A toy model for molecular condensates in Bose gases

The occurrence of a molecular Bose-Einstein condensate is studied for an atomic system near a zero energy resonance of the binary scattering process, with a large and positive scattering length. The interaction potential is modeled by a pseudo-potential having one bound state. Using a variational Gaussian ansatz for the $N$-body density operator, we discuss the thermodynamic properties at low temperature and the relative stability of the system towards the formation of an atomic Bose-Einstein condensate. We also derive an approximate Gross-Pitaevskii equation for the molecular condensate leading to the prediction of a Bogoliubov spectrum.Comment: 4 pages, latex, no figure

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

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

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

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 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

Variational self-consistent theory for trapped Bose gases at finite temperature

We apply the time-dependent variational principle of Balian-V\'en\'eroni to a system of self-interacting trapped bosons at finite temperature. The method leads to a set of coupled non-linear time dependent equations for the condensate density, the thermal cloud and the anomalous density. We solve numerically these equations in the static case for a harmonic trap. We analyze the various densities as functions of the radial distance and the temperature. We find an overall good qualitative agreement with recent experiments as well as with the results of many theoretical groups. We also discuss the behavior of the anomalous density at low temperatures owing to its importance to account for many-body effects.Comment: 8 pages, 8 figure