Multimode Bose-Hubbard model for quantum dipolar gases in confined geometries

Abstract

We theoretically consider ultracold polar molecules in a wave guide. The particles are bosons, they experience a periodic potential due to an optical lattice oriented along the wave guide and are polarised by an electric field orthogonal to the guide axis. The array is mechanically unstable by opening the transverse confinement in the direction orthogonal to the polarizing electric field and can undergo a transition to a double-chain (zigzag) structure. For this geometry we derive a multi-mode generalized Bose-Hubbard model for determining the quantum phases of the gas at the mechanical instability taking into account the quantum fluctuations in all directions of space. Our model limits the dimension of the numerically relevant Hilbert subspace by means of an appropriate decomposition of the field operator, which is obtained from a field theoretical model of the linearzigzag instability. We determine the phase diagrams of small systems using exact diagonalization and find that, even for tight transverse confinement, the aspect ratio between the two transverse trap frequencies controls not only the classical but also the quantum properties of the ground state in a non-trivial way. Convergence tests at the linear-zigzag instability demonstrate that our multi-mode generalized Bose-Hubbard model can catch the essential features of the quantum phases of dipolar gases in confined geometries with a limited computational effort. arXiv:1704.00948v1 [cond-mat.quant-gas]

Quantum phases of dipolar bosons in one-dimensional optical lattices

“…( 10), have been extensively reported, for instance, in Refs. [11,22]. These derivations allow one to link the Bose-Hubbard coefficients with the experimental parameters.…”

“…The model at the basis of our analysis is the onedimensional extended Bose-Hubbard Hamiltonian ĤBH , that reads [8,11]:…”

“…In a lattice the effect of a two-body potential results in interaction terms, proportional to the onsite densities on both contributing lattice sites, as well as in socalled correlated tunnelling terms, where hopping from site to site depends on the occupation of the neighboring sites [7,8,11]. Detailed studies of the extended Bose-Hubbard model for dipolar gases typically included only the density-density interaction terms.…”

Superfluid phases induced by the dipolar interactions

“…These terms are responsible for density modulations within the lattice [16][17][18][19][20][21][22][23][24][25][26][27] and for topological incompressible phases in one dimension [28][29][30][31][32]. Moreover, the onsite contribution of the dipolar potential typically renormalizes the contact interactions and can make the gas unstable [18,[33][34][35]. Ab initio derivations of the Bose-Hubbard model show that interactions are also responsible for the appearance of correlated hopping terms, which can be of the same order as the density-density interactions terms [12,34,[36][37][38].…”

“…Moreover, the onsite contribution of the dipolar potential typically renormalizes the contact interactions and can make the gas unstable [18,[33][34][35]. Ab initio derivations of the Bose-Hubbard model show that interactions are also responsible for the appearance of correlated hopping terms, which can be of the same order as the density-density interactions terms [12,34,[36][37][38].…”