Hubbard model for ultracold bosonic atoms interacting via zero-point-energy–induced three-body interactions

Abstract

We show that for ultra-cold neutral bosonic atoms held in a three-dimensional periodic potential or optical lattice, a Hubbard model with dominant, attractive three-body interactions can be generated. In fact, we derive that the effect of pair-wise interactions can be made small or zero starting from the realization that collisions occur at the zero-point energy of an optical lattice site and the strength of the interactions is energy dependent from effective-range contributions. We determine the strength of the two-and three-body interactions for scattering from van-der-Waals potentials and near Fano-Feshbach resonances. For van-der-Waals potentials, which for example describe scattering of alkaline-earth atoms, we find that the pair-wise interaction can only be turned off for species with a small negative scattering length, leaving the 88 Sr isotope a possible candidate. Interestingly, for collisional magnetic Feshbach resonances this restriction does not apply and there often exist magnetic fields where the two-body interaction is small. We illustrate this result for several known narrow resonances between alkali-metal atoms as well as chromium atoms. Finally, we compare the size of the three-body interaction with hopping rates and describe limits due to three-body recombination.In 1998 Jaksch et al. [1] suggested that laser-cooled atomic samples can be held in optical lattices, periodic potentials created by counter-propagating laser beams. These three-dimensional lattices have spatial periods between 400 nm and 800 nm and depths V 0 as high as V 0 /h ∼ 1 MHz, where h is Planck's constant. An ensemble of atoms then realize either the fermionic or bosonic Hubbard model, where atoms hop from site to site and interact only when on the same site. The interaction driven quantum phase transition of this model was first realized by Ref. [2].Today, optical lattices are seen as a natural choice in which to simulate other many-body Hamiltonians. These include Hamiltonians with complex band structure such as double-well lattices [3-6], two-dimensional hexagonal lattices [6][7][8][9], as well as those with spin-momentum couplings possibly leading to topological matter [10,11]. Quantum phase transitions in these Hamiltonians enable ground-state wavefunctions with unusual order parameters, such as pair superfluids and striped phases [12][13][14]. Phase transitions in Hamiltonians with long-range dipole-dipole interactions using atoms or molecules with large magnetic or electric dipole moments can also be studied. Finally, atoms in optical lattices can be used to measure gravitational acceleration (little-g) [15][16][17], shed light on non-linear measurements [18][19][20][21], and be used for quantum information processing.Over the last ten years ultra-cold atom experiments have also investigated few-body phenomena. In particular, three-body interactions have been studied through Efimov physics of strongly interacting atoms observed as resonances in three-body recombination, where three colliding atoms create a dimer and a...

Universal bound states of one-dimensional bosons with two- and three-body attractions

“…In particular, when a 3D < 0 and |a 3D | ≪ l ⊥ , the N -body to dimer binding-energy ratios predicted from Eqs. (2), (7), (14), and (17) read…”

“…(7). While a 3 ≫ |a 2 | ≫ l ⊥ is naturally realized for weakly interacting bosons with |a 3D | ≪ l ⊥ , we study the system with an arbitrary −∞ < a 3 /a 2 < +∞ because the two-body and threebody interactions are independently tunable in principle with ultracold atoms [14][15][16][17]. As far as both interactions are weak in the sense of |a 2 |, a 3 ≫ l ⊥ , low-energy physics of the system at |E| ≪ 1/(ml 2 ⊥ ) is universal, i.e., depends only on the two scattering lengths.…”

Semisuper Efimov Effect of Two-Dimensional Bosons at a Three-Body Resonance

“…Such double fine-tuning is generally challenging, but it may be possible in ultracold atom experiments. In fact, there have been a number of proposed schemes to implement vanishing two-body but strong three-body interactions both in a free space [18] and in an optical lattice [19][20][21]. Once the three-body resonance without the two-body interaction is achieved in a two-dimensional Bose system [22], the emergent semisuper Efimov states of four bosons may be observed in ultracold atom experiments through resonantly enhanced atom losses by varying a detuning parameter [23][24][25].…”

Quantum droplet of one-dimensional bosons with a three-body attraction

“…From this perspective, ultracold atoms offer valuable opportunities where interparticle interactions can be controlled at will [6]. While interesting physics is usually aimed at by amplifying the two-body interaction, one can also extinguish it to realize unique systems governed by the three-body interaction [7][8][9][10]. Whether such novel systems without two-body but with tunable three-body interactions exhibit interesting physics remains largely unexplored and thus can be an important research frontier in ultracold atoms.…”