Recent Experiments with Bose-Condensed Gases at JILA

We consider a binary mixture of two overlapping Bose-Einstein condensates in two different hyperfine states of \Rb87 with nearly identical magnetic moments. Such a system has been simply realized through application of radiofrequency and microwave radiation which drives a two-photon transition between the two states. The nearly identical magnetic moments afford a high degree of spatial overlap, permitting a variety of new experiments. We discuss some of the conditions under which the magnetic moments are identical, with particular emphasis placed on the requirements for a time-averaged orbiting potential (TOP) magnetic trap.Comment: 9 pages, 5 figures; corrected post-publication editio

Mentoring and Self-Management Career Strategies For Entrepreneurs

The purpose of this article is to examine the literature on self management and mentoring to develop practical methods of enhancing the career success of entrepreneurs. The authors believe that both behavioural and cognitive self-management strategies can be useful to entrepreneurs. These techniques include goal-setting, self-observation, self-rewards, cueing, self-talk, visualization and the active reframing of obstacles into opportunities. In addition, the varying roles and functions of mentors, including emotional, vocational and role modelling support, will have many positive benefits for both entrepreneurial proteges and mentors. Recommendations for furture research and an entrepreneurial model of career development are provided

Mentoring and Self-Management Career Strategies For Entrepreneurs

The purpose of this article is to examine the literature on self management and mentoring to develop practical methods of enhancing the career success of entrepreneurs. The authors believe that both behavioural and cognitive self-management strategies can be useful to entrepreneurs. These techniques include goal-setting, self-observation, self-rewards, cueing, self-talk, visualization and the active reframing of obstacles into opportunities. In addition, the varying roles and functions of mentors, including emotional, vocational and role modelling support, will have many positive benefits for both entrepreneurial proteges and mentors. Recommendations for furture research and an entrepreneurial model of career development are provided

Quantum Dynamics of Three Coupled Atomic Bose-Einstein Condensates

The simplest model of three coupled Bose-Einstein Condensates (BEC) is investigated using a group theoretical method. The stationary solutions are determined using the SU(3) group under the mean field approximation. This semiclassical analysis using the system symmetries shows a transition in the dynamics of the system from self trapping to delocalization at a critical value for the coupling between the condensates. The global dynamics are investigated by examination of the stable points and our analysis shows the structure of the stable points depends on the ratio of the condensate coupling to the particle-particle interaction, undergoes bifurcations as this ratio is varied. This semiclassical model is compared to a full quantum treatment, which also displays the dynamical transition. The quantum case has collapse and revival sequences superposed on the semiclassical dynamics reflecting the underlying discreteness of the spectrum. Non-zero circular current states are also demonstrated as one of the higher dimensional effects displayed in this system.Comment: Accepted to PR

Bose-Einstein condensation in shallow traps

In this paper we study the properties of Bose-Einstein condensates in shallow traps. We discuss the case of a Gaussian potential, but many of our results apply also to the traps having a small quadratic anharmonicity. We show the errors introduced when a Gaussian potential is approximated with a parabolic potential, these errors can be quite large for realistic optical trap parameter values. We study the behavior of the condensate fraction as a function of trap depth and temperature and calculate the chemical potential of the condensate in a Gaussian trap. Finally we calculate the frequencies of the collective excitations in shallow spherically symmetric and 1D traps.Comment: 6 pages, 4 figure

Finite temperature excitations of a trapped Bose gas

We present a detailed study of the temperature dependence of the condensate and noncondensate density profiles of a Bose-condensed gas in a parabolic trap. These quantitites are calculated self-consistently using the Hartree-Fock-Bogoliubov equations within the Popov approximation. Below the Bose-Einstein transition the excitation frequencies have a realtively weak temperature dependence even though the condensate is strongly depleted. As the condensate density goes to zero through the transition, the excitation frequencies are strongly affected and approach the frequencies of a noninteracting gas in the high temperature limit.Comment: 4 pages, Latex, 4 postscript figures. Submitted to Physical Review Letter

Bose-Einstein condensation in a two-dimensional, trapped,interacting gas

We study Bose-Einstein condensation phenomenon in a two-dimensional (2D) system of bosons subjected to an harmonic oscillator type confining potential. The interaction among the 2D bosons is described by a delta-function in configuration space. Solving the Gross-Pitaevskii equation within the two-fluid model we calculate the condensate fraction, ground state energy, and specific heat of the system. Our results indicate that interacting bosons have similar behavior to those of an ideal system for weak interactions.Comment: LaTeX, 4 pages, 4 figures, uses grafik.sty (included), to be published in Phys. Rev. A, tentatively scheduled for 1 October 1998 (Volume 58, Number 4

Scaling and thermodynamics of a trapped Bose-condensed gas

We investigate the thermodynamics of a Bose gas interacting with repulsive forces and confined in a harmonic trap. We show that the relevant parameters of the system (temperature, number N of atoms, harmonic oscillator length, deformation of the trap, s-wave scattering length) fix its large N thermodynamic behaviour through two dimensionless scaling parameters. These are the reduced temperature t=T/T^0_c and the ratio \eta between the T=0 value of the chemical potential, evaluated in the Thomas-Fermi limit, and the critical temperature T_c^0 of the non-interacting model. The scaling functions relative to the condensate fraction, energy, chemical potential and moment of inertia are calculated within the Popov approximation.Comment: 10 pages, REVTEX, 5 figures, also available at http://anubis.science.unitn.it/~oss/bec/BEC.htm