Pattern Formation in Dipolar Cold Atomic Quantum Gases Confined by a Flattened Trap
(2025) FYSK04 20251Department of Physics
Mathematical Physics
- Abstract
- This thesis investigates the pattern formation of supersolid states in dipolar Bose-Einstein condensates (BECs) of highly magnetic Dysprosium-162 confined in a flattened trap geometry. This is done by solving the extended Gross-Pitaevskii equation (eGPE), a framework that was developed to examine BECs. The eGPE incorporates contact interaction, the dipole-dipole interaction (DDI), and quantum fluctuations via the Lee-Huang-Yang (LHY) correction. The flat trap modifies the potential landscape by modifying the interplay between the different interactions, in comparison to the more traditional harmonic trap. Key findings include the emergence of a ring phase characterized by a central density minimum, isolated droplets arranged symmetrically... (More)
- This thesis investigates the pattern formation of supersolid states in dipolar Bose-Einstein condensates (BECs) of highly magnetic Dysprosium-162 confined in a flattened trap geometry. This is done by solving the extended Gross-Pitaevskii equation (eGPE), a framework that was developed to examine BECs. The eGPE incorporates contact interaction, the dipole-dipole interaction (DDI), and quantum fluctuations via the Lee-Huang-Yang (LHY) correction. The flat trap modifies the potential landscape by modifying the interplay between the different interactions, in comparison to the more traditional harmonic trap. Key findings include the emergence of a ring phase characterized by a central density minimum, isolated droplets arranged symmetrically in a ring form at low particle numbers and contact interaction strengths, and stripe-like patterns as an intermediate phase between the previous two. The competition between the anisotropic dipole-dipole attraction, repulsive contact interactions, and stabilizing quantum fluctuations is what gives rise to these unique phases. This work emphasizes the crucial role that trap geometry plays in determining which phase the supersolid takes on. (Less)
- Popular Abstract
- When Atoms Dance: The Secret Patterns of Quantum Matter
In our everyday lives we encounter material in one of the three phases that were taught in school: solid, liquid and gas. Now imagine a state of matter that has both a rigid crystal structure like a solid and flows like a superfluid, that is frictionless flow. Seems like a state found in sci-fi movies, yet it exists, this paradoxical state is what is known as a supersolid. A state of matter near absolute zero where atoms arrange themselves into orderly patterns while flowing without any resistance.
Using dysprosium-162, a highly magnetic atom that is ultra cooled, we simulate how geometry shapes the quantum behaviour. The atoms act like quantum bar magnets when trapped in a... (More) - When Atoms Dance: The Secret Patterns of Quantum Matter
In our everyday lives we encounter material in one of the three phases that were taught in school: solid, liquid and gas. Now imagine a state of matter that has both a rigid crystal structure like a solid and flows like a superfluid, that is frictionless flow. Seems like a state found in sci-fi movies, yet it exists, this paradoxical state is what is known as a supersolid. A state of matter near absolute zero where atoms arrange themselves into orderly patterns while flowing without any resistance.
Using dysprosium-162, a highly magnetic atom that is ultra cooled, we simulate how geometry shapes the quantum behaviour. The atoms act like quantum bar magnets when trapped in a pancake-shaped confinement, therefore experiencing a long-range anisotropic dipole-dipole interaction. Their long-range attraction combined with short-range repulsion gives birth to striking patterns: rings, scattered droplets, and jagged stripes.
The secret to these patterns lies in the geometry. Traditional traps, shaped like gentle bowls, let atoms cluster at the center. By flattening the trap, the atoms will spread outwards, creating a more uniform density of atoms. In this altered landscape, magnetic forces force atoms into rows and grids, while quantum fluctuations tiny, unavoidable shivers in the system act as glue, stabilizing structures that would otherwise collapse. The dance between the interactions and trap geometry forms a ring phase, a phase with a hollow center, and particles around the perimeter of the trap. Reduce both the atom count and contact interaction, and quantum fluctuations fracture the ring into discrete droplets, each a self-contained superfluid island. Increase the atom count, and overcrowding forces droplets to merge, stretching into irregular stripes a chaotic yet ordered phase where magnetic anisotropy battles repulsion.
This beautiful dance between the interactions is decoded by solving the extended Gross-Pitaevskii equation (eGPE). A mathematical framework that accounts for atomic collisions, magnetic pulls, and quantum corrections via the Lee-Huang-Yang term acting as the atomic glue mentioned above. Simulations such as these act as virtual labs, revealing how trap geometry or atom number enables the formation of distinct ordered phases. Without this tool, observing supersolids would remain confined to niche experiments, as real-world setups struggle with stability at such extreme conditions.
Beyond the beauty of supersolids there are real world implications to this paradoxical phase. For instance, the ring phase could act as a quantum sensor, its hollow center sensitive to magnetic fields or rotations. This phase may also be the key to understanding the nuclear pasta in ultradense neutron stars and white dwarfs. Because these celestial objects exhibit similar interaction as the ones discussed in the paragraph above. The next frontier lies in controlling these phases. Could we nudge droplets into precise arrays, like quantum dots in a circuit? Or rotate the trap to imprint vortices quantum whirlpools into the ring’s void?
Atoms form patterns that unify solid and fluid behaviour. Equations lay a path for what labs are still unable to touch. Geometry defies laws even in the emptiness, a reminder that the most beautiful dances can be found in the most icy places. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/9194568
- author
- Al-Suhaili, Younis Tiea Harby LU
- supervisor
- organization
- course
- FYSK04 20251
- year
- 2025
- type
- M2 - Bachelor Degree
- subject
- language
- English
- id
- 9194568
- date added to LUP
- 2025-06-09 08:40:22
- date last changed
- 2025-06-09 08:40:22
@misc{9194568,
abstract = {{This thesis investigates the pattern formation of supersolid states in dipolar Bose-Einstein condensates (BECs) of highly magnetic Dysprosium-162 confined in a flattened trap geometry. This is done by solving the extended Gross-Pitaevskii equation (eGPE), a framework that was developed to examine BECs. The eGPE incorporates contact interaction, the dipole-dipole interaction (DDI), and quantum fluctuations via the Lee-Huang-Yang (LHY) correction. The flat trap modifies the potential landscape by modifying the interplay between the different interactions, in comparison to the more traditional harmonic trap. Key findings include the emergence of a ring phase characterized by a central density minimum, isolated droplets arranged symmetrically in a ring form at low particle numbers and contact interaction strengths, and stripe-like patterns as an intermediate phase between the previous two. The competition between the anisotropic dipole-dipole attraction, repulsive contact interactions, and stabilizing quantum fluctuations is what gives rise to these unique phases. This work emphasizes the crucial role that trap geometry plays in determining which phase the supersolid takes on.}},
author = {{Al-Suhaili, Younis Tiea Harby}},
language = {{eng}},
note = {{Student Paper}},
title = {{Pattern Formation in Dipolar Cold Atomic Quantum Gases Confined by a Flattened Trap}},
year = {{2025}},
}