Exotic Few-Body Bound States in a Lattice

Abstract

Strongly-interacting ultra-cold atoms in tight-binding optical lattice potentials provide an ideal platform to realize the fundamental Hubbard model. Here, after outlining the elementary single particle solution, we review and expand our recent work on complete characterization of the bound and scattering states of two and three bosonic atoms in a one-dimensional optical lattice. In the case of two atoms, there is a family of interaction-bound "dimer" states of co-localized particles that exists invariantly for either attractive or repulsive on-site interaction, with the energy below or above the two-particle scattering continuum, respectively. Adding then the third particle-"monomer"-we find that, apart from the simple strongly-bound "trimer" corresponding to all three particles occupying the same lattice site, there are two peculiar families of weakly-bound trimers with energies below and above the monomer-dimer scattering continuum, the corresponding binding mechanism being an effective particle exchange interaction.

Ultracold bosons with short-range interaction in regular optical lattices

“…[211][212][213] analytically and numerically for negative U but the result can be easily generalized to arbitrary U . Later it was discussed in the context of ultracold atoms [214][215][216][217][218][219][220]. The energy spectrum consists of the scattering states of a pair of asymptotically free particles and the bound state.…”

Frustrated collisions and unconventional pairing on a quantum superlattice

“…A simple generalization of our results to include periodic boundary conditions shows that the two-body ground states in finite lattices with repulsive interaction correspond to partially paired states with a bound state in the continuum [21]. Our exact solutions are also of relevance to ultracold, low-density gases in optical superlattices where the physics is most influenced by pairwise collisions; they represent a novel advance in the field of few-body physics on a lattice, which have attracted much interest recently (see [25] and references therein). Moreover, for bosons, our wave functions can be used to construct trial functions of product (Jastrow) type for the many-body problem [26] in the dilute regime.…”

Heterodimer of two distinguishable atoms in a one-dimensional optical lattice

“…Several groups have elaborated on the theory [1][2][3][4][5], and at least a qualitative agreement with the experiments [1] has been established. Most of the dimer models discuss two identical bosons, but theoretical analyses of two distinguishable atoms have been presented [6][7][8][9][10]. There are also experiments on two different atomic species confined in an optical lattice [11][12][13][14][15][16][17], although at the moment we know of none that has specifically addressed lattice dimers.…”