306 research outputs found
Exotic few-body bound states in a lattice
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
Three-body bound states in a lattice
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 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
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