Global Analysis of Data on the Spin-orbit-coupled A1Σ+ and b3Πu States of Cs2

We present experimentally derived potential curves and spin-orbit interaction functions for the strongly perturbed A1+ u and b3u states of the cesium dimer. The results are based on data from several sources. Laser-induced fluorescence Fourier transform spectroscopy (LIF FTS) was used some time ago in the Laboratoire Aim´e Cotton primarily to study the X1+ g state. More recent work at Tsinghua University provides information from moderate resolution spectroscopy on the lowest levels of the b3± 0u states as well as additional high resolution data. From Innsbruck University, we have precision data obtained with cold Cs2 molecules. Recent data from Temple University was obtained using the optical-optical double resonance polarization spectroscopy technique, and finally, a group at the University of Latvia has added additional LIF FTS data. In the Hamiltonian matrix, we have used analytic potentials (the Expanded Morse Oscillator form) with both finite-difference (FD) coupled-channels and discrete variable representation (DVR) calculations of the term values. Fitted diagonal and off-diagonal spin-orbit functions are obtained and compared with ab initio results from Temple and Moscow State universities

The angular momentum of a magnetically trapped atomic condensate

For an atomic condensate in an axially symmetric magnetic trap, the sum of the axial components of the orbital angular momentum and the hyperfine spin is conserved. Inside an Ioffe-Pritchard trap (IPT) whose magnetic field (B-field) is not axially symmetric, the difference of the two becomes surprisingly conserved. In this paper we investigate the relationship between the values of the sum/difference angular momentums for an atomic condensate inside a magnetic trap and the associated gauge potential induced by the adiabatic approximation. Our result provides significant new insight into the vorticity of magnetically trapped atomic quantum gases.Comment: 4 pages, 1 figure

The Gross-Pitaevskii Equation for Bose Particles in a Double Well Potential: Two Mode Models and Beyond

There have been many discussions of two-mode models for Bose condensates in a double well potential, but few cases in which parameters for these models have been calculated for realistic situations. Recent experiments lead us to use the Gross-Pitaevskii equation to obtain optimum two-mode parameters. We find that by using the lowest symmetric and antisymmetric wavefunctions, it is possible to derive equations for a more exact two-mode model that provides for a variable tunneling rate depending on the instantaneous values of the number of atoms and phase differences. Especially for larger values of the nonlinear interaction term and larger barrier heights, results from this model produce better agreement with numerical solutions of the time-dependent Gross-Pitaevskii equation in 1D and 3D, as compared with previous models with constant tunneling, and better agreement with experimental results for the tunneling oscillation frequency [Albiez et al., cond-mat/0411757]. We also show how this approach can be used to obtain modified equations for a second quantized version of the Bose double well problem.Comment: RevTeX, 14 pages, 14 figure

Optimization of Generalized Multichannel Quantum Defect reference functions for Feshbach resonance characterization

This work stresses the importance of the choice of the set of reference functions in the Generalized Multichannel Quantum Defect Theory to analyze the location and the width of Feshbach resonance occurring in collisional cross-sections. This is illustrated on the photoassociation of cold rubidium atom pairs, which is also modeled using the Mapped Fourier Grid Hamiltonian method combined with an optical potential. The specificity of the present example lies in a high density of quasi-bound states (closed channel) interacting with a dissociation continuum (open channel). We demonstrate that the optimization of the reference functions leads to quantum defects with a weak energy dependence across the relevant energy threshold. The main result of our paper is that the agreement between the both theoretical approaches is achieved only if optimized reference functions are used.Comment: submitte to Journal of Physics

Breakdown of the scale invariance in the vicinity of Tonks-Girardeau gas

In this article, we consider the monopole excitations of the harmonically trapped Bose gas in the vicinity of the Tonks-Girardeau limit. Using Girardeau's Fermi-Bose duality and subsequently an effective fermion-fermion odd-wave interaction, we obtain the dominant correction to the scale-invariance-protected value of the excitation frequency, for microscopically small excitation amplitudes. We produce a series of diffusion Monte Carlo results that confirm our analytic prediction for three particles. And less expectedly, our result stands in excellent agreement with the result of a hydrodynamic simulation of the microscopically large but macroscopically small excitations.Comment: 8 pages, 3 figure

Electronic Structure of Atoms in Magnetic Quadrupole Traps

We investigate the electronic structure and properties of atoms exposed to a magnetic quadrupole field. The spin-spatial as well as generalized time reversal symmetries are established and shown to lead to a two-fold degeneracy of the electronic states in the presence of the field. Low-lying as well as highly excited Rydberg states are computed and analyzed for a broad regime of field gradients. The delicate interplay between the Coulomb and various magnetic interactions leads to complex patterns of the spatial spin polarization of individual excited states. Electromagnetic transitions in the quadrupole field are studied in detail thereby providing the selection rules and in particular the transition wavelengths and corresponding dipole strengths. The peculiar property that the quadrupole magnetic field induces permanent electric dipole moments of the atoms is derived and discussed.Comment: 17 pages, 13 figures, accepted for publication in PR

Explosion of a collapsing Bose-Einstein condensate

We show that elastic collisions between atoms in a Bose-Einstein condensate with attractive interactions lead to an explosion that ejects a large fraction of the collapsing condensate. We study variationally the dynamics of this explosion and find excellent agreement with recent experiments on magnetically trapped Rubidium-85. We also determine the energy and angular distribution of the ejected atoms during the collapse.Comment: Four pages of ReVTeX and five postscript figure

Visualizing the Coupling between Red and Blue Stark States Using Photoionization Microscopy

In nonhydrogenic atoms in a dc electric field, the finite size of the ionic core introduces a coupling between quasibound Stark states that leads to avoided crossings between states that would otherwise cross. Near an avoided crossing, the interacting states may have decay amplitudes that cancel each other, decoupling one of the states from the ionization continuum. This well- known interference narrowing effect, observed as a strongly electric field- dependent decrease in the ionization rate, was previously observed in several atoms. Here we use photoionization microscopy to visualize interference narrowing in helium atoms, thereby explicitly revealing the mechanism by which Stark states decay. The interference narrowing allows measurements of the nodal patterns of red Stark states, which are otherwise not observable due to their intrinsic short lifetime

Nonadiabatic Dynamics of Atoms in Nonuniform Magnetic Fields

Dynamics of neutral atoms in nonuniform magnetic fields, typical of quadrupole magnetic traps, is considered by applying an accurate method for solving nonlinear systems of differential equations. This method is more general than the adiabatic approximation and, thus, permits to check the limits of the latter and also to analyze nonadiabatic regimes of motion. An unusual nonadiabatic regime is found when atoms are confined from one side of the z-axis but are not confined from another side. The lifetime of atoms in a trap in this semi-confining regime can be sufficiently long for accomplishing experiments with a cloud of such atoms. At low temperature, the cloud is ellipsoidal being stretched in the axial direction and moving along the z-axis. The possibility of employing the semi-confining regime for studying the relative motion of one component through another, in a binary mixture of gases is discussed.Comment: 1 file, 17 pages, RevTex, 2 table

Hidden Sp(2s+1)- or SO(2s+1)-symmetry and new exactly solvable models in ultracold atomic systems

The high spin ultracold atom models with a special form of contact interactions, i.e., the scattering lengthes in the total spin-$2,4 \cdots$ channels are equal but may be different from that in the spin-0 channel, is studied. It is found that those models have either $Sp(2s+1)$-symmetry for the fermions or $SO(2s+1)$-symmetry for the bosons in the spin sector. Based on the symmetry analysis, a new class of exactly solvable models is proposed and solved via the Bethe ansatz. The ground states for repulsive fermions are also discussed.Comment: 6 pages, 2 figure