Higher energy collective excitations in trapped Bose condensates

Abstract

We investigate theoretically the collective excitations of trapped Bose condensates with energies of the order of the chemical potential of the system. For the MIT sodium Bose condensate in a Cloverleaf trap, we find interesting level crossing behavior for high energy excitations and calculate the spatial magnetic dipole moments for selective creation of condensate excitations.

Numerical approach to the ground and excited states of a Bose-Einstein condensed gas confined in a completely anisotropic trap

“…Evidently, the magnitude of the excitation energy, relative to the ground state µ, does not alone provide a sufficient indication of its convergence to the hydrodynamic limit. A similar number-dependence for the higher-lying excitations of a cylindrically-symmetric condensate has also been recently obtained [53]. FIG.…”

“…Evidently, a robust numerical process is required which rapidly damps out the errors as the iteration sequence proceeds. One rather crude approach is to use a linear combination of the solutions from the (i − 1) th and i th steps to initiate the iteration process for the (i + 1) th step [53,54]; the proper linear combination may be found by numerical experimentation. The approach used by the present authors, known as Direct Inversion in the Iterative Subspace (DIIS) [35], is a more systematic version of the above that uses the information from all of the previous iterations.…”

Finite-temperature excitations of Bose gases in anisotropic traps

“…The measurement of their excitation frequencies provides a good opportunity to analyze the applicability of different approximations and numerical approaches in many-body-theory. Zero temperature calculations with different number of atoms in the condensate [5,6] are in excellent agreement with the corresponding spectra measured in the JILA-TOP [1] and the MIT trap [3]. The frequently used starting point for the theoretical studies are the coupled Bogoliubov equations.…”

Collective excitations in Bose-Einstein condensates in triaxially anisotropic parabolic traps

“…In the Bose-Einstein condensates of alkali-metal vapors in traps these collective sound waves have a discrete spectrum which is determined by the shapes of the trapping potential and of the condensate. Many experimental [1][2][3] and theoretical [4][5][6][7][8][9][10][11][12] studies have been devoted to their study. For Bose-Einstein condensates at zero temperature which are sufficiently large to validate the Thomas-Fermi approximation Stringari [9] found an analytical solution for the sound modes and their eigenfrequencies for the case of spherically symmetric parabolic traps.…”