### Session I4: Ultracold Scattering and Interactions

Chair: Marjatta Lyyra, Temple University
Room: Nittany Lion Inn Ballroom AB

 Thursday, May 29, 2008 8:00AM - 8:12AM I4.00001: Atomic rubidium, the workhorse of theoretical collision physics Boudewijn Verhaar , Eric van Kempen , Servaas Kokkelmans Since the first realizations of Bose-Einstein condensates in ultracold atomic gases in 1995, the 85Rb and 87Rb atomic species have acted as the workhorses of experimental developments in this field. Parallel to and partly preceding this work the same isotopes figured also as workhorses for successful theoretical attempts aiming at unravelling the needed information on interaction properties like scattering lengths and Feshbach resonances\footnote{Hugo Boesten, PhD thesis Eindhoven University (1996, ISBN 90-386-0019-4)}. The purpose of this contribution is to describe recent developments of this theoretical work, based on an adiabatic variant of the accumulated phase method, which gives rise to the most reliable and accurate predictions of interaction properties available to date for any alkali atomic gas\footnote {See preliminary description by E. van Kempen, S. Kokkelmans, D. Heinzen, and B. Verhaar, Phys. Rev. Lett. 88, 093201 (2002).}. The method can be readily applied to predict interaction properties between two different atomic species, once a limited set of experimental data is available to determine the accumulated phases. Thursday, May 29, 2008 8:12AM - 8:24AM I4.00002: Systematic assignment of Feshbach resonances via an asymptotic bound state model Maikel Goosen , Servaas Kokkelmans We present an Asymptotic Bound state Model (ABM), which is useful to predict Feshbach resonances. The model utilizes asymptotic properties of the interaction potentials to represent coupled molecular wavefunctions. The bound states of this system give rise to Feshbach resonances, localized at the magnetic fields of intersection of these bound states with the scattering threshold. This model was very successful to assign measured Feshbach resonances in an ultra cold mixture of $^6$Li and $^{40}$K atoms\footnote{E. Wille, F.M. Spiegelhalder, G. Kerner, D. Naik, A. Trenkwalder, G. Hendl, F. Schreck, R. Grimm, T.G. Tiecke, J.T.M. Walraven, S.J.J.M.F. Kokkelmans, E. Tiesinga, P.S. Julienne, arXiv:0711.2916}. For this system, the accuracy of the determined scattering lengths is comparable to full coupled channels results. However, it was not possible to predict the width of the resonances. We discuss how an incorporation of threshold effects will improve the model, and we apply it to a mixture of $^{87}$Rb and $^{133}$Cs atoms, where recently Feshbach resonances have been measured. Thursday, May 29, 2008 8:24AM - 8:36AM I4.00003: Total control over ultracold interactions via electric and magnetic fields Servaas Kokkelmans , Bout Marcelis , Boudewijn Verhaar The scattering length is commonly used to characterize the strength of ultracold atomic interactions, since it is the leading parameter in the low-energy expansion of the scattering phase shift. Its value can be modified via a magnetic field, by using a Feshbach resonance. However, the effective range term, which is the second parameter in the phase shift expansion, determines the width of the resonance and gives rise to important properties of ultracold gases. Independent control over this parameter is not possible by using a magnetic field only. We demonstrate that a combination of magnetic and electric fields can be used to get independent control over both parameters, which leads to full control over elastic ultracold interactions\footnote{B.~Marcelis, B.~Verhaar, and S.~Kokkelmans, arXiv:0710.0733}. Thursday, May 29, 2008 8:36AM - 8:48AM I4.00004: Heteronuclear Feshbach resonances in a mixture of ultracold $^{87}$Rb and $^{133}$Cs K. Pilch , A. Lange , A. Prantner , G. Kerner , F. Ferlaino , H.-C. Naegerl , R. Grimm We present the first observation of heteronuclear Feshbach resonances in a bosonic mixture of ultracold $^{133}$Cs and $^{87}$Rb. We give an overview of our experimental setup and the procedure of all-optical sample preparation. One of the key ingredients is the use of simultaneous degenerate Raman sideband cooling on both species. We perform Feshbach spectroscopy on a mixture of $\sim$10$^{6}$ atoms, optically trapped at a temperature of a few $\mu$K, by recording trap loss. We find a rich structure of interspecies Feshbach resonances within a magnetic field ranging from 0G to 300G. A consistent assignment of the observed Feshbach resonances will allow us to quantify the interspecies collisional properties. We discuss potential pathways towards obtaining a double-degenerate bosonic quantum gas and towards the production of ground state RbCs molecules. Thursday, May 29, 2008 8:48AM - 9:00AM I4.00005: Few-body physics with ultracold Cs atoms and molecules Steven Knoop , Francesca Ferlaino , Martin Berninger , Michael Mark , Hanns-Christoph Naegerl , Rudolf Grimm Ultracold atomic gases are versatile systems to study few-body physics because of full control over the external and internal degrees of freedom and the magnetic tunability of the scattering properties using Feshbach resonances. Here we experimentally study three- and four-body physics by investigating ultracold (30-250 nK) atom-dimer and dimer-dimer collisions with Cs Feshbach molecules in various molecular states and Cs atoms in different hyperfine states. Resonant enhancement of the atom-dimer relaxation rate is observed in a system of three identical bosons and interpreted as being induced by a trimer state, possibly an Efimov state. A strong magnetic field dependence of the relaxation rate is also observed when the atoms are transferred to a different hyperfine sublevel. For dimer-dimer collisions we have observed a suppression of the collisional loss rate. Thursday, May 29, 2008 9:00AM - 9:12AM I4.00006: Universal Analysis of Three-Body Recombination of $^{87}$Rb Atoms Eric Braaten , Daekyoung Kang , Lucas Platter , Hans-Werner Hammer The 3-body recombination rate at threshold for identical bosons with a large scattering length $a$ is a universal function proportional to $a^4$ with a coefficient that is a log-periodic function of $a$. The Garching group has recently measured 3-body recombination in a Bose-Einstein condensate of $^{87}$Rb atoms near a Feshbach resonance. Their results in the large scattering length region are compatible with the universal prediction if we allow for systematic errors in the measurement and in the calibration of the magnetic field. We determine the Efimov parameter in the universal formula by fitting the Garching data. We then use universal results to predict the scattering lengths at which there are local minima in the recombination rate, recombination resonances, and dimer relaxation resonances. Thursday, May 29, 2008 9:12AM - 9:24AM I4.00007: Three-Body Recombination of Identical Bosons with a Large Positive Scattering Length at Nonzero Temperature Daekyoung Kang , Lucas Platter , Eric Braaten , Hans Hammer For identical bosons with a large scattering length, the dependence of the 3-body recombination rate on the collision energy is determined by universal functions of a single scaling variable. There are six scaling functions for angular momentum zero and one scaling function for each higher partial wave. We calculate these universal functions by solving the Skorniakov-Ter-Martirosian equation. The results for the 3-body recombination as a function of the collision energy are in good agreement with previous results from solving the 3-body Schrodinger equation for He-4 atoms. The universal scaling functions can be used to calculate the 3-body recombination rate at nonzero temperature. We obtain an excellent fit to the data from the Innsbruck group for Cs-133 atoms with a large positive scattering length. Thursday, May 29, 2008 9:24AM - 9:36AM I4.00008: Finite Range Corrections in Few-Body Systems of Cold Atoms Lucas Platter A non-relativistic three-body system with large two-body scattering length displays fascinating features, as for example discrete scale invariance in recombination and bound state observables. While the implications of zero-range interactions are well understood, it is also desirable to understand the impact of finite range corrections of the underlying interaction. This allows for an assessment of the limits of universality but also increases the range of applicability of universal approaches. I will discuss the calculation of range corrections within the framework of an effective field theory (EFT). This EFT allows for a model-independent and systematically improvable calculation of observables of few-body systems with large scattering length. I will present results for the Helium-4 trimer and will discuss applications of this formalism to the three-body recombination of identical boson. Thursday, May 29, 2008 9:36AM - 9:48AM I4.00009: Efimov states embedded in the continuum Seth T. Rittenhouse , N.P. Mehta , J.P. D'Incao , Chris H. Greene By considering a multichannel generalization of the Fermi pseudopotential, we calculate the adiabatic hyperspherical potential curves for three interacting bosons. The resulting energy landscape has a rich and complex structure showing multiple length scales and internal symmetries. Our model indicates the existence of a universal diabatic potential curve which supports a series of quasistable Efimov states embedded in the three-body continuum. These states are energetically far removed from the scattering threshold, and can be accessed using spectroscopic methods, opening experimental possibilities for the exploration of a new realm of Efimov physics Thursday, May 29, 2008 9:48AM - 10:00AM I4.00010: Extracting Efimov physics from three-body recombination at finite energy Yujun Wang , J.P. D'Incao , B.D. Esry We have identified energy-dependent features in the three-body recombination rate that can trace their origin to Efimov physics. These features manifest themselves as log-periodic sinusoidal modulations of the rates as a function of energy. This log-periodic behavior provides the link to Efimov physics. Using a model two-body interaction, we calculate the recombination rate numerically for identical bosons and for the Cs-Li mixture. We show, however, that the energy modulations are more clear in Cs+Cs+Li recombination. We will also discuss the issues important for observing these features experimentally. Thursday, May 29, 2008 10:00AM - 10:12AM I4.00011: Analysis of the Four-Boson System with Large Scattering Length Javier von Stecher , Jose P. D'Incao , Chris H. Greene We investigate the properties of four-boson systems interacting through a short-range two-body potential. Tuning the scattering length close to unitarity, we analyze the universal aspects of such systems. Combining correlated Gaussian calculations with a hyperspherical treatment, we obtain hyperspherical effective potentials and study the collisional aspects for such bosonic systems. In particular, we consider possible Efimov trimer formation due to dimer-dimer collisions. Thursday, May 29, 2008 10:12AM - 10:24AM I4.00012: Finite energy effects on dimer-dimer collisions in two-spin ultracold Fermi gases Jose P. D'Incao , Seth T. Rittenhouse , Nirav P. Mehta , Chris H. Greene We demonstrate important properties of few-body parameters which may offer deeper insight into the many-body phenomena in two-spin Fermi gases at finite temperatures. Our results indicate, for instance, that previously obtained zero energy results for the dimer-dimer scattering length can have a limited applicability to a finite temperature ultracold gas near a Feshbach resonance. In order to account for finite temperature effects we have calculated the energy dependent {\em complex} dimer-dimer scattering length, $a_{dd}(E)$, where the real and imaginary parts correspond to contributions from elastic and inelastic collisions, respectively. Our results were obtained by solving the four-body Schr\"odinger equation in the hyperspherical adiabatic representation which, despite the high complexity of the problem, offers a simple, intuitive, and quantitative picture for the collision processes. This work was supported by the National Science Foundation.