36 research outputs found
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
Four-body Efimov effect
We study three same spin state fermions of mass M interacting with a
distinguishable particle of mass m in the unitary limit where the interaction
has a zero range and an infinite s-wave scattering length. We predict an
interval of mass ratio 13.384 < M/m < 13.607 where there exists a purely
four-body Efimov effect, leading to the occurrence of weakly bound tetramers
without Efimov trimers.Comment: 4 pages, 2 figure
The effect of self-affine fractal roughness of wires on atom chips
Atom chips use current flowing in lithographically patterned wires to produce
microscopic magnetic traps for atoms. The density distribution of a trapped
cold atom cloud reveals disorder in the trapping potential, which results from
meandering current flow in the wire. Roughness in the edges of the wire is
usually the main cause of this behaviour. Here, we point out that the edges of
microfabricated wires normally exhibit self-affine roughness. We investigate
the consequences of this for disorder in atom traps. In particular, we consider
how closely the trap can approach the wire when there is a maximum allowable
strength of the disorder. We comment on the role of roughness in future
atom--surface interaction experiments.Comment: 7 pages, 7 figure
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
Three fully polarized fermions close to a p-wave Feshbach resonance
We study the three-body problem for three atomic fermions, in the same spin
state, experiencing a resonant interaction in the p-wave channel via a Feshbach
resonance represented by a two-channel model. The rate of inelastic processes
due to recombination to deeply bound dimers is then estimated from the
three-body solution using a simple prescription. We obtain numerical and
analytical predictions for most of the experimentally relevant quantities that
can be extracted from the three-body solution: the existence of weakly bound
trimers and their lifetime, the low-energy elastic and inelastic scattering
properties of an atom on a weakly bound dimer (including the atom-dimer
scattering length and scattering volume), and the recombination rates for three
colliding atoms towards weakly bound and deeply bound dimers. The effect of
"background" non-resonant interactions in the open channel of the two-channel
model is also calculated and allows to determine which three-body quantities
are `universal' and which on the contrary depend on the details of the model.Comment: 31 pages, 12 figure
Pseudopotential in resonant regimes
The zero-range potential approach is extended for the description of
situations where two-body scattering is resonant in arbitrary partial waves.
The formalism generalizes the Fermi pseudopotential which can be used only for
s-wave broad resonances. In a given channel, the interaction is described
either in terms of a contact condition on the wave function or with a family of
pseudopotentials. We show that it is necessary to introduce a regularized
scalar product for wave functions obtained in the zero-range potential
formalism (except for the Fermi pseudopotential). This metrics shows that the
geometry of these Hilbert spaces depends crucially on the interaction.Comment: 12 pages - 1 figur
Efimov Trimers near the Zero-crossing of a Feshbach Resonance
Near a Feshbach resonance, the two-body scattering length can assume any
value. When it approaches zero, the next-order term given by the effective
range is known to diverge. We consider the question of whether this divergence
(and the vanishing of the scattering length) is accompanied by an anomalous
solution of the three-boson Schr\"odinger equation similar to the one found at
infinite scattering length by Efimov. Within a simple zero-range model, we find
no such solutions, and conclude that higher-order terms do not support Efimov
physics.Comment: 8 pages, no figures, final versio
Efimov physics beyond three particles
Efimov physics originally refers to a system of three particles. Here we
review recent theoretical progress seeking for manifestations of Efimov physics
in systems composed of more than three particles. Clusters of more than three
bosons are tied to each Efimov trimer, but no independent Efimov physics exists
there beyond three bosons. The case of a few heavy fermions interacting with a
lighter atom is also considered, where the mass ratio of the constituent
particles plays a significant role. Following Efimov's study of the (2+1)
system, the (3+1) system was shown to have its own critical mass ratio to
become Efimovian. We show that the (4+1) system becomes Efimovian at a mass
ratio which is smaller than its sub-systems thresholds, giving a pure five-body
Efimov effect. The (5+1) and (6+1) systems are also discussed, and we show the
absence of 6- and 7-body Efimov physics there
Universal physics of 2+1 particles with non-zero angular momentum
The zero-energy universal properties of scattering between a particle and a
dimer that involves an identical particle are investigated for arbitrary
scattering angular momenta. For this purpose, we derive an integral equation
that generalises the Skorniakov - Ter-Martirosian equation to the case of
non-zero angular momentum. As the mass ratio between the particles is varied,
we find various scattering resonances that can be attributed to the appearance
of universal trimers and Efimov trimers at the collisional threshold.Comment: 6 figure