Applied Martijn's feedback to the conventions and introduction chapter.

Author: jvdoorn

.zed/settings.json

@@ -11,5 +11,10 @@
         }
       }
     }
+  },
+  "languages": {
+    "LaTeX": {
+      "soft_wrap": "editor_width"
+    }
   }
 }

chapters/conventions.tex

@@ -1,8 +1,6 @@
 \chapter*{Conventions}
 \label{chap:conventions}
-In this thesis we regularly have to project 3D structures onto a 2D plane. To clarify the x-, y- and z-directions, they have been color coded. This is done consistently throughout the thesis and matches with the colors assigned to the axes by COMSOL. The x-direction is colored in \textcolor{x_axis_color}{red}, the y-direction in \textcolor{y_axis_color}{green} and the z-direction in \textcolor{blue}{blue}. Additionally an attempt has been made to optimize figures for colorblind readers based on Paul Tol's color schemes\cite{paul_tol}.
-
-Furthermore, when a damping rate ($\gamma$) or Q-factor is given, we use the following definition:
+In this tehsis, when a damping rate ($\gamma$) or Q-factor is given, we use the following definition:
 \begin{equation*}
     Q = \omega_0 \frac{\text{energy stored}}{\text{dissipation}} = \frac{\omega_0}{\gamma}
 \end{equation*}

chapters/introduction.tex

@@ -1,4 +1,11 @@
 \chapter{Introduction}
-The Hensen Lab aims to understand the interplay of quantum mechanics and gravity. Recently a experiment was proposed by \citeauthor{bose_spin_2017} to probe the quantum mechanical nature of gravity. The central idea is to entangle two particles through gravity which is only possible if gravity is a quantum entity. The idea is to levitate two small ($\approx \qty{1}{\micro\meter}$) particles and cool them to their ground state. The particles are dropped through a Stern-Gerlach interferometer and the entanglement is measured by the interference pattern.
+\label{chap:introduction}
+The twentieth century brought us two major cornerstones in physics: quantum mechanics and general relativity. Whilst quantum mechanics successfully describes physics at the smallest scales and general relativity describes physics at the largest scales, a unified theory of quantum gravity is still missing. To test wether gravity is a quantum entity (the existence of gravitons) an experiment was proposed by \textcite{bose_spin_2017}.
 
-Currently, we as a group, are working towards the levitation of micrometer sized particles. Previous projects within our group worked on the levitation of a \qty{100}{\micro\meter} sized particle in a planar magnetic Paul Trap\cite{eli, mart}. This trap was realised on PCB and the goal of this project is to miniturize the trap. Miniturization is key to reach the quantum regime. Furthermore a on-chip trap enables easier integration with other components such as NV centers.
+The experiment proposed by \citeauthor{bose_spin_2017} suggests to entangle two particles through gravity. If this is possible, it would be a direct proof that gravity is a quantum entity. To realise this experiment, we need two small ($\approx \qty{1}{\micro\meter}$) but massive particles isolated from their environment and cooled to their ground state. An electronic spin is attached to the particles and a $\pi/2$-pulse is applied to the spins. This creates a superposition of spins. The particles are then dropped through a Stern-Gerlach interferometer which turns the superposition of spins into a superposition of positions. The two particles are then allowed to interact through gravity. This interaction entangles the particles. The outcome of the experiment is measured by the interference of the particles.
+
+In this thesis we focus on the levitation of micrometer sized particles using a planar magnetic Paul trap. A magnetic Paul trap uses ac magnetic fields to obtain stable levitation. This builds on previous work within our group where a \qty{250}{\micro\meter} cubic \ce{NdFeB} magnet was levitated in a planar magnetic Paul trap realised on a PCB\cite{eli, mart}. In order to work towards the quantum regime, the system needs to be miniaturized.
+
+Two other well known levitation techniques are optical (eigenfrequencies between \qtyrange{10}{300}{\kilo\hertz}) and electrical traps (eigenfrequencies between \qtyrange{1}{10}{\kilo\hertz})\cite{levitodynamics}. Compared to these techniques, magnetic traps have the disadvantage of having a lower eigenfrequency (\qtyrange{1}{10}{\kilo\hertz}), often require cryogenic temperatures and no on-chip integration exists\cite{levitodynamics}. The advantage however is that magnetic traps have to potential to levitate much larger and heavier particles.
+
+The cryogenic neccecity originates from the fact that many magnetic traps use the Meissner effect to levitate a particle. An alternative to this however is to use non-static magnetic fields which then also satisfies Earnshaw's theorem. Previous work has shown this to be possible\cite{perdriat,eli,mart}. The goal of this project is to create a on-chip variant of the magnetic Paul trap. Besides the advantage of a on-chip design, this will also increase the eigenfrequency of the trap\cite{perdriat}.

sources.bib

@@ -163,3 +163,20 @@ @article{huillery_spin-mechanics_2020
 	keywords = {Quantum Physics},
 	file = {Full Text PDF:/Users/julian/Zotero/storage/IRX8MIHH/Huillery et al. - 2020 - Spin-mechanics with levitating ferromagnetic particles.pdf:application/pdf},
 }
+
+@article{levitodynamics,
+	title = {Levitodynamics: Levitation and control of microscopic objects in vacuum},
+	volume = {374},
+	issn = {1095-9203},
+	doi = {10.1126/science.abg3027},
+	shorttitle = {Levitodynamics},
+	abstract = {The control of levitated nano- and micro-objects in vacuum—which capitalizes on scientific achievements in the fields of atomic physics, control theory, and optomechanics—is of considerable interest. The ability to couple the motion of levitated systems to internal degrees of freedom, as well as to external forces and systems, provides opportunities for science and technology. Attractive research directions, ranging from fundamental quantum physics to commercial sensors, have been unlocked by the many recent experimental achievements, including motional ground-state cooling of an optically levitated nanoparticle. Here we review the status, challenges, and prospects of levitodynamics, the multidisciplinary research area devoted to understanding, controlling, and using levitated nano- and micro-objects in vacuum.},
+	pages = {eabg3027},
+	number = {6564},
+	journaltitle = {Science (New York, N.Y.)},
+	shortjournal = {Science},
+	author = {Gonzalez-Ballestero, C. and Aspelmeyer, M. and Novotny, L. and Quidant, R. and Romero-Isart, O.},
+	date = {2021-10-08},
+	pmid = {34618558},
+	file = {Submitted Version:/Users/julian/Zotero/storage/UT2IBH82/Gonzalez-Ballestero et al. - 2021 - Levitodynamics Levitation and control of microscopic objects in vacuum.pdf:application/pdf},
+}

thesis.tex

@@ -2,7 +2,7 @@
 
 \input{preamble}
 
-\title{On Chip Planar Magnetic Paul Traps for Ferromagnetic Particles}
+\title{On-Chip Planar Magnetic Paul Trap Design}
 
 \author{J.C.B. van Doorn, BSc}
 \degree{Master of Science}