# Magnetic dipole-dipole interactions in atomic Bose-Einstein condensates computational simulation

# Intro

This was written while a graduate student in Yong Chen's Quantum Matter and Devices Lab at Purdue University.

Available here are codes written in MATLAB of modeling the effects of magnetic dipole-dipole interactions in Bose-Einstein Condensates (BECs). These codes were developed by YP Chen and AJ Olson, and are released under the New BSD License.

To download a .zip of the code, click this link.

# Description

The codes below were used in the paper "Effects of magnetic dipole-dipole interactions in atomic Bose-Einstein condensates with tunable s-wave interactions" by AJ Olson, D Whitenack, and YP Chen. The paper provides a description of the theory used in in these codes. Please note the code has not been polished and are provided as is for the interested reader.

# Zip File contents

**asVsLambda_multiNum:**script to solve and plot the BEC axial and radial size over a range of scattering lengths, trap aspect ratios, and atom numbers. Keeps the average trap frequency constant when varying the aspect ratio.**faspectTrapOnBEC:**function to solve the BEC axial and radial sizes over a range of trap aspect ratios, keeping the average trap frequency constant when varying the aspect ratio.**fChooseAtom:**function used to choose which atomic species to model**feqnexpand:**equation of the ODE to be solved for the TOF expansion of a BEC when trap is off**feqntrap:**equation of the ODE to be solved when the BEC is in the trapping potential.**feqntrapdynamic:**equation of the ODE to be solved for the in-trap dynamics of a BEC with any initial state.**feqntrapdynamic:**equation of the ODE to be solved for the in-trap dynamics of a BEC with any initial state.**fexpand:**function to solve the free expansion BEC aspect ratio in time**fexpandModSize:**same as**fexpand.m**, but allows to change the scattering length upon release from the trapping potential.**fintrapevolve:**function to solve the BEC in-trap aspect ratio as a function of time. Used for in-trap dynamics.**ftrapequilib:**function to solve the in-situ BEC size and aspect ratio as function of the s-wave scattering length.**fig_4evolutionsExample:**script to plot a figure similar to the 4 part ones in the paper.**fig_AspVsAsn:**script to plot a figure of the trap aspect ratio given a set scattering length and range of trap aspect ratios.**fig_surfPlotOfDipolarInt:**provides a surface plot of the dipolar interaction potential. Not used in paper.

# License

Released under New BSD License. Copyright (c) 2012, Abraham J. Olson, Yong P. Chen. All rights reserved.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

- Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
- Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
- Neither the name of the organization nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.