85 research outputs found
Coalescence of Two Impurities in a Trapped One-dimensional Bose Gas
We study the ground state of a one-dimensional (1D) trapped Bose gas with two
mobile impurity particles. To investigate this set-up, we develop a variational
procedure in which the coordinates of the impurity particles are slow-like
variables. We validate our method using the exact results obtained for small
systems. Then, we discuss energies and pair densities for systems that contain
of the order of one hundred atoms. We show that bosonic non-interacting
impurities cluster. To explain this clustering, we calculate and discuss
induced impurity-impurity potentials in a harmonic trap. Further, we compute
the force between static impurities in a ring ({\it {\`a} la} the Casimir
force), and contrast the two effective potentials: the one obtained from the
mean-field approximation, and the one due to the one-phonon exchange. Our
formalism and findings are important for understanding (beyond the polaron
model) the physics of modern 1D cold-atom systems with more than one impurity.Comment: 10 pages, 6 figures, published versio
Universal physics of bound states of a few charged particles
We study few-body bound states of charged particles subject to attractive
zero-range/short-range plus repulsive Coulomb interparticle forces. The
characteristic length scales of the system at zero energy are set by the
Coulomb length scale and the Coulomb-modified effective range
. We study shallow bound states of charged particles with
and show that these systems obey universal scaling laws
different from neutral particles. An accurate description of these states
requires both the Coulomb-modified scattering length and the effective range
unless the Coulomb interaction is very weak (). Our findings are
relevant for bound states whose spatial extent is significantly larger than the
range of the attractive potential. These states enjoy universality -- their
character is independent of the shape of the short-range potential.Comment: 8 pages, 6 figures, extended discussion, results unchanged, to appear
in Phys. Lett.
Occurrence conditions for two-dimensional Borromean systems
We search for Borromean three-body systems of identical bosons in two
dimensional geometry, i.e. we search for bound three-boson system without bound
two-body subsystems. Unlike three spatial dimensions, in two-dimensional
geometry the two- and three-body thresholds often coincide ruling out Borromean
systems. We show that Borromean states can only appear for potentials with
substantial attractive and repulsive parts. Borromean states are most easily
found when a barrier is present outside an attractive pocket. Extensive
numerical search did not reveal Borromean states for potentials without an
outside barrier. We outline possible experimental setups to observe Borromean
systems in two spatial dimensions.Comment: 9 pages, 5 figures, published versio
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