Operator-Algebraic Approach to the Yrast Spectrum of Weakly Interacting Trapped Bosons

We present an operator-algebraic approach to deriving the low-lying quasi-degenerate spectrum of weakly interacting trapped N bosons with total angular momentum \hbar L for the case of small L/N, demonstrating that the lowest-lying excitation spectrum is given by 27 g n_3(n_3-1)/34, where g is the strength of the repulsive contact interaction and n_3 the number of excited octupole quanta. Our method provides constraints for these quasi-degenerate many-body states and gives higher excitation energies that depend linearly on N.Comment: 7 pages, one figur

Effect of anharmonicities in the critical number of trapped condensed atoms with attractive two-body interaction

We determine the quantitative effect, in the maximum number of particles and other static observables, due to small anharmonic terms added to the confining potential of an atomic condensed system with negative two-body interaction. As an example of how a cubic or quartic anharmonic term can affect the maximum number of particles, we consider the trap parameters and the results given by Roberts et al. [Phys. Rev. Lett. 86, 4211 (2001)]. However, this study can be easily transferred to other trap geometries to estimate anharmonic effects.Comment: Total of 5 pages, 3 figures and 1 table. To appear in Phys. Rev.

Bistability and macroscopic quantum coherence in a BEC of ^7Li

We consider a Bose-Einstein condensate (BEC) of $^7Li$ in a situation where the density undergoes a symmetry breaking in real space. This occurs for a suitable number of condensed atoms in a double well potential, obtained by adding a standing wave light field to the trap potential. Evidence of bistability results from the solution of the Gross-Pitaevskii equation. By second quantization, we show that the classical bistable situation is in fact a Schr\"odinger cat (SC) and evaluate the tunneling rate between the two SC states. The oscillation between the two states is called MQC (macroscopic quantum coherence); we study the effects of losses on MQC.Comment: 8 pages, 11 figures. e-mail: [email protected]

Multi frequency evaporative cooling to BEC in a high magnetic field

We demonstrate a way to circumvent the interruption of evaporative cooling observed at high bias field for $^{87}$Rb atoms trapped in the (F=2, m=+2) ground state. Our scheme uses a 3-frequencies-RF-knife achieved by mixing two RF frequencies. This compensates part of the non linearity of the Zeeman effect, allowing us to achieve BEC where standard 1-frequency-RF-knife evaporation method did not work. We are able to get efficient evaporative cooling, provided that the residual detuning between the transition and the RF frequencies in our scheme is smaller than the power broadening of the RF transitions at the end of the evaporation ramp.Comment: 12 pages, 2 figure

Free expansion of Bose-Einstein condensates with quantized vortices

The expansion of Bose-Einstein condensates with quantized vortices is studied by solving numerically the time-dependent Gross-Pitaevskii equation at zero temperature. For a condensate initially trapped in a spherical harmonic potential, we confirm previous results obtained by means of variational methods showing that, after releasing the trap, the vortex core expands faster than the radius of the atomic cloud. This could make the detection of vortices feasible, by observing the depletion of the density along the axis of rotation. We find that this effect is significantly enhanced in the case of anisotropic disc-shaped traps. The results obtained as a function of the anisotropy of the initial configuration are compared with the analytic solution for a noninteracting gas in 3D as well as with the scaling law predicted for an interacting gas in 2D.Comment: 5 pages, 6 postscript figure

Bose-Einstein condensation with magnetic dipole-dipole forces

Ground-state solutions in a dilute gas interacting via contact and magnetic dipole-dipole forces are investigated. To the best of our knowledge, it is the first example of studies of the Bose-Einstein condensation in a system with realistic long-range interactions. We find that for the magnetic moment of e.g. chromium and a typical value of the scattering length all solutions are stable and only differ in size from condensates without long-range interactions. By lowering the value of the scattering length we find a region of unstable solutions. In the neighborhood of this region the ground state wavefunctions show internal structures not seen before in condensates. Finally, we find an analytic estimate for the characteristic length appearing in these solutions.Comment: final version, 4 pages, 4 figure

Loading a vapor cell magneto-optic trap using light-induced atom desorption

Low intensity white light was used to increase the loading rate of $^{87}$Rb atoms into a vapor cell magneto-optic trap by inducing non-thermal desorption of Rb atoms from the stainless steel walls of the vapor cell. An increased Rb partial pressure reached a new equilibrium value in less than 10 seconds after switching on the broadband light source. After the source was turned off, the partial pressure returned to its previous value in $1/e$ times as short as 10 seconds.Comment: 7 pages, 6 figure

Evaporative cooling of trapped fermionic atoms

We propose an efficient mechanism for the evaporative cooling of trapped fermions directly into quantum degeneracy. Our idea is based on an electric field induced elastic interaction between trapped atoms in spin symmetric states. We discuss some novel general features of fermionic evaporative cooling and present numerical studies demonstrating the feasibility for the cooling of alkali metal fermionic species $^6$Li, $^{40}$K, and $^{82,84,86}$Rb. We also discuss the sympathetic cooling of fermionic hyperfine spin mixtures, including the effects of anisotropic interactions.Comment: to be publishe

Instantons and radial excitations in attractive Bose-Einstein condensates

Imaginary- and real-time versions of an equation for the condensate density are presented which describe dynamics and decay of any spherical Bose-Einstein condensate (BEC) within the mean field appraoch. We obtain quantized energies of collective finite amplitude radial oscillations and exact numerical instanton solutions which describe quantum tunneling from both the metastable and radially excited states of the BEC of 7Li atoms. The mass parameter for the radial motion is found different from the gaussian value assumed hitherto, but the effect of this difference on decay exponents is small. The collective breathing states form slightly compressed harmonic spectrum, n=4 state lying lower than the second Bogolyubov (small amplitude) mode. The decay of these states, if excited, may simulate a shorter than true lifetime of the metastable state. By scaling arguments, results extend to other attractive BEC-s.Comment: 6 pages, 3 figure

Self-Trapping, Quantum Tunneling and Decay Rates for a Bose Gas with Attractive Nonlocal Interaction

We study the Bose-Einstein condensation for a cloud of $^7$Li atoms with attractive nonlocal (finite-range) interaction in a harmonic trap. In addition to the low-density metastable branch, that is present also in the case of local interaction, a new stable branch appears at higher densities. For a large number of atoms, the size of the cloud in the stable high-density branch is independent of the trap size and the atoms are in a macroscopic quantum self-trapped configuration. We analyze the macroscopic quantum tunneling between the low-density metastable branch and the high-density one by using the istanton technique. Moreover we consider the decay rate of the Bose condensate due to inelastic two- and three-body collisions.Comment: 5 pages, 4 figures, submitted to Phys. Rev.