### Session V5: Theory of Cold Atom Systems

Chair: William Reinhardt, University of Washington
Room: Knoxville Convention Center 301AB

 Friday, May 19, 2006 1:30PM - 1:42PM V5.00001: Thermodynamic properties and thermometry of 1D Bose gases. Karen Kheruntsyan , Hui Hu , Peter Drummond We investigate the thermodynamic properties of an array of independent 1D Bose gases formed by a two-dimensional optical lattice. In particular, we calculate the total entropy of the system and compare it with the respective result for the 3D Bose-Einstein condensate as a function of the temperature and the interaction strength. This allows us to analyze how the temperature of the system is altered upon an adiabatic transfer of the 3D gas into an array of 1D tubes. The calculation is based on the exact finite temperature solution for a uniform 1D Bose gas, combined with the local density approximation [1]. The results can be applied to the recent experimental measurements of the local pair correlations in 1D Bose gases [2], which potentially can include finite temperature effects and no fitting parameters. In addition, we point out that the pair correlation function can be used as a thermometer for 1D Bose gases, under conditions when the density profiles become insensitive to temperature changes. [1] K. V. Kheruntsyan, D. M. Gangardt, P. D. Drummond, G. V. Shlyapnikov, Phys. Rev. A 71, 053615 (2005). [2] T. Kinoshita, T. Wenger, D. S. Weiss, Phys. Rev. Lett. 95, 190406 (2005). Friday, May 19, 2006 1:42PM - 1:54PM V5.00002: Effective Hamiltonian for Strongly Interacting Atoms in Low Dimensions Jason Kestner , Luming Duan For a dilute atomic gas in a strong transverse trapping potential, one normally expects that the transverse mode will be in the trap ground state. We show, however, that for the strongly interacting gas under a Feshbach resonance, the ground state of the system includes a large fraction of atoms in excited states of the trap, even if the gas is very dilute and the trap is very strong. This is due to an effect wherein trapping with a characteristic length $a_t$ along the transverse dimension(s) induces a pairing of characteristic length $a_t$ along the untrapped dimension(s). This typically enhances the coupling to many times the trap frequency and forces consideration of the conventionally neglected excited states of the trap when forming the effective Hamiltonian. Therefore, we introduce a dressed molecule state comprising a superposition of the bare molecule and the atomic Cooper pairs in excited trap states. Using an operator projection method, we derive the coupling between the dressed molecules and the unexcited atoms, which is a function of the physical detuning. We use this Hamiltonian to determine the confinement-induced shift of resonance in one and two dimensions and the resonance width. Friday, May 19, 2006 1:54PM - 2:06PM V5.00003: Light induced Abelian and non-Abelian gauge fields for ultracold atoms Michael Fleischhauer , Julius Ruseckas , Gediminas Juzeliunas , Patrik Oehberg The adiabatic motion of ultra-cold, multi-level atoms in spatially varying laser fields creating a dark state can give rise to effective gauge potentials. We show that these potentials lead to effective magnetic fields if the light fields possess a relative orbital angular momentum. This allows to study quantum-Hall like effects in ultra-cold atomic gases in various geometries. If the atom-light interaction creates several degenerate adiabatic eigenstates, the associated gauge potentials are non-Abelian. A pair of such degenerate dark states emerges e.g. if laser fields couple three internal states of an atom to a fourth common one under pairwise two--photon-resonance conditions. For this so-called tripod scheme we derive general conditions for truly non-Abelian gauge potentials and discuss special examples. In particular we show that using orthogonal laser beams with orbital angular momentum an effective magnetic field can be generated that has a monopole component. Friday, May 19, 2006 2:06PM - 2:18PM V5.00004: A Hyperspherical Treatment of the N-Fermion problem. Seth T. Ritenhouse , Javier von Stecher , Chris H. Greene , M. Cavagnero Hyperspherical methods provide for an interesting approach to studying the N body problem. ~We develop this unconventional description for the ground state and collective oscillations of the two-component normal Fermi gas with two-body s and p-wave contact interactions in an isotropic trap. ~The many-body problem can be accurately reduced to a linear, one-dimensional Schr\"{o}dinger equation in a single collective coordinate, the hyperradius (the root mean square radius) R of the N-atom system. ~The calculated properties of the Fermi gas ground state~are shown to be in close agreement with results from the Hartree-Fock (HF) approximation over a wide range of interspecies scattering lengths while the collective breathing mode excitation energy deviates qualitatively from HF predictions. ~The hyperspherical method also suggests that the Fermi gas may collapse for sufficiently large and negative scattering lengths. Friday, May 19, 2006 2:18PM - 2:30PM V5.00005: Quantum logic in Group-II neutral atoms via nuclear-exchange interactions David Hayes , Ivan Deutsch , Paul Julienne The spin exchange-interaction provides a means of producing an entangling quantum-logic gate, the square-root of SWAP, at the heart protocols employing single electron quantum dots. This is typically accompanied by strong Coulomb interactions and commensurate decoherence due to strong coupling of charge degrees of freedom to the noisy environment. We propose a protocol utilizing a \textit{nuclear-exchange} interaction that occurs through ultra-cold collisions of identical spin $\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$}$ Group-II \textit{neutral} atoms. A natural advantage is gained by storing the quantum information in nuclear spin states with long coherence times. Unlike NMR protocols based on weak magnetic dipole-dipole interaction, the nuclear exchange interaction stems from strong s-wave scattering of electrons. Nuclear exchange is ensured by the Fermi symmetry of the overall wave function. We have studied this protocol in the context of $^{171}$Yb atoms trapped in far-off resonance optical dipole traps. Using numerical analysis, we show that high-fidelity operation is possible through controlled collisions in varied double-well trapping potentials. Friday, May 19, 2006 2:30PM - 2:42PM V5.00006: A quasi-hermitian pseudo potential for higher partial-wave scattering Iris Reichenbach , Andrew Silberfarb , Rene Stock , Ivan Deutsch The dynamics of ultracold atoms in traps is an ideal platform for studies of quantum condensed matter, topological field theories, and quantum information processing. At the heart of these many-body systems are two-body interactions mediated by the molecular potentials of the respective dimer. Simultaneous treatment of the short-range molecular potential and long-range trapping potential is facilitated through the use of a pseudopotential, as seen in recent studies where s-wave scattering dominates. We extend this to higher- order partial waves, important for identical fermions and situations beyond the Wigner-threshold law. This pseudopotential is quasi- Hermitian, leading to a complete biorthonormal set of eigenfunctions. We apply this model to study trap-induced resonances occurring for colliding atoms in separated traps. Friday, May 19, 2006 2:42PM - 2:54PM V5.00007: Efficient Massively-Parallel Approach for Soving the Time-Dependent Schrodinger Equation B.I. Schneider , S.X. Hu , L.A. Collins A variety of problems in physics and chemistry require the solution of the time-dependent Schr{\"{o}}dinger equation (TDSE), including atoms and molecules in oscillating electromagnetic fields, atomic collisions, ultracold systems, and materials subjected to external forces. We describe an approach in which the Finite Element Discrete Variable Representation (FEDVR) is combined with the Real-Space Product (RSP) algorithm to generate an efficient and highly accurate method for the solution of both the linear and nonlinear TDSE. The FEDVR provides a highly-accurate spatial representation using a minimum number of grid points (N) while the RSP algorithm propagates the wavefunction in O(N) operations per time step. Parallelization of the method is transparent and is implemented by distributing one or two spatial dimension across the available processors within the Message-Passing-Interface (MPI) scheme. The complete formalism and a number of three-dimensional (3D) examples are given. ~ ~ ~ ~ ~ ~ Friday, May 19, 2006 2:54PM - 3:06PM V5.00008: Imaginary-time methods for finding ground states of fermion atomic gases Jochen Wachter , Murray Holland , Marilu Chiofalo Steepest descent methods using imaginary-time propagation of the Gross-Pitaevskii equation have been extremely useful for finding ground states in Bose-Einstein condensed systems. We have extended these methods to treat interacting fermion gases. In particular, we can find zero-temperature ground states for density matrix equations. We apply this method to the BCS theory of superconductivity and the two-channel model of the Bose-Fermi crossover problem. Friday, May 19, 2006 3:06PM - 3:18PM V5.00009: Atom-molecule conversion at a Feshbach resonance in a dilute gas Juha Javanainen We study the efficiency of atom-molecule conversion in a sweep of the magnetic field across a Feshbach resonance in a nondegenerate gas. We first integrate numerically the time dependent Schroedinger equation for a pair of atoms converting into a molecule. The atom-molecule conversion efficiency turns out to have an unexpected scaling property. To find the conversion efficiency in a dilute gas, we then average the two-atom result over all collisions available for a “spectator” atom, a process made quite simple by the scaling property. In accordance with the experiments [Hodby et al., PRL 94, 120402], the conversion efficiency is proportional to phase space density of the atomic gas. However, not entirely in accordance with the experiments, we find a difference between fermions and bosons. Friday, May 19, 2006 3:18PM - 3:30PM V5.00010: Consequences of Fermi liquid theory close to the s-wave Feshbach resonances Sergio Gaudio , Jason Jackiewicz , Kevin Bedell In a previous paper cond-mat/ 0505306 we developed a Fermi liquid theory for a two component Fermi gas, close to a Feshbach resonance. In this talk, we will present some recent results on thermodynamic properties of the normal phase, within the same theory, which can be used to test the validity of the Fermi liquid description.