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Quantum ring with tangential dipoles

López Jurado, Carmen LU (2021) FYSK02 20211
Mathematical 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 Lee-Huang-Yang 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 Lee-Huang-Yang 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
Bose-Einstein 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
Bose-Einstein 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 doughnut-shaped 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:
author
López Jurado, Carmen LU
supervisor
organization
course
FYSK02 20211
year
type
M2 - Bachelor Degree
subject
keywords
Bose-Einstein condensate, Quantum Droplets, Gross-Pitaevskii equation
language
English
id
9061918
date added to LUP
2021-08-05 14:17:02
date last changed
2021-08-05 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 Lee-Huang-Yang 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}},
}