Dipolar Molecules in Optical Lattices

We study the extended Bose-Hubbard model describing an ultracold gas of dipolar molecules in an optical lattice, taking into account all on-site and nearest-neighbor interactions, including occupation-dependent tunneling and pair tunneling terms. Using exact diagonalization and the multiscale entanglement renormalization ansatz, we show that these terms can destroy insulating phases and lead to novel quantum phases. These considerable changes of the phase diagram have to be taken into account in upcoming experiments with dipolar molecules.

Figure 1

Dependence of the dipolar part (subscript $D$) of $U$, $V$, $T$, and $P$ on the lattice flattening $\kappa$ for lattice depth $V_0=6E_R$ and $\gamma =52$.

Figure 2

We plot various properties of the exact ground state of a half-filled system as a function of dipole moment $d$. Fig. (a) shows the contribution of the CB states to the ground state of the system for $N=8$. In Fig. (b) we plot the one-particle and two-particle correlation functions ${\varphi }_i$ and ${\Phi }_i$. The dotted line shows ${\varphi }_i$ when we neglect the terms $T$ and $P$. When $T$, $P\ne 0$, the solid line and dash-dotted line shows ${\varphi }_i$ and ${\Phi }_i$ respectively as a function of dipole moment $d$. In Fig. (c) we plot the fidelity susceptibility $\chi (d)$ for the half-filled system for different system sizes. In Fig. (d) we have shown the structure-factor $S$ at different ordering wave vectors for the half-filled system with 16 sites.

Figure 3

ED phase diagram without (left) and with (right) taking into account $T$ and $P$. The color denotes the superfluidity fractions, ${\varphi }_i$ and ${\Phi }_i$. Neglecting $T$ and $P$, for large enough $d$ and $\mu$ the system is always in an insulating phase and the average number of particles is a multiple of $1/2$. CB (${\mathrm{CB}}_2$) denotes a checkerboard phase where sites with 0 and 1 (2) particles alternate. Including the new terms, the insulating phases vanish for large enough $d$, and a PSF appears. We truncate the Hilbert space at a maximal occupation number of 4 particles per site. We exclude data points where the occupation number becomes too high (white region).

Figure 4

Results for the BH Hamiltonian (1) in a chain with $N=128$ using MERA with $m=8$, revealing checkerboard (CB and ${\mathrm{CB}}_2$) order, as well as superfluid (SF and SF’) and pair-superfluid phases (PSF). (a) Mean occupation, (b) mean SF order parameter, (c) mean PSF order parameter, and (d) mean NN density correlations.

Figure 5

The one-particle and two-particle correlation functions ${\varphi }_i$ (solid line) and ${\Phi }_i$ (dotted line) as a functions of dipole moment $d$ when the full dipolar interactions are taken into account corresponds qualitatively to the calculations truncated at NNs (Fig. 2). The large ${\Phi }_i$ and negative ${\varphi }_i$ when terms $T$ and $P$ are taken into account indicate the breakdown of the CB phase to a PSF. Calculations for ED at half-filling with $N=16$.