#### 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 $1.03N^{-1/6}$.

#### Recommended Citation

Sze, Michelle Wynne Ching, "The Road Less Traveled: Resonant Bose-Einstein Condensates Via a Hyperspherical Lowest-Order Constrained Variational Approach" (2019). *Physics Graduate Theses & Dissertations*. 288.

https://scholar.colorado.edu/phys_gradetds/288

## Comments

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