Date of Award

Spring 1-1-2019

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

First Advisor

John L. Bohn

Second Advisor

Eric A. Cornell

Third Advisor

Jose P. D' Incao

Fourth Advisor

Victor Gurarie

Fifth Advisor

Carl Lineberger

Abstract

In this work, we study the ground state properties of a system of $N$ harmonically trapped bosons of mass $m$ interacting with two-body contact interactions, from small to large scattering lengths. This is accomplished in a hyperspherical coordinate system that is flexible enough to describe both the overall scale of the gas and two-body correlations. By adapting the lowest-order constrained variational (LOCV) method, we are able to semi-quantitatively attain Bose-Einstein condensate ground state energies even for gases with infinite scattering length. In the large particle number limit, our method provides analytical estimates for the energy per particle $E_0/N \approx 2.5 N^{1/3} \hbar \omega$ and two-body contact $C_2/N \approx 16 N^{1/6}\sqrt{m\omega/\hbar}$ for a Bose gas on resonance, where $\omega$ is the trap frequency. Further, by considering only two-body correlations, we note that a sudden quench from small to large scattering lengths leads to out-of-equilibrium resonant BEC. As an alternative, we propose a two-step scheme that involves an intermediate scattering length, between $0$ and $\infty$, which serves to maximize the transfer probability of $N$ bosons in a harmonic trap with frequency $\omega$ to the resonant state. We find that the intermediate scattering length should be $a\approx3.16N^{-2/3}\sqrt{\hbar/(m\omega)}$, and that it produces an optimum transition probability of $1.03N^{-1/6}$.

Comments

Equations in the abstract were not expressable in HTML or UTF-8 encoding. Retained them with Matlab formatting.

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