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Large Trimers from Three-Body Interactions in One-Dimensional Lattices

Arthur Christianen, John Sous

Published Jun 27, 2018• 0 citations
OpenAlex

Abstract

Few-body bound states have been extensively explored in cold atomic gases with a desire to realize large molecular complexes. Here, we investigate the formation of trimers in an infinite one-dimensional lattice with hard-core two- and three-body interactions of relevance to Rydberg atoms and polar molecules in optical lattices, and other physical systems such as the fractional Hall states. We determine the stability regions for attractively and repulsively bound trimers. We discover a regime of large spatially extended trimers that are stabilized by the interplay of attractive two-body, $U$ , and repulsive three-body, $V$ , interactions and persist despite extremely large $V$. These bound states present a new direction in the search for large few-body complexes in cold atoms.

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Few-body bound states have been extensively explored in cold atomic gases with a desire to realize large molecular complexes. Here, we investigate the formation of trimers in an infinite one-dimensional lattice with hard-core two- and three-body interactions of relevance to Rydberg atoms and polar molecules in optical lattices, and other physical systems such as the fractional Hall states. We determine the stability regions for attractively and repulsively bound trimers. We discover a regime of large spatially extended trimers that are stabilized by the interplay of attractive two-body, UUU , and repulsive three-body, VVV , interactions and persist despite extremely large VVV. These bound states present a new direction in the search for large few-body complexes in cold atoms.
We investigate the formation of trimers in an infinite one-dimensional lattice model of hard-core particles with single-particle hopping ttt and and nearest-neighbor two-body UUU and three-body VVV interactions of relevance to Rydberg atoms and polar molecules. For sufficiently attractive $U\ensuremath{\le}\ensuremath{-}2t$ and positive V>0V>0V>0 a large trimer is stabilized, which persists as $V\ensuremath{\rightarrow}\ensuremath{\infty}$, while both sufficiently attractive UUU and VVV bind a small trimer. The excited state above this small trimer is also bound and has a large extent; its behavior as $V\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$ resembles that of the large ground-state trimer. These large bound states appear to admit a continuum description. Furthermore, we find that in the limit $V\ensuremath{\gg}t,\phantom{\rule{0.16em}{0ex}}U<\ensuremath{-}2t$ the bound-state behavior qualitatively evolves with larger ∣U∣|U|∣U∣ from a state described by the scattering of three far separated particles to a state of a compact dimer scattering with a single particle.
We study the phase diagram of ultra-cold bosonic polar molecules loaded on a two-dimensional optical lattice of hexagonal symmetry controlled by external electric and microwave fields. Following a recent proposal in (Büchler et al 2007 Nat. Phys. 3 726), such a system is described by an extended Bose–Hubbard model of hard-core bosons that includes both extended two- and three-body repulsions. Using quantum Monte-Carlo simulations, exact finite cluster calculations and the tensor network renormalization group, we explore the rich phase diagram of this system, resulting from the strongly competing nature of the three-body repulsions on the honeycomb lattice. Already in the classical limit, they induce complex solid states with large unit cells and macroscopic ground-state degeneracies at different fractional lattice fillings. For the quantum regime, we obtain effective descriptions of the various phases in terms of emerging valence bond crystal states and quantum dimer models. Furthermore, we access the experimentally relevant parameter regime and determine the stability of the crystalline phases towards strong two-body interactions.
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.
When quantum particles are confined into lower dimensions, an effective three-body interaction inevitably arises and may cause significant consequences. Here we study bosons in one dimension with weak two-body and three-body interactions and predict the existence of two three-body bound states when both interactions are attractive. Their binding energies are universal functions of the two-body and three-body scattering lengths and have direct relevance to a broad range of quasi-one-dimensional systems realized with ultracold atoms.
We pursue three-body bound states in a one-dimensional tight-binding lattice described by the Bose-Hubbard model with strong on-site interaction. Apart from the simple strongly bound ``trimer'' state corresponding to all three particles occupying the same lattice site, we find two novel kinds of weakly bound trimers with energies below and above the continuum of scattering states of a single-particle (``monomer'') and a bound-particle pair (``dimer''). The corresponding binding mechanism can be inferred from an effective Hamiltonian in the strong-coupling regime which contains an exchange interaction between the monomer and the dimer. In the limit of very strong on-site interaction, the exchange-bound trimers attain a universal value of the binding energy. These phenomena can be observed with cold atoms in optical lattices.
We determine the phase diagram of a one-dimensional system of hard-core lattice bosons interacting via repulsive three-body interactions by analytic methods and extensive quantum Monte Carlo simulations. Such three-body interactions can be derived from a microscopic theory for polar molecules trapped in an optical lattice. Depending on the strength of the interactions and the particle density, we find superfluid and solid phases, the latter appearing at an unconventional filling of the lattice and displaying a coexistence of charge-density wave and bond orders.