Levitation and control of particles with internal degrees of freedom

Levitodynamics is a fast growing field that studies the levitation and manipulation of micro- and nanoobjects, fuelled by both fundamental physics questions and technological applications. Due to the isolated nature of trapped particles, levitated systems are highly decoupled from the environment, and offer experimental possibilities that are absent in clamped nanomechanical oscillators. In particular, a central question in quantum physics is how the transition between the classical and quantum world materializes, and levitated objects represent a promising avenue to study this intermediate regime. In the last years, most levitation experiments have been restricted to optically trapped silica nanoparticles in vacuum, controlling the particle's position with intensity modulated laser beams. However, the use of optical traps severely constrains the experiments that can be performed, because few particle materials can withstand the optical absorption and resulting heating in vacuum. This completely prevents the use of objects with internal degrees of freedom, which---coupled to mechanical variables---offer a clear path towards the study of quantum phenomena at the macroscale. In this thesis, we address these issues by considering other types of trap and feedback schemes, achieving excellent control on the dynamics of optically active nanoparticles. With stochastic calculus, simulations and experiments, we study the dynamics of trapped particles in different regimes, considering also a hybrid quadrupole-optical trapping scheme. Then, using a Paul trap of our own design, we demonstrate the trapping, interrogation and feedback cooling of a nanodiamond hosting a single NV center in vacuum, a clear candidate to perform quantum physics experiments at the single spin level. Finally, we discuss and implement an optimal controller to cool the center of mass motion of an optically levitated nanoparticle. The feedback is realized by exerting a Coulomb force on a charged particle with a pair of electrodes, and thus requires no optics.La levitodinàmica és un camp de la física en ràpida expansió que estudia la levitació i manipulació de micro- i nano-objectes, empesa per la possibilitat de solucionar trencaclosques de física fonamental i de desenvolupar noves aplicacions tecnològiques. Gràcies al gran aïllament de les partícules en levitació, l’evolució dels sistemes levitodinàmics està molt desacoplada del seu entorn. Per consegüent, permeten fer experiments que no serien possibles en nanooscil·ladors mecànics sobre substrat. En particular, una qüestió central en física consisteix en entendre com es produeix la transició entre els mons clàssic i quàntic; els objectes en levitació permeten estudiar aquest règim intermedi de manera innovadora. En els últims anys, la majoria d’experiments de levitodinàmica s’han limitat a atrapar òpticament partícules de sílice en el buit, tot controlant la posició de la partícula amb feixos làser modulats. Tot i així, l’ús de trampes òptiques suposa un obstacle a l’hora d’exportar aquests experiments a règims més diversos perquè, a baixes pressions, pocs materials són capaços de suportar les altes temperatures resultants de l’absorció de llum làser. Això impedeix l’ús d’objectes amb graus de llibertat interns, que –acoplats a variables mecàniques– suposen un full de ruta clar per estudiar fenòmens quàntics a escala macroscòpica En aquesta tesi, adrecem aquestes qüestions tot considerant altres tipus de trampa i tècniques de feedback, i assolim un control excel·lent de la dinàmica de nanopartícules òpticament actives en levitació. Mitjançant càlcul estocàstic, simulacions i experiments, estudiem la dinàmica de les partícules en règims diversos, àdhuc considerant un esquema híbrid de trampa de Paul-òptica. A continuació, utilitzant una trampa de Paul, demostrem experimentalment l’atrapament, interrogació i feedback-cooling en el buit d’un nanodiamant que conté un únic NV− center, un clar candidat per a la realització d’experiments de física quàntica amb un únic spin. Finalment, estudiem i implementem un controlador òptim per a refredar el centre de massa d’una partícula òpticament levitada. El feedback es realitza exercint una força de Coulomb sobre una partícula carregada positivament mitjançant un parell d’elèctrodes, i per tant no requereix elements òptic

Levitodynamics toward force nano-sensors in vacuum

Premi Extraordinari de Doctorat, promoció 2018-2019. Àmbit de CiènciesLevitodynamics addresses the levitation and manipulation of micro- and nanoresonators with the purpose of studying their dynamics. This emerging field has attracted much attention over the last few years owing to unprecedented performances in terms of mechanical quality factors, cooling rates at room temperature, and ultra-high force sensitivities. In this thesis, I establish the use of an optically levitated and electrically driven charged silica nanoparticle as a promising and reliable force sensor in vacuum. The first two experiments discussed in this work seek a deeper knowledge and a higher control of the levitated system. Firstly, I suggest and demonstrate a novel protocol to measure the mass of the particle up to 2% accuracy using its electrically driven motion. This method improves by more than one order of magnitude the state-of-the-art mass measurements in standard optical tweezers schemes. Then, leveraging on these results, a second experiment is performed to address important open issues regarding the morphology of the nanoparticles used, with particular interest in their surface chemistry and in the understanding of mass-losses due to water desorption from the silica spheres. Finally, backed up by extensive theoretical background in nonlinear mechanical oscillators, I investigate the stochastic bistable dynamics of a parametrically driven nanoresonator in the nonlinear regime, discussing the potential of noise-activated stochastic switching and stochastic resonance as unconventional force detection schemes.La levitodinámica estudia la manipulación de micro y nanorresonadores en levitación con el objetivo de controlar su dinámica. Este nuevo campo ha atraído mucha atención en los últimos años gracias a sus prestaciones sin precedentes en términos de factores de calidad mecánica, posibilidad de enfriamiento del centro de masas a temperatura ambiente y altas sensibilidades en la detección de fuerzas. En esta tesis, establezco un sensor de fuerza basado en el uso de una nanopartícula de sílice levitada ópticamente en el vacío que, gracias a su carga, puede ser accionada mediante campos eléctricos. Los dos primeros experimentos discutidos en este trabajo intentan conseguir un conocimiento más profundo y un mayor control del sistema levitado. En primer lugar, se propone y demuestra un nuevo protocolo para la medida de la masa de la partícula en levitación con una precisión del 2% basado en el estudio de la dinámica forzada cuando la partícula es accionada eléctricamente. Este método mejora en más de un orden de magnitud las mediciones de la masa de la partícula en plataformas de pinzas ópticas estándar. Aprovechando este desarrollo, se realiza un segundo experimento para estudiar importantes problemas relacionados con las propiedades físicas y químicas de las nanopartículas utilizadas, con especial interés en su química superficial y en la comprensión de las pérdidas de masa onbservadas debidas a la desorción de agua de las esferas de sílice. Finalmente, gracias a una amplia base teórica en osciladores mecánicos no lineales, investigo la dinámica estocástica biestable de un nanoresonador accionado paramétricamente en el régimen no lineal, discutiendo el potencial de las transiciones estocásticas activadas por ruido externo y la resonancia estocástica como esquemas de detección de fuerza no convencionales.Postprint (published version

Spectral Analysis and Parameter Estimation in Fibre Levitated Optomechanics

In levitated optomechanics, nano-scale objects are optically trapped so that their motion can be studied. These trapped nanoparticles are held in a 3D quadratic potential and act as damped harmonic oscillators; they are thermally and mechanically decoupled from the apparatus and their position is measured interfer-ometrically to picometre accuracy. These systems are well suited to sensing and metrology applications, as any external disturbance of the particle can be observed using the scattered trapping light.When examining the motion of a levitated nanoparticle, it’s position is recorded and used to estimate a power spectral density (PSD), from which state parameters can be estimated. In this thesis an experi-mental setup is presented, optimised for maximum collection of particle position information in 1D, using a fibre-based parabolic mirror trap and heterodyne measurement system in order to produce spectra with minimal noise and unwanted artefacts.A novel application of the Middleton expansion from RF engineering is used to generate a complete power spectrum that depends on the physical parameters of the system. This method treats the particle as a stochastic harmonic oscillator, phase modulated by a Gaussian random process with known PSD. We reproduce the PSD of intensity at a detector, a quantity that is sinusoidally dependent on particle posi-tion. This technique generates a single, full PSD using modified Bessel functions, and does not depend on assumptions about the relative phases of the interfered fields, highlighting the non-linear dependence of measured signal on position. Theoretical spectra are fitted to a measured PSD and the phase modulation depth is extracted; this is used to calculate the particle oscillation amplitude and, by an equipartition ar-gument, the centre of mass temperature to mass ratio. State parameters are tracked as environmental conditions change and an increase in centre of mass temperature as a function of decreasing background gas pressure is observed

The study of atomic quasi-stable states, decoherence and cooling of mesoscale particles

Quantum mechanics, since its very beginning, has totally changed the way we understand nature. The past hundred years have seen great successes in the application of quantum physics, including atomic spectra, laser technology, condensed matter physics and the remarkable possibility for quantum computing, etc. This thesis is dedicated to a small regime of quantum physics. In the first part of the thesis, I present the studies of atomic quasi-stable states, which refer to those Rydberg states of an atom that are relatively stable in the presence of strong fields. Through spectrally probing the quasi-stable states, series of survival peaks are found. If the quasi-stable electrons were created by ultraviolet (UV) lasers with two different frequencies, the survival peaks could be modulated by continuously changing the phase difference between the UV and the IR laser. The quantum simulation, through directly solving the Schr¨odinger equation, matches the experimental results performed with microwave fields, and our studies should provide a guidance for future experiments. Despite the huge achievements in the application of quantum theory, there are still some fundamental problems that remain unresolved. One of them is the so-called quantum-to-classical transition, which refers to the expectation that the system behaves in a more classical manner when the system size increases. This basic question was not well answered until decoherence theory was proposed, which states that the coherence of a quantum system tends to be destroyed by environmental interruptions. Thus, if a system is well isolated from its environment, it is in principle possible to observe macroscopic quantum coherence. Quite recently, testing quantum principles n the macroscale has become a hot topic due to rapic technological developments. A very promising platform for testing macroscale quantum physics is a laser levitated nanoparticle, and cooling its mechanical motion to the ground state is the first step. In the second part of this thesis, we develop the theory of decoherence for a mesoscopic system’s rotational degrees of freedom. Combining decoherence in the translational degrees of freedom, the system’s shot noise heating is discussed. We then focus on cooling the nanoparticle in the laser-shot-noise-dominant regime using two different feedback cooling schemes: the force feedback cooling and the parametric feedback cooling. Both quantum and classical calculations are performed, and an exact match is observed. We also explore the parameters that could possibly affect the cooling trend, where we find that the cooling limit for both cooling schemes strongly depends on the position measurement efficiency, and it poses good questions for researchers interested in achieving ground state cooling: what is the best measurement efficiency for a given measurement setup and what can be done to get a better measurement efficiency