiple species, exotic phases such as supersolid or pair-superfluid appear. In this Letter, we show for the first time that the coexistence of effective multiple species and long-range interactions leads to the formation of a novel pair-supersolid phase, namely, a supersolid of composites. We propose a possible implementation with dipolar bosons in a bilayer two-dimensional optical lattice.

Figure 1

Schematic representation of two 2D optical lattice layers populated with dipolar bosons polarized perpendicularly to the lattice plane. The particles feel repulsive on site $U$ and nearest-neighbor $U_{\mathrm{NN}}$ interactions. Interlayer tunneling is completely suppressed, while a nearest-neighbor interlayer attractive interaction $W$ is present.

Figure 2

Pair insulating lobes for $\nu =0$, $1/2$, 1, $3/2$ (thick lines); lobes with respect to single particle-hole excitations (thin blue lines) for the dominant configurations in the ground state at $J=0.05U$; and $\mu =-0.4375U$, namely $m_i=0$ and $m_j=1$, 2 (for $i$, $j$ nearest neighboring sites). The inset shows a zoom of the pair phase diagram.

Figure 3

Phase diagram of the effective Hamiltonian, with $U_{\mathrm{NN}}=0.025U$, $W=-0.95U$, which can be obtained for $d_{\perp }=0.37d$. The black full lines are the semianalytic solution of Eq. (5) indicating the boundaries of the insulating lobes for the checkerboard ($\nu =1/2$) and the doubly occupied checkerboard ($\nu =1$). The black dashed lines are the boundaries of the insulating lobes for 1st order expansion of $H_{\mathrm{eff}}$. The shaded area is the PSS phase predicted by the Gutzwiller approach. The red line indicates the estimated limit of validity of $H_{\mathrm{eff}}^{(0)}$. The blue dash-dotted line indicates the upper limit of the region where the mapping onto 7 is almost exact.