334 research outputs found
Low-density, one-dimensional quantum gases in a split trap
We investigate degenerate quantum gases in one dimension trapped in a
harmonic potential that is split in the centre by a pointlike potential. Since
the single particle eigenfunctions of such a system are known for all strengths
of the central potential, the dynamics for non-interacting fermionic gases and
low-density, strongly interacting bosonic gases can be investigated exactly
using the Fermi-Bose mapping theorem. We calculate the exact many-particle
ground-state wave-functions for both particle species, investigate soliton-like
solutions, and compare the bosonic system to the well-known physics of Bose
gases described by the Gross-Pitaevskii equation. We also address the
experimentally important questions of creation and detection of such states.Comment: 7 pages, 5 figure
Ground state properties of a one-dimensional condensate of hard core bosons in a harmonic trap
The exact N-particle ground state wave function for a one-dimensional
condensate of hard core bosons in a harmonic trap is employed to obtain
accurate numerical results for the one-particle density matrix, occupation
number distribution of the natural orbitals, and momentum distribution. Our
results show that the occupation of the lowest orbital varies as N^{0.59}, in
contrast to N^{0.5} for a spatially uniform system, and N for a true BEC.Comment: 10 pages, 6 figures, submitted to Phys. Rev.
Ultracold atoms in one-dimensional optical lattices approaching the Tonks-Girardeau regime
Recent experiments on ultracold atomic alkali gases in a one-dimensional
optical lattice have demonstrated the transition from a gas of soft-core bosons
to a Tonks-Girardeau gas in the hard-core limit, where one-dimensional bosons
behave like fermions in many respects. We have studied the underlying many-body
physics through numerical simulations which accommodate both the soft-core and
hard-core limits in one single framework. We find that the Tonks-Girardeau gas
is reached only at the strongest optical lattice potentials. Results for
slightly higher densities, where the gas develops a Mott-like phase already at
weaker optical lattice potentials, show that these Mott-like short range
correlations do not enhance the convergence to the hard-core limit.Comment: 4 pages, 3 figures, replaced with published versio
Measurement of one-particle correlations and momentum distributions for trapped 1D gases
van Hove's theory of scattering of probe particles by a macroscopic target is
generalized so as to relate the differential cross section for atomic ejection
via stimulated Raman transitions to one-particle momentum-time correlations and
momentum distributions of 1D trapped gases. This method is well suited to
probing the longitudinal momentum distributions of 1D gases in situ, and
examples are given for bosonic and fermionic atoms.Comment: 4 pages, 2 .eps figure
Breakdown of time-dependent mean-field theory for a one-dimensional condensate of impenetrable bosons
We show that the time-dependent nonlinear Schrodinger equation of mean-field
theory has limited utility for a one-dimensional condensate of impenetrable
bosons. Mean-field theory with its associated order parameter predicts
interference between split condensates that are recombined, whereas an exact
many-body treatment shows minimal interference.Comment: 4 pages, 2 EPS figure
Quasi-one-dimensional Bose gases with large scattering length
Bose gases confined in highly-elongated harmonic traps are investigated over
a wide range of interaction strengths using quantum Monte Carlo techniques. We
find that the properties of a Bose gas under tight transverse confinement are
well reproduced by a 1d model Hamiltonian with contact interactions. We point
out the existence of a unitary regime, where the properties of the quasi-1d
Bose gas become independent of the actual value of the 3d scattering length. In
this unitary regime, the energy of the system is well described by a hard rod
equation of state. We investigate the stability of quasi-1d Bose gases with
positive and negative 3d scattering length.Comment: 5 pages, 3 figure
Limits of control for quantum systems: kinematical bounds on the optimization of observables and the question of dynamical realizability
In this paper we investigate the limits of control for mixed-state quantum
systems. The constraint of unitary evolution for non-dissipative quantum
systems imposes kinematical bounds on the optimization of arbitrary
observables. We summarize our previous results on kinematical bounds and show
that these bounds are dynamically realizable for completely controllable
systems. Moreover, we establish improved bounds for certain partially
controllable systems. Finally, the question of dynamical realizability of the
bounds for arbitary partially controllable systems is shown to depend on the
accessible sets of the associated control system on the unitary group U(N) and
the results of a few control computations are discussed briefly.Comment: 5 pages, orginal June 30, 2000, revised September 28, 200
Density distributions for trapped one-dimensional spinor gases
We numerically evaluate the density distribution of a spin-1 bosonic
condensate in its ground state within a modifed Gross-Pitaevskii theory, which
is obtained by the combination of the exact solution of the corresponding
integrable model with the local density approximation. Our study reveals that
atoms in the m_F = 0 state are almost completely suppressed for the
anti-ferromagnetic interactions in both weakly and strongly interacting
regimes, whereas all three components remain non-vanishing for ferromagnetic
interactions. Specially, when the system is in the Tonks-Girardeau (TG) regime,
obvious Fermi-like distribution emerges for each component. We also discuss the
possible deviation of the spatial distribution from the Fermi-like distribution
when the spin-spin interaction is strong enough.Comment: 6 pages, 3 figures, version to be published in Phys. Rev.
An exactly solvable model of the BCS-BEC crossover
We discuss an integrable model of interacting Fermions in one dimension, that
allows an exact description of the crossover from a BCS- to a Bose-like
superfluid. This model bridges the Gaudin-Yang model of attractive spin 1/2
Fermions to the Lieb-Liniger model of repulsive Bosons. Using a geometric
resonance in the one-dimensional scattering length, the inverse coupling
constant varies from minus infinity to plus infinity while the system evolves
from a BCS-like state through a Tonks gas to a weakly interacting Bose gas of
dimers. We study the ground state energy, the elementary density and spin
excitations, and the correlation functions. An experimental realization with
cold atoms of such a one-dimensional BCS-BEC crossover is proposed.Comment: corrected typos, minor modifications, submitted versio
Optical dipole traps and atomic waveguides based on Bessel light beams
We theoretically investigate the use of Bessel light beams generated using
axicons for creating optical dipole traps for cold atoms and atomic
waveguiding. Zeroth-order Bessel beams can be used to produce highly elongated
dipole traps allowing for the study of one-dimensional trapped gases and
realization of a Tonks gas of impentrable bosons. First-order Bessel beams are
shown to be able to produce tight confined atomic waveguides over centimeter
distances.Comment: 20 pages, 5 figures, to appear in Phys. Rev.
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