Dipolar Molecules in Optical Lattices

Abstract

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. PACS numbers: 37.10Jk,67.85.Hj,75.40.Cx Trapping and manipulating ultracold gases in optical lattices has allowed the realization of many-body physics in a controlled environment. For atoms interacting via contact interaction, a quantum phase transition from a superfluid (SF) to a Mott insulator (MI) has been predicted and observed [1]. In the simplest case, these systems can be theoretically described by the Bose-Hubbard (BH) model, which has two parameters: a tunneling J and an on-site interaction U [2, 3]. A natural extension of the Bose-Hubbard model comes from including longrange interactions between particles. Experiments on ultracold polar molecules have renewed interest in extended Bose-Hubbard models which can model such systems in optical lattices [4][5][6][7]. Because of the strong electric dipole moment of polar molecules, long-range interactions play a crucial role in the collective behavior of the system, leading to the appearance of states with long-range order, like various structured insulating states, supersolids, Wigner crystals, pair-supersolids, etc. [9][10][11][12][13][14][15].In this Letter, we study the ground-state of dipolar molecules in a 2D square optical lattice with a harmonic trapping along the polarization direction of the dipoles. We derive a modified BH model which includes additional occupation-dependent nearest-neighbor (NN) hopping processes arising from long-range dipolar interactions in the lowest Bloch band. Usually, interactioninduced hopping terms are neglected when discussing dipolar bosonic molecules. In this Letter, we show that these terms considerably change the physics of dipolar soft-core bosons. Soft-core bosons in square and onedimensional lattices have been discussed in the literature within the extended Hubbard model, focusing on the presence of stable supersolidity [17,18]. In the usual case with only NN interaction, at sufficient dipolar strength, the ground states at half-and unit-filling are checkerboard (CB) insulating states. Using exact diagonalization (ED) and multiscale entanglement renormalization ansatz (MERA), we solve the one-dimensional extended Hubbard model including the novel occupationdependent NN hopping processes. We find that with increasing dipolar interaction, the system enters from the CB phases to a novel state which has a one-particle superfluid (SF) and pair-superfluid (PSF) properties. Particularly we find a region where both of them coexists with the SF order parameter has alternating sign at ...

Analysis of the classical phase space and energy transfer for two rotating dipoles with and without external electric field

“…Using the initial conditions (15), the equations of motion (8) are integrated up to a final time t f , and we compute the normalized time-averaged momenta P from Eq. (16). As in the field-free system, we are using a dipole-dipole interaction with strength χ = 10 −5 , and a final time t f = 5 × 10 4 .…”

“…On the other hand side, cooling and trapping cold molecules in an optical lattice allows to fix their positions while exploiting their interactions [12,13]. The latter becomes particularly interesting for strongly polar diatomic systems where the dipole-dipole interaction is sufficiently long-range that novel structural as well as dynamical and collective behaviors can be expected [14][15][16]. External electric fields provide then a versatile tool to control these interactions, e.g.…”

Fermionized Dipolar Bosons Trapped in a Harmonic Trap

“…In particular, recent experimental progress has opened up perspectives for achieving systems with particles interacting through the dipole-dipole interaction (DDI) [1,2], which has inspired great interest in understanding their properties [3][4][5][6]. There has also been a growing interest in studying entanglement properties of quantum composite systems, since their entangled states are an essential ingredient for quantum computation.…”

Dipolar-induced resonance for ultracold bosons in a quasi-one-dimensional optical lattice

“…Trapping a dipolar system into lower dimensions stabilizes it with respect to two-body [11] and many-body [12] instabilities caused by the attractive part of the 3D DDI. This has prompted detailed studies of dipolar systems in 2D and quasi-2D [13,14], bilayer [15], and quasi-1D [16][17][18][19] geometries.…”