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IOSR Journal of Engineering

Theoretical Analysis of Different External trapping potential used in experimental of BEC

Noori.H.N. Al-Hashimi Al-Hashimi

Published Nov 1, 2012• 2 citations
Publisher

Abstract

This paper will focus on theoretical treatment of external trapping potentials which are usually used in experimental that lead to produced Bose-Einstein condensation BEC in ultra cold gases.Several types of trapping potentials such as one dimensional BEC in a harmonic oscillator potential (HOP), one dimensional BEC in a double well potential DWP, and one dimensional BEC in a harmonic plus optical lattice potential HOLP are analyze.These analyses give us the overall view of the region of confinement that the external trapping potentials have employed.

DOI
10.9790/3021-021110105

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This paper will focus on theoretical treatment of external trapping potentials which are usually used in experimental that lead to produced Bose-Einstein condensation BEC in ultra cold gases.Several types of trapping potentials such as one dimensional BEC in a harmonic oscillator potential (HOP), one dimensional BEC in a double well potential DWP, and one dimensional BEC in a harmonic plus optical lattice potential HOLP are analyze.These analyses give us the overall view of the region of confinement that the external trapping potentials have employed.
This paper will focus on theoretical study of BEC in one dimension with weakly attractive interactions in particular in a symmetric harmonic oscillator potential.In this case, the ground state may not be symmetric state, which is in contrast to a BEC with repulsive interaction.The behaviors of the wave function under the influences of different external trapping potentials usually used in experiments that lead to produced Bose-Einstein condensation in ultra cold gases is analysis.Several values of harmonic trapping potentials are used.These analyses give us the overall view of the region of confinement that the external trapping potentials have employed and the influence of some terms in Gross-Pitaevskii equation.
Summary form only given. Since the experimental realization of Bose-Einstein condensation in the magnetically trapped quantum atomic gases, there have now been an enormous quantity of theory devoted to the properties of the trapped Bose-Einstein condensates (BEC). Motivated by the existing experiments, the bulk of the theoretical work has assumed a harmonic trap. Although recently a few papers have considered the consequences of exposing a BEC to a periodic optical potential, BEC confined in an optical lattice is still a new topic in this area. In the work, we develop theory to study the stationary and propagating properties of a Bose-Einstein condensate in an optical lattice. Instead of using an infinite optical lattice, we study the realistic case where the BEC is formed in a finite trapping potential and then is exposed to an infinite periodic potential created by off-resonance multiple laser beams.
Bose–Einstein Condensation (BEC) of both the ideal and the weakly inter-acting cold alkali gases confined by anisotropic harmonic oscillator poten-tials is investigated in this paper. It is shown that the transition point is shifted towards lower temperatures because of the trapped potentials, and the specific heat below the transition point is no longer proportional to T 3/2 . Expressions of modified condensation temperature, internal energy and the specific heat are derived for the ideal trapped gases explicitly. Moreover, the effect of interactions among the atoms on the transition temperature is also given and discussed.
We discuss thermal and dynamical properties of Bose condensates confined by an external potential. First we analyze the Bose-Einstein transition temperature for an ideal Bose gas in a generic power-law potential and d-dimensional space. Then we investigate the effect of the shape of the trapping potential on the properties of a weakly-interacting Bose condensate. We show that using exotic trapping potentials the condensate can exhibit interesting coherent quantum phenomena, like superfluidity and tunneling. In particular, we consider toroidal and double-well potentials. The theoretical results are compared with recent experiments.
Shorttitle: The first experimental achievement of Bose Einstein condensation (BEC) in dilute alkali gases in 1995 has developed a renewed interest both theoretical and experimental. Lot of work has already been done over the last decade to study the different aspects of this condensation, mainly based on mean-field theories, hyperspherical approaches and quantum Monte Carlo methods. This thesis work presents an approximate many-body approach to investigate mainly the static (ground state) properties of the condensate, incorporating realistic inter-atomic interactions. Potential harmonic expansion method (PHEM), which includes two-body correlations only and disregards three or higher body correlations, has been adopted to analyze this condensate. This is ideally suited for BEC, which is required to be extremely dilute for its experimental realization. This treatment and analysis should be useful for the physics community especially working with weakly interacting ultra cold atoms, bosons and fermions as well.
In recent years, the study of cigar shaped Bose?Einstein condensate (BEC) under a variety of external confinements has attracted a great deal of attention, from both theoretical and experimental researchers. We report a unified model for obtaining explicit solutions under various kinds of physically relevant space- and time-modulated external traps and nonlinearities for the cigar shaped BEC. Our novel mechanism paves the way to investigate the system for a family of potential functions unified as a physical parameter of the system. We apply and illustrate our results for a number of exactly solvable quantum mechanical potentials; harmonic, double-well, P?sch?Teller, Morse, Toda lattice and power-law as some of the applications of our model. Expressions of the condensate density are provided for these potentials. In addition, as an application of our model, we have illustrated the condensate dynamics for harmonic, double-well and P?sch?Teller potentials. In the presence of loss/gain for a P?sch?Teller potential, the condensate density shows an interesting collapse and revival.