Update abstract.

Author: jvdoorn

abstract.tex

@@ -1 +1 @@
-TODO: Abstract
+The twentieth century for physics was marked by the succesfull theories of quantum mechanics and the theory of general relativity. However, a unification of these two theories has not yet been achieved and is one of the biggest challenges in modern physics. To test the quantum nature of gravity, \citeauthor{bose_spin_2017} proposed an experiment to entangle two massive particles through gravity\cite{bose_spin_2017}. This thesis is a step towards this experiment and builds on our previous work \cite{janse_characterization_2024,eli,mart}. We succesfully demonstrate stable levitation of a \ce{NdFeB} particle with a diameter of $\qty{12}{\micro\meter}$ in an on-chip planar magnetic Paul trap. Levitation was observed at atmospheric pressure all the way down to $\qty{1E-4}{\milli\bar}$. At atmospheric pressure we succesfully observed the $x$, $y$, $\gamma$ and $\beta$ modes, but with very low Q-factors ($Q \approx 5$). At lower pressures the Q-factor increases ($Q \approx 3000$), and we are limited by a different source of damping. The on-chip design opens the possibility to integrate the trap with NV centers to groundstate cool the particle. We expect that we will be able to trap a $\qty{1}{\micro\meter}$ particle using the same method.

chapters/conclusion.tex

@@ -6,6 +6,6 @@ \chapter{Conclusion and outlook}
 
 The direct gaps in our knowledge are: the dependence of the Q-factor on pressure for the $z$, $\gamma$ and $\beta$-mode; the dependence of $\omega_z$ on $B_0$; the dependence of $z_0$ on $B_2'$; and the origin of the damping at low pressures. We note that the damping of the \zmode is statistically significantly higher than the damping of the \xmode and \ymode. This might shed light on the origin of the damping, but further investigation is needed. We suggest performing a time dependent simulation in COMSOL and to determine the relation between $\gamma$ and $i_1$.
 
-When measuring using a laser at low pressures we observed a loss of magnetization. A future project will work on interferometric readout, which allows us to use a lower laser intensity. This will enable us to fill most of our knowledge gaps about the parameter dependences. In addition to this we are also looking to increase the remnant magnetization of the particle and to reach a higher $\vec{B_0}$ field by adding a core to the Helmholtz coils.
+When measuring using a laser at low pressures we observed a loss of magnetization. A future project will work on interferometric readout, which allows us to use a lower laser intensity. This will enable us to fill most of our knowledge gaps about the parameter dependences. In addition to this we are also looking to increase the remnant magnetization of the particle and to reach a higher $\vec{B_0}$ field by adding a core to the Helmholtz coils. In addition to this we are also looking to trap a smaller (\qty{1}{\micro\meter} diameter) particle as a step towards the quantum regime. We expect that we will be able to trap this particle using the same approach as we used for the \qty{12}{\micro\meter} particle.
 
-Even more long term we are looking to use NV centers. If we replace the cover glass with a diamond we can use the NV centers as a readout. Due to the movement of the particle the emission of the NV centers will split in two bands due to the Zeeman splitting of the $\ket{+1}$ and $\ket{-1}$ states of the NV centers. An additional use of the NV centers is to cool the particle using sideband cooling, similar to the work of \textcite{delord_spin-cooling_2020}. A key step in this case are high eigenfrequencies and good Q-factors in order to reach a sideband resolved regime. The idea is to use the rotational modes (which have a order of magnitude of \qty{1}{\kilo\hertz}) to cool the particle. These rotational modes can be `boosted' by using an elongated particle\cite{huillery_spin-mechanics_2020}.
+Even more long term we are looking to use NV centers. If we replace the cover glass with a diamond we can use the NV centers as a readout. Due to the movement of the particle the emission of the NV centers will split in two bands due to the Zeeman splitting of the $\ket{+1}$ and $\ket{-1}$ states of the NV centers. An additional use of the NV centers is to cool the particle using sideband cooling, similar to the work of \textcite{delord_spin-cooling_2020}. A key step in this case are high eigenfrequencies and good Q-factors in order to reach a sideband resolved regime. The idea is to use the rotational modes (which have an order of magnitude of \qty{1}{\kilo\hertz}) to cool the particle. These rotational modes can be `boosted' by using an elongated particle\cite{huillery_spin-mechanics_2020}.

chapters/discussion.tex

@@ -6,7 +6,9 @@ \section*{Laser heating}
 As mentioned in \autoref{chap:results}, the particle lost its magnetization when irradiated with the laser at low pressures ($<\qty{1}{\milli\bar}$). Decreasing the laser intensity also ment a smaller SNR. Due to this tradeoff a decision was made to only use camera measurements at low pressure. A comparision between the two methods will follow. Besides the total loss of magnetization we are also not sure how well the particle retains its magnetization over time. In addition to this we are also not sure what the resulting magnetization is since we do not reach the saturation field. A future project will focus on designing a device that can fully saturate the particle.
 
 \section*{Damping at low pressures}
-We observed a limit in the Q-factor for pressures below \qty{1E-2}{\milli\bar}. Attempts to model this have been unsuccessful and do not match the experimental results (see \autoref{tab:dissipation}). Proper modelling of the dissipation should involve a time dependent simulation in COMSOL instead of using a Lorentz term. The main reason for this is that a displacement of the particle brings it closer to its surrounding meaning any effects due to the magnetization of the particle will be stronger. Another source of damping could be eddy currents inside the particle itself. In addition to this we should consider additional sources of dampign, such as noise from the electronics or anisotropy (differences in magnetization) inside the particle\cite{millen}. Additionally, a recent paper also discusses eddy currents in more detail and how they would behave in superconductors as well\cite{fuwa_stable_2023}. If the damping is caused by eddy currents inside the particle, then we should expect a relation between $\gamma$ and $i_1$.
+We observed a limit in the Q-factor for pressures below \qty{1E-2}{\milli\bar}. Attempts to model this have been unsuccessful and do not match the experimental results (see \autoref{tab:dissipation}). Proper modelling of the dissipation should involve a time dependent simulation in COMSOL instead of using a Lorentz term. The main reason for this is that a displacement of the particle brings it closer to its surrounding meaning any effects due to the magnetization of the particle will be stronger. Another source of damping could be eddy currents inside the particle itself. In addition to this we should consider additional sources of damping, such as noise from the electronics or anisotropy (differences in magnetization) inside the particle\cite{millen}. Additionally, a recent paper also discusses eddy currents in more detail and how they would behave in superconductors as well\cite{fuwa_stable_2023}. If the damping is caused by eddy currents inside the particle, then we should expect a relation between $\gamma$ and $i_1$.
+
+A statistical test (see \autoref{tab:gamma-t-test}) suggests that the damping of the \zmode is significantly higher than the damping of the \xmode and \ymode. This might shed light on the origin of the damping, but it may also be caused by non-linear effects in the trap. Due to the difficulty of observing the \zmode, we needed quite strong driving forces which can cause non-linear effects. Improvements in the detection of the particle position will allow us to measure the \zmode at lower driving forces.
 
 \section*{Laser v.s. camera readout}
 The disadvantages and advantages of the camera and laser readout are summarized in \autoref{tab:laser-vs-camera-readout}.

figures/optics.jpg

@@ -4,10 +4,10 @@
 
 \title{On-Chip Planar Magnetic Paul Trap Design}
 
-\author{J.C.B. van Doorn, BSc}
+\author{J.C.B. van Doorn, B.Sc.}
 \degree{Master of Science}
 \studentid{s2518074}
-\supervisor{M. Janse, MSc \\ \hspace*{\fill}Dr.ir. B.J. Hensen}
+\supervisor{M. Janse, M.Sc. \\ \hspace*{\fill}Dr.ir. B.J. Hensen}
 \corrector{Dr. W. Löffler}
 
 \abstract{\input{abstract}}