Initial version of the conclusion.

Author: jvdoorn

chapters/conclusion.tex

@@ -1,16 +1,11 @@
-\chapter{Conclusion}
+\chapter{Conclusion and outlook}
 \label{chap:conclusion}
-In this thesis we have shown successful levitation of a \qty{12}{\micro\meter} sized \ce{NdFeB} particle in a planar magnetic Paul trap. The trap was fabricated using a combination of nanofabrication techniques. Levitation was observed at atmospheric pressure all the way down to \qty{1E-4}{\milli\bar}. At atmospheric pressure we succesfully observed the $x$/$y$ and $\gamma$/$\tilde\beta$ modes. Due to the low Q-factors at atmospheric pressure it was not possible to tell the difference between the $x$ and $y$ mode or the $\gamma$ and $\beta$ mode. The dependence of $\omega_{x,y}$ on $i_1$ and $\Omega$ follows the expected relation from theory.
+In this thesis we have shown successful levitation of a \qty{12}{\micro\meter} sized \ce{NdFeB} particle in a planar magnetic Paul trap. The trap was fabricated using a combination of nanofabrication techniques. 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. Due to the low Q-factors at atmospheric pressure it was not possible to tell the difference between the $x$ and $y$ mode or the $\gamma$ and $\beta$ modes. The dependence of $\omega_{x,y}$ on $i_1$ and $\Omega$ follows the expected relation from theory.
 
-At lower pressures the Q-factors increase untill we reach roughly \qty{1E-2}{\milli\bar} where the Q-factor tends to a constant value. We attribute this to Eddy current damping, though we do not know where it occurs exactly. Further more careful measurements of the Q-factors at low pressures are needed to determine the origin of the damping.
+At lower pressures the Q-factors increase untill we reach roughly \qty{1E-2}{\milli\bar} where the Q-factor tends to a constant value. We attribute this to Eddy current damping, though we do not know where it occurs exactly. Further more careful measurements of the Q-factors at low pressures are needed to determine the origin of the damping. At low pressures we also observed the \zmode. Again at low pressures we saw the expected relation between $\omega_{x,y,z}$ on $\Omega$.
 
-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. We also suspect that the levitation height is very low, because of this we think that we do not need a hole in the top cover glass. In the future this will help us to use diamonds with NV centers to couple to the particle more easily.
-TODO: Readout or also sideband cooling
-- Many spins to cool
-- Many spins to change angular momentum
-- Single spin for stern gerlach experiment
+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 teh \xmode and \ymode. This might shed light on the origin of the damping but further investigation is needed.
 
-- smaller particle
-- elongated particle (Huellery, Gabriel etet ferromagnet diamond)
-- hoger B0 veld (met kern)
-- magnetisatie (Milan)
+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.
+
+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 experience Zeeman splitting. 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 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}.

sources.bib

@@ -122,3 +122,44 @@ @article{bose_spin_2017
 	note = {Publisher: American Physical Society},
 	file = {Accepted Version:/Users/julian/Zotero/storage/ULT33IGJ/Bose et al. - 2017 - Spin Entanglement Witness for Quantum Gravity.pdf:application/pdf;APS Snapshot:/Users/julian/Zotero/storage/3H7AXYIM/PhysRevLett.119.html:text/html},
 }
+
+@article{delord_spin-cooling_2020,
+	title = {Spin-cooling of the motion of a trapped diamond},
+	volume = {580},
+	rights = {2020 The Author(s), under exclusive licence to Springer Nature Limited},
+	issn = {1476-4687},
+	url = {https://www.nature.com/articles/s41586-020-2133-z},
+	doi = {10.1038/s41586-020-2133-z},
+	abstract = {Observing and controlling macroscopic quantum systems has long been a driving force in quantum physics research. In particular, strong coupling between individual quantum systems and mechanical oscillators is being actively studied1–3. Whereas both read-out of mechanical motion using coherent control of spin systems4–9 and single-spin read-out using pristine oscillators have been demonstrated10,11, temperature control of the motion of a macroscopic object using long-lived electronic spins has not been reported. Here we observe a spin-dependent torque and spin-cooling of the motion of a trapped microdiamond. Using a combination of microwave and laser excitation enables the spins of nitrogen–vacancy centres to act on the diamond orientation and to cool the diamond libration via a dynamical back-action. Furthermore, by driving the system in the nonlinear regime, we demonstrate bistability and self-sustained coherent oscillations stimulated by spin–mechanical coupling, which offers the prospect of spin-driven generation of non-classical states of motion. Such a levitating diamond—held in position by electric field gradients   under vacuum—can operate as a ‘compass’ with controlled dissipation and has potential use in high-precision torque sensing12–14, emulation of the spin-boson problem15 and probing of quantum phase transitions16. In the single-spin limit17 and using ultrapure nanoscale diamonds, it could allow quantum non-demolition read-out of the spin of nitrogen–vacancy centres at ambient conditions, deterministic entanglement between distant individual spins18 and matter-wave interferometry16,19,20.},
+	pages = {56--59},
+	number = {7801},
+	journaltitle = {Nature},
+	author = {Delord, T. and Huillery, P. and Nicolas, L. and Hétet, G.},
+	urldate = {2025-02-03},
+	date = {2020-04},
+	langid = {english},
+	note = {Publisher: Nature Publishing Group},
+	keywords = {Optics and photonics, Quantum physics},
+	file = {Full Text PDF:/Users/julian/Zotero/storage/ZRXWR5S9/Delord et al. - 2020 - Spin-cooling of the motion of a trapped diamond.pdf:application/pdf},
+}
+
+
+@article{huillery_spin-mechanics_2020,
+	title = {Spin-mechanics with levitating ferromagnetic particles},
+	volume = {101},
+	issn = {2469-9950, 2469-9969},
+	url = {http://arxiv.org/abs/1903.09699},
+	doi = {10.1103/PhysRevB.101.134415},
+	abstract = {We propose and demonstrate first steps towards schemes where the librational mode of levitating ferromagnets is strongly coupled to the electronic spin of Nitrogen-Vacancy ({NV}) centers in diamond. Experimentally, we levitate ferromagnets in a Paul trap and employ magnetic fields to attain oscillation frequencies in the hundreds of {kHz} range with Q factors close to \$10{\textasciicircum}4\$. These librational frequencies largely exceed the decoherence rate of {NV} centers in typical {CVD} grown diamonds offering prospects for sideband resolved operation. We also prepare and levitate composite diamond-ferromagnet particles and demonstrate both coherent spin control of the {NV} centers and read-out of the particle libration using the {NV} spin. Our results will find applications in ultra-sensitive gyroscopy and bring levitating objects a step closer to spin-mechanical experiments at the quantum level.},
+	pages = {134415},
+	number = {13},
+	journaltitle = {Physical Review B},
+	shortjournal = {Phys. Rev. B},
+	author = {Huillery, P. and Delord, T. and Nicolas, L. and Bossche, M. Van Den and Perdriat, M. and Hétet, G.},
+	urldate = {2025-02-03},
+	date = {2020-04-13},
+	eprinttype = {arxiv},
+	eprint = {1903.09699 [quant-ph]},
+	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},
+}