23 research outputs found
Many-body state and dynamic behaviour of the pair-correlation function of a small Bose-Einstein condensate confined in a ring potential
We investigate the many-body state and the static and the dynamic behaviour
of the pair-correlation function of a Bose-Einstein condensate with a finite
atom number, which is confined in a quasi-one-dimensional toroidal/annular
potential, both for repulsive, and for attractive interactions. We link the
dynamic pair-correlation function that we evaluate with the problem of quantum
time crystals. For weak repulsive interatomic interactions and a finite number
of atoms the pair-correlation function shows a periodic temporal behaviour,
which disappears in the limit of a large atom number, in agreement with general
arguments. Finally we provide some insight into older results of attractive
interactions, where the time-crystalline behaviour exists only in the limit of
a large atom number.Comment: Revised version, accepted for publicatio
Solitary waves of Bose-Einstein condensed atoms confined in finite rings
Motivated by recent progress in trapping Bose-Einstein condensed atoms in
toroidal potentials, we examine solitary-wave solutions of the nonlinear
Schr\"odinger equation subject to periodic boundary conditions. When the
circumference of the ring is much larger than the size of the wave, the density
profile is well approximated by that of an infinite ring, however the density
and the velocity of propagation cannot vanish simultaneously. When the size of
the ring becomes comparable to the size of the wave, the density variation
becomes sinusoidal and the velocity of propagation saturates to a constant
value.Comment: 6 pages, 2 figure
Solitary-wave solutions in binary mixtures of Bose-Einstein condensates under periodic boundary conditions
We derive solitary-wave solutions within the mean-field approximation in
quasi-one-dimensional binary mixtures of Bose-Einstein condensates under
periodic boundary conditions, for the case of an effective repulsive
interatomic interaction. The particular gray-bright solutions that give the
global energy minima are determined. Their characteristics and the associated
dispersion relation are derived. In the case of weak coupling, we diagonalize
the Hamiltonian analytically to obtain the full excitation spectrum of
"quantum" solitary-wave solutions.Comment: 11 pages, 2 figure
The absence of fragmentation in Bose-Einstein condensates
A Bose-Einstein condensate produced by a Hamiltonian which is rotationally or
translationally symmetric is fragmented as a direct result of these symmetries.
A corresponding mean-field unfragmented state, with an identical energy to
leading order in the number of particles, can generally be constructed. As a
consequence, vanishingly weak symmetry-breaking perturbations destabilize the
fragmented state, which would thus be extremely difficult to realize
experimentally, and lead to an unfragmented condensate.Comment: Typographical errors correcte
Solitary waves in mixtures of Bose gases confined in annular traps
A two-component Bose-Einstein condensate that is confined in a
one-dimensional ring potential supports solitary-wave solutions, which we
evaluate analytically. The derived solutions are shown to be unique. The
corresponding dispersion relation that generalizes the case of a
single-component system shows interesting features.Comment: 4 pages, 1 figur
Solitary waves and yrast states in Bose-Einstein condensed gases of atoms
Considering a Bose-Einstein condensed gas confined in one dimension with
periodic boundary conditions, we demonstrate that, very generally,
solitary-wave and rotational excitations coincide. This exact equivalence
allows us to establish connections between a number of effects that are present
in these two problems, many of which have been studied using the mean-field
approximation.Comment: Revised version, where the generality of our arguments is presented
more clearl
Excitation spectrum of a two-component Bose-Einstein condensate in a ring potential
A mixture of two distinguishable Bose-Einstein condensates confined in a ring
potential has numerous interesting properties under rotational and
solitary-wave excitation. The lowest-energy states for a fixed angular momentum
coincide with a family of solitary-wave solutions. In the limit of weak
interactions, exact diagonalization of the many-body Hamiltonian is possible
and permits evaluation of the complete excitation spectrum of the system.Comment: 4 pages, 1 figur