588 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
Few-Body Route to One-Dimensional Quantum Liquids
Gapless many-body quantum systems in one spatial dimension are universally
described by the Luttinger liquid effective theory at low energies.
Essentially, only two parameters enter the effective low-energy description,
namely the speed of sound and the Luttinger parameter. These are highly system
dependent and their calculation requires accurate non-perturbative solutions of
the many-body problem. Here, we present a simple method that only uses
collisional information to extract the low-energy properties of these systems.
Our results are in remarkable agreement with available results for integrable
models and from large scale Monte Carlo simulations of one-dimensional helium
and hydrogen isotopes. Moreover, we estimate theoretically the critical point
for spinodal decomposition in one-dimensional helium-4, and show that the
exponent governing the divergence of the Luttinger parameter near the critical
point is exactly 1/2, in excellent agreement with Monte Carlo simulations.Comment: 8 pages, 6 figures, including supplementary materia
Universality and tails of long range interactions in one dimension
Long-range interactions and, in particular, two-body potentials with
power-law long-distance tails are ubiquitous in nature. For two bosons or
fermions in one spatial dimension, the latter case being formally equivalent to
three-dimensional -wave scattering, we show how generic asymptotic
interaction tails can be accounted for in the long-distance limit of scattering
wave functions. This is made possible by introducing a generalisation of the
collisional phase shifts to include space dependence. We show that this
distance dependence is universal, in that it does not depend on short-distance
details of the interaction. The energy dependence is also universal, and is
fully determined by the asymptotic tails of the two-body potential. As an
important application of our findings, we describe how to eliminate finite-size
effects with long-range potentials in the calculation of scattering phase
shifts from exact diagonalisation. We show that even with moderately small
system sizes it is possible to accurately extract phase shifts that would
otherwise be plagued with finite-size errors. We also consider multi-channel
scattering, focusing on the estimation of open channel asymptotic interaction
strengths via finite-size analysis.Comment: 7 pages, 3 figure
Effective field theory of interactions on the lattice
We consider renormalization of effective field theory interactions by
discretizing the continuum on a tight-binding lattice. After studying the
one-dimensional problem, we address s-wave collisions in three dimensions and
relate the bare lattice coupling constants to the continuum coupling constants.
Our method constitutes a very simple avenue for the systematic renormalization
in effective field theory, and is especially useful as the number of
interaction parameters increases.Comment: 7 pages, 0 figure
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
Elementary excitations of chiral Bose-Einstein condensates
We study the collective modes of a Bose-Einstein condensate subject to an
optically induced density-dependent gauge potential. The corresponding
interacting gauge theory lacks Galilean invariance, yielding an exotic
superfluid state. The nonlinear dynamics in the presence of a current
nonlinearity and an external harmonic trap are found to give rise to dynamics
which violate Kohn's theorem; where the frequency of the dipole mode strongly
depends on the strength of the mass current in the gas. The linearised spectrum
reveals how the centre of mass and shape oscillations are coupled, whereas in
the strongly nonlinear regime the dynamics is irregular.Comment: General improvements, corrections and references adde
Vortex dynamics in superfluids governed by an interacting gauge theory
We study the dynamics of a vortex in a quasi two-dimensional Bose gas
consisting of light matter coupled atoms forming two-component pseudo spins.
The gas is subject to a density dependent gauge potential, hence governed by an
interacting gauge theory, which stems from a collisionally induced detuning
between the incident laser frequency and the atomic energy levels. This
provides a back-action between the synthetic gauge potential and the matter
field. A Lagrangian approach is used to derive an expression for the force
acting on a vortex in such a gas. We discuss the similarities between this
force and the one predicted by Iordanskii, Lifshitz and Pitaevskii when
scattering between a superfluid vortex and the thermal component is taken into
account.Comment: 9 pages. Comments are welcom
Quantized vortices in interacting gauge theories
We consider a two-dimensional weakly interacting ultracold Bose gas whose
constituents are two-level atoms. We study the effects of a synthetic
density-dependent gauge field that arises from laser-matter coupling in the
adiabatic limit with a laser configuration such that the single-particle
zero-order vector potential corresponds to a constant synthetic magnetic field.
We find a new exotic type of current non-linearity in the Gross-Pitaevskii
equation which affects the dynamics of the order parameter of the condensate.
We investigate the rotational properties of this system, focusing in particular
on the physical conditions that make the nucleation of a quantized vortex in
the system energetically favourable with respect to the non rotating solution.
We point out that two different physical interpretations can be given to this
new non linearity: firstly it can be seen as a local modification of the mean
field coupling constant, whose value depends on the angular momentum of the
condensate. Secondly, it can be interpreted as a density modulated angular
velocity given to the cloud. Looking at the problem from both of these
viewpoints, we analyze the physical conditions that make a single vortex state
energetically favourable. In the Thomas-Fermi limit, we show that the effect of
the new nonlinearity is to induce a rotation to the condensate, where the
transition from non-rotating to rotating states depends on the density of the
cloud.Comment: 6 pages, one figure. General improvement
Driven Topological Systems in the Classical Limit
Periodically-driven quantum systems can exhibit topologically non-trivial
behaviour, even when their quasi-energy bands have zero Chern numbers. Much
work has been conducted on non-interacting quantum-mechanical models where this
kind of behaviour is present. However, the inclusion of interactions in
out-of-equilibrium quantum systems can prove to be quite challenging. On the
other hand, the classical counterpart of hard-core interactions can be
simulated efficiently via constrained random walks. The non-interacting model
proposed by Rudner et al. [Phys. Rev. X 3, 031005 (2013)], has a special point
for which the system is equivalent to a classical random walk. We consider the
classical counterpart of this model, which is exact at a special point even
when hard-core interactions are present, and show how these quantitatively
affect the edge currents in a strip geometry. We find that the interacting
classical system is well described by a mean-field theory. Using this we
simulate the dynamics of the classical system, which show that the interactions
play the role of Markovian, or time dependent disorder. By comparing the
evolution of classical and quantum edge currents in small lattices, we find
regimes where the classical limit considered gives good insight into the
quantum problem.Comment: 15 pages, 15 figures, new content on the quantum mode
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