515 research outputs found
Bose-Einstein condensates with vortices in rotating traps
We investigate minimal energy solutions with vortices for an interacting
Bose-Einstein condensate in a rotating trap. The atoms are strongly confined
along the axis of rotation z, leading to an effective 2D situation in the x-y
plane. We first use a simple numerical algorithm converging to local minima of
energy. Inspired by the numerical results we present a variational Ansatz in
the regime where the interaction energy per particle is stronger than the
quantum of vibration in the harmonic trap in the x-y plane, the so-called
Thomas-Fermi regime. This Ansatz allows an easy calculation of the energy of
the vortices as function of the rotation frequency of the trap; it gives a
physical understanding of the stabilisation of vortices by rotation of the trap
and of the spatial arrangement of vortex cores. We also present analytical
results concerning the possibility of detecting vortices by a time-of-flight
measurement or by interference effects. In the final section we give numerical
results for a 3D configuration.Comment: 15 pages, 16 figures, to be published in Eur. Phys. Jour. D; one
reference update
Three fermions in a box at the unitary limit: universality in a lattice model
We consider three fermions with two spin components interacting on a lattice
model with an infinite scattering length. Low lying eigenenergies in a cubic
box with periodic boundary conditions, and for a zero total momentum, are
calculated numerically for decreasing values of the lattice period. The results
are compared to the predictions of the zero range Bethe-Peierls model in
continuous space, where the interaction is replaced by contact conditions. The
numerical computation, combined with analytical arguments, shows the absence of
negative energy solution, and a rapid convergence of the lattice model towards
the Bethe-Peierls model for a vanishing lattice period. This establishes for
this system the universality of the zero interaction range limit.Comment: 6 page
Creation and detection of a mesoscopic gas in a non-local quantum superposition
We investigate the scattering of a quantum matter wave soliton on a barrier
in a one dimensional geometry and we show that it can lead to mesoscopic
Schr\"odinger cat states, where the atomic gas is in a coherent superposition
of being in the half-space to the left of the barrier and being in the
half-space to the right of the barrier. We propose an interferometric method to
reveal the coherent nature of this superposition and we discuss in details the
experimental feasibility.Comment: 4 pages, 1 figur
One particle in a box: the simplest model for a Fermigas in the unitary limit
We consider a single quantum particle in a spherical box interacting with a
fixed scatterer at the center, to construct a model of a degenerate atomic
Fermi gas close to a Feshbach resonance. One of the key predictions of the
model is the existence of two branches for the macroscopic state of the gas, as
a function of the magnetic field controlling the value of the scattering
length.This model is able to draw a qualitative picture of all the different
features recently observed in a degenerate atomic Fermi gas close to the
resonance, even in the unitary limit
BCS Theory for Trapped Ultracold Fermions
We develop an extension of the well-known BCS-theory to systems with trapped
fermions. The theory fully includes the quantized energy levels in the trap.
The key ingredient is to model the attractive interaction between two atoms by
a pseudo-potential which leads to a well defined scattering problem and
consequently a BCS-theory free of divergences. We present numerical results for
the BCS critical temperature and the temperature dependence of the gap. They
are used as a test of existing semi-classical approximations.Comment: 4 pages, 3 figures, submitted to PR
Modeling interactions for resonant p-wave scattering
In view of recent experiments on ultra-cold polarized fermions, the
zero-range potential approach is generalized to situations where two-body
scattering is resonant in the p-wave channel. We introduce a modified scalar
product which reveals a deep relation between the geometry of the Hilbert space
and the interaction. This formulation is used to obtain a simple interpretation
for the transfer rates between atomic and molecular states within a two
branches picture of the many-body system close to resonance. At resonance, the
energy of the dilute gas is found to vary linearly with density.Comment: 4 page
Achieving a BCS transition in an atomic Fermi gas
We consider a gas of cold fermionic atoms having two spin components with
interactions characterized by their s-wave scattering length . At positive
scattering length the atoms form weakly bound bosonic molecules which can be
evaporatively cooled to undergo Bose-Einstein condensation, whereas at negative
scattering length BCS pairing can take place. It is shown that, by
adiabatically tuning the scattering length from positive to negative
values, one may transform the molecular Bose-Einstein condensate into a highly
degenerate atomic Fermi gas, with the ratio of temperature to Fermi temperature
. The corresponding critical final value of
which leads to the BCS transition is found to be about one half, where is
the Fermi momentum.Comment: 4 pages, 1 figure. Phys. Rev. Lett. in pres
Dipole-dipole instability of atom clouds in a far-detuned optical dipole trap
The effect of the dipole-dipole interaction on the far-off-resonance optical
dipole trapping scheme is calculated by a mean-field approach. The trapping
laser field polarizes the atoms and the accompanying dipole-dipole energy shift
deepens the attractive potential minimum in a pancake-shaped cloud. At high
density the thermal motion cannot stabilize the gas against self-contraction
and an instability occurs. We calculate the boundary of the stable and unstable
equilibrium regions on a two-dimensional phase diagram of the atom number and
the ratio of the trap depth to the temperature. We discuss the limitations
imposed by the dipole-dipole instability on the parameters needed to reach
Bose-Einstein condensation in an optical dipole trap.Comment: 8 pages, 3 figure
Single-Particle Momentum Distribution of an Efimov trimer
Experimental progress in the study of strongly interacting ultracold atoms
has recently allowed the observation of Efimov trimers. We study theoretically
a non-conventional observable for these trimer states, that may be accessed
experimentally, the momentum distribution n(k) of the constitutive bosonic
particles. The large momentum part of the distribution is particularly
intriguing: In addition to the expected 1/k^4 tail associated to contact
interactions, it exhibits a subleading tail 1/k^5 which is a hall-mark of
Efimov physics and leads to a breakdown of a previously proposed expression of
the energy as a functional of the momentum distribution.Comment: This is a subpart of the (too long to be published) work
arXiv:1001.0774. This subpart has 11 pages and 2 figures. Revised version
correcting minor error
Ground states of dipolar gases in quasi-1D ring traps
We compute the ground state of dipoles in a quasi-one-dimensional ring trap
using few-body techniques combined with analytic arguments. The effective
interaction between two dipoles depends on their center-of-mass coordinate and
can be tuned by varying the angle between dipoles and the plane of the ring.
For weak enough interactions, the state resembles a weakly interacting Fermi
gas or an (inhomogeneous) Lieb-Liniger gas. A mapping between the Lieb-Liniger
and the dipolar-gas parameters in and beyond the Born approximation is
established, and we discuss the effect of inhomogeneities based on a
local-density approximation. For strongly repulsive interactions, the system
exhibits crystal-like localization of the particles. Their inhomogeneous
distribution may be understood in terms of a simple few-body model as well as a
local-density approximation. In the case of partially attractive interactions,
clustered states form for strong enough coupling, and the dependence of the
state on particle number and orientation angle of the dipoles is discussed
analytically.Comment: 15 pages, 10 figure
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