Quantum ring with tangential dipoles
(2021) FYSK02 20211Mathematical Physics
Department of Physics
 Abstract
 This Bachelor thesis studies the formation of quantum droplets in a dilute dipolar Bose Einstein Condensate
with the initial shape of a torus. The main question to address is how this formation occurs as the magnetic
dipole moment of the particles changes orientation with respect to the xy plane.
The (mostly) attractive dipolar, and the repulsive contact and LeeHuangYang interactions of the gas are
studied first in a theoretical way, and afterwards using a numerical simulation that solves the wave function
of the system and computes its ground state energy.
After such study, two main conclusions were drawn. The first one says that independently from the magnetic
dipole moment orientation, droplet formation is possible when... (More)  This Bachelor thesis studies the formation of quantum droplets in a dilute dipolar Bose Einstein Condensate
with the initial shape of a torus. The main question to address is how this formation occurs as the magnetic
dipole moment of the particles changes orientation with respect to the xy plane.
The (mostly) attractive dipolar, and the repulsive contact and LeeHuangYang interactions of the gas are
studied first in a theoretical way, and afterwards using a numerical simulation that solves the wave function
of the system and computes its ground state energy.
After such study, two main conclusions were drawn. The first one says that independently from the magnetic
dipole moment orientation, droplet formation is possible when attractive and repulsive interactions have very
similar behaviour, with attraction being slightly stronger than repulsion. Regarding the second one, from all
the orientations examined, the one with which droplets have the smallest ground state energy is indeed the
xy plane orientation. (Less)  Popular Abstract
 Everything started in 1925, when A. Einstein predicted the existence of a new state of matter: the
BoseEinstein Condensate (BEC). He wondered what would happen if a gas whose particles do not
interact with each other experienced an almost zero temperature. The outcome? All the particles
would be in their minimum possible energy, in other words, they would condense into the state of
minimum energy of that gas.
Although it was not until 1995 when experimental physicists were able to realize a BEC, theoretical
physicists have not stopped working on this exotic state of matter. In real life particles do interact with
each other, so the next step in this journey was to include this feature into Einstein’s mathematical
model.
Once a... (More)  Everything started in 1925, when A. Einstein predicted the existence of a new state of matter: the
BoseEinstein Condensate (BEC). He wondered what would happen if a gas whose particles do not
interact with each other experienced an almost zero temperature. The outcome? All the particles
would be in their minimum possible energy, in other words, they would condense into the state of
minimum energy of that gas.
Although it was not until 1995 when experimental physicists were able to realize a BEC, theoretical
physicists have not stopped working on this exotic state of matter. In real life particles do interact with
each other, so the next step in this journey was to include this feature into Einstein’s mathematical
model.
Once a model for BECs with interactions was established, it was time to find out the properties of
these gases that result from those interactions. Some recently found properties are supersolidity,
superfluidity and droplet formation. A BEC is in the superfluid (sub)state when its particles flow with
no friction, leading to indefinitely rotating vortices also called persistent currents. On the other
hand, when a BEC is in the supersolid (sub)state, particles are ordered following a certain pattern and
at the same time can flow as if the condensate was in the superfluid state. Regarding droplet
formation, BECs can form these droplets when the attractive and repulsive particle interactions of the gas
are balanced in a certain way.
Supersolidity, superfluidity and droplet formation are the properties M. Nilsson Tengstrand et al.
were working on. They created a mathematical model for a rotating dipolar BEC in the
form of a doughnut. Apparently, it is possible to obtain this form by applying a magnetic field
perpendicular to the doughnutshaped gas. Regarding the term dipolar, the particles of this BEC had an
intrinsic property called magnetic dipole moment. This property can be imagined as an arrow oriented
in a particular direction and having a specific length, indicating the tendency of the arrow to align with
an external magnetic field (the larger the arrow, the more prone it is to align). The team chose the
magnetic dipole moments of the BEC to be aligned in the direction of the mentioned magnetic field.
After simulating the mathematical model for the gas in a computer, they saw that an interesting
behaviour emerged.
Tengstrand and the rest of the team focused on a gas whose dipole moments were parallel to the external field
and therefore perpendicular to the doughnut plane. This bachelor thesis tried to answer the following: how
would supersolidity, superfluidity and droplet formation be affected if the direction of the dipole
moments was changed to be oriented precisely in the doughnut plane?
Although at the end there was no time to study supersolidity and superfluidity, we could study the
quantum droplet formation for the same gas but being static. We tested several orientations of
the dipoles, and the most important result suggests that when the dipoles are completely horizontal,
the system reaches its minimum energy value. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/studentpapers/record/9061918
 author
 López Jurado, Carmen ^{LU}
 supervisor

 Stephanie Reimann ^{LU}
 Jakob Bengtsson ^{LU}
 organization
 course
 FYSK02 20211
 year
 2021
 type
 M2  Bachelor Degree
 subject
 keywords
 BoseEinstein condensate, Quantum Droplets, GrossPitaevskii equation
 language
 English
 id
 9061918
 date added to LUP
 20210805 14:17:02
 date last changed
 20210805 14:17:02
@misc{9061918, abstract = {{This Bachelor thesis studies the formation of quantum droplets in a dilute dipolar Bose Einstein Condensate with the initial shape of a torus. The main question to address is how this formation occurs as the magnetic dipole moment of the particles changes orientation with respect to the xy plane. The (mostly) attractive dipolar, and the repulsive contact and LeeHuangYang interactions of the gas are studied first in a theoretical way, and afterwards using a numerical simulation that solves the wave function of the system and computes its ground state energy. After such study, two main conclusions were drawn. The first one says that independently from the magnetic dipole moment orientation, droplet formation is possible when attractive and repulsive interactions have very similar behaviour, with attraction being slightly stronger than repulsion. Regarding the second one, from all the orientations examined, the one with which droplets have the smallest ground state energy is indeed the xy plane orientation.}}, author = {{López Jurado, Carmen}}, language = {{eng}}, note = {{Student Paper}}, title = {{Quantum ring with tangential dipoles}}, year = {{2021}}, }