Feshbach Resonances and Medium Effects in ultracold atomic Gases

We develop an effective low energy theory for multi-channel scattering of cold atomic alkali atoms with particular focus on Feshbach resonances. The scattering matrix is expressed in terms of observables only and the theory allows for the inclusion of many-body effects both in the open and in the closed channels. We then consider the frequency and damping of collective modes for Fermi gases and demonstrate how medium effects significantly increase the scattering rate determining the nature of the modes. Our results obtained with no fitting parameters are shown to compare well with experimental data.Comment: Presented at the 5th workshop on Critical Stability, Erice, Italy 13-17 October 2008. 8 pages, 3 figures. Figure caption correcte

Few-body precursor of the Higgs mode in a superfluid Fermi gas

We demonstrate that an undamped few-body precursor of the Higgs mode can be investigated in a harmonically trapped Fermi gas. Using exact diagonalisation, the lowest monopole mode frequency is shown to depend non-monotonically on the interaction strength, having a minimum in a crossover region. The minimum deepens with increasing particle number, reflecting that the mode is the few-body analogue of a many-body Higgs mode in the superfluid phase, which has a vanishing frequency at the quantum phase transition point to the normal phase. We show that this mode mainly consists of coherent excitations of time-reversed pairs, and that it can be selectively excited by modulating the interaction strength, using for instance a Feshbach resonance in cold atomic gases.Comment: 9 pages, 7 figure

Tunable Wigner States with Dipolar Atoms and Molecules

We study the few-body physics of trapped atoms or molecules with electric or magnetic dipole moments aligned by an external field. Using exact numerical diagonalization appropriate for the strongly correlated regime, as well as a classical analysis, we show how Wigner localization emerges with increasing coupling strength. The Wigner states exhibit non-trivial geometries due to the anisotropy of the interaction. This leads to transitions between different Wigner states as the tilt angle of the dipoles with the confining plane is changed. Intriguingly, while the individual Wigner states are well described by a classical analysis, the transitions between different Wigner states are strongly affected by quantum statistics. This can be understood by considering the interplay between quantum-mechanical and spatial symmetry properties. Finally, we demonstrate that our results are relevant to experimentally realistic systems.Comment: 4 pages, 6 figure

Spin diffusion in trapped clouds of strongly interacting cold atoms

We show that puzzling recent experimental results on spin diffusion in a strongly interacting atomic gas may be understood in terms of the predicted spin diffusion coefficient for a generic strongly interacting system. Three important features play a central role: a) Fick's law for diffusion must be modified to allow for the trapping potential, b) the diffusion coefficient is inhomogeneous, due to the density variations in the cloud and c) the diffusion approximation fails in the outer parts of the cloud, where the mean free path is long.Comment: 4 pages, 6 figures, minor modifications to the text and figures in 2. versio

The Specific Heat of a Trapped Fermi Gas: an Analytical Approach

We find an analytical expression for the specific heat of a Fermi gas in a harmonic trap using a semi-classical approximation. Our approximation is valid for kT>hw and in this range it is shown to be highly accurate. We comment on the semi-classical approximation, presenting an explanation for this high accuracy.Comment: To be published in Physics Letters A. 7 pages (RevTex) and 2 figures (postscript

Polarons and Molecules in a Two-Dimensional Fermi Gas

We study an impurity atom in a two-dimensional Fermi gas using variational wave functions for (i) an impurity dressed by particle-hole excitations (polaron) and (ii) a dimer consisting of the impurity and a majority atom. In contrast to three dimensions, where similar calculations predict a sharp transition to a dimer state with increasing interspecies attraction, we show that the polaron ansatz always gives a lower energy. However, the exact solution for a heavy impurity reveals that both a two-body bound state and distortions of the Fermi sea are crucial. This reflects the importance of particle-hole pairs in lower dimensions and makes simple variational calculations unreliable. We show that the energy of an impurity gives important information about its dressing cloud, for which both ans\"atze give inaccurate results.Comment: 5 pages, 2 figures, minor change

Clock shifts in a Fermi gas interacting with a minority component: a soluble model

We consider the absorption spectrum of a Fermi gas mixed with a minority species when majority fermions are transferred to another internal state by an external probe. In the limit when the minority species is much more massive than the majority one, we show that the minority species may be treated as static impurities and the problem can be solved in closed form. The analytical results bring out the importance of vertex corrections, which change qualitatively the nature of the absorption spectrum. It is demonstrated that large line shifts are not associated with resonant interactions in general. We also show that the commonly used ladder approximation fails when the majority component is degenerate for large mass ratios between the minority and majority species and that bubble diagrams, which correspond to the creation of many particle--hole pairs, must be taken into account. We carry out detailed numerical calculations, which confirm the analytical insights and we point out the connection to shadowing phenomena in nuclear physics.Comment: 8 pages, 4 figures, NORDITA-2010-