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The Casimir-Polder Effect and Quantum Friction Across Timescales Handelt Es Sich Um Meine Eigen- Ständig Erbrachte Leistung

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The Casimir-Polder Effect and Quantum Friction Across Timescales Handelt Es Sich Um Meine Eigen- Ständig Erbrachte Leistung THECASIMIR-POLDEREFFECT ANDQUANTUMFRICTION ACROSSTIMESCALES JULIANEKLATT Physikalisches Institut Fakultät für Mathematik und Physik Albert-Ludwigs-Universität THECASIMIR-POLDEREFFECTANDQUANTUMFRICTION ACROSSTIMESCALES DISSERTATION zu Erlangung des Doktorgrades der Fakultät für Mathematik und Physik Albert-Ludwigs Universität Freiburg im Breisgau vorgelegt von Juliane Klatt 2017 DEKAN: Prof. Dr. Gregor Herten BETREUERDERARBEIT: Dr. Stefan Yoshi Buhmann GUTACHTER: Dr. Stefan Yoshi Buhmann Prof. Dr. Tanja Schilling TAGDERVERTEIDIGUNG: 11.07.2017 PRÜFER: Prof. Dr. Jens Timmer Apl. Prof. Dr. Bernd von Issendorff Dr. Stefan Yoshi Buhmann © 2017 Those years, when the Lamb shift was the central theme of physics, were golden years for all the physicists of my generation. You were the first to see that this tiny shift, so elusive and hard to measure, would clarify our thinking about particles and fields. — F. J. Dyson on occasion of the 65th birthday of W. E. Lamb, Jr. [54] Man kann sich darüber streiten, ob die Welt aus Atomen aufgebaut ist, oder aus Geschichten. — R. D. Precht [165] ABSTRACT The quantum vacuum is subject to continuous spontaneous creation and annihi- lation of matter and radiation. Consequently, an atom placed in vacuum is being perturbed through the interaction with such fluctuations. This results in the Lamb shift of atomic levels and spontaneous transitions between atomic states — the properties of the atom are being shaped by the vacuum. Hence, if the latter is be- ing shaped itself, then this reflects in the atomic features and dynamics. A prime example is the Casimir-Polder effect where a macroscopic body, introduced to the vacuum in which the atom resides, causes a position dependence of the Lamb shift. This manifests in a force which draws the atom towards the body. In this dissertation, we present a theory which captures non-stationary aspects of this effect. In configurations such as the Casimir-Polder interaction between an excited atom and a body, or an atom which is in non-parallel relative motion with respect to the body that it interacts with, the Casimir-Polder potential acquires a non-trivial time and velocity-dependence. The former leads to pronunciated tran- sients and the latter to the emergence of quantum friction forces. Previously es- tablished methods to study the Casimir-Polder effect most prominently rely on the fluctuation-dissipation theorem, which cannot treat non-stationarity at all; time- dependent perturbation theory, which places an intrinsic bound on the time scales which can be considered; and semi-group Markovian quantum master equations, which allow to study the approximate time-dependence of the aforementioned non- stationary configurations but are blind to both transient behavior and the asymp- totic breakdown of exponential relaxation as known for systems of bound spectra. In this thesis, we present a non-Markovian quantum master equation approach to the Casimir-Polder effect and quantum friction forces. Our formulation is valid across all timescales – it describes transient, post-transient, as well as the asymp- totic atomic dynamics. It allows to infer non-equilibrium correlation functions of an atom which is weakly coupled to a body-assisted field and hence enables us to study both the internal and external dynamics both excited atoms and atoms in non-parallel motion with respect to a nearby body. As a first step, we study an atom which is at rest with respect to a nearby macro- scopic body. We combine the time-convolutionsless projection operator technique (TCL) for quantum master equations and quasi-stationary decay theory in order to describe the internal dynamics of that atom by virtue of a time-dependent Lamb shift and rate of spontaneous decay. The atomic dynamics generated by these two objects exhibit a transient Gaussian decay of excited-state populations, intermediate exponential relaxation and asymptotically algebraic decay. Our re- sults hence reproduce the correct perturbative, Markovian and asymptotic limits as known from time-dependent perturbation theory, Markovian quantum master equations and quasi-stationary decay theory, respectively. Subsequently, we em- ploy our quantum master equation in order to derive the dynamics of two-point correlation functions of atomic observables in the weak-coupling regime. The two- point correlation function of the atom’s electric dipole moment then enables us to vii derive the time-dependent Casimir-Polder potential as experienced by an initially excited atom. After having laid the foundation for describing non-stationary Casimir-Polder con- figurations, in a second step, we study the influence of relative motion onto our quantum master equation and the dynamics of atomic correlation functions. We derive the time-dependent quantum friction force experienced by an atom which moves through a body-assisted field as well as spectral signatures of motion such as the velocity-dependence of the atomic Lamb shift and rate of spontaneous decay. We hence present a conclusive, time-dependent, formulation of the Casimir-Polder effect and quantum friction which allows us to investigate both the internal and external dynamics of excited atoms and/or atoms in arbitrarily directed motion with respect to a nearby body. We find that for vertically moving atoms, both spec- tral signatures of motion and the quantum friction force exceed their respective parallel-motion counterparts by an order of magnitude. Lastly, our calculations constitute the first derivation of the quantum friction force to all orders in relative velocity and thereby elucidate the quantum friction debate concerning the leading order in velocity of that force. being valid across all time scales, our description reveals the limitations of all three previous approaches as rooted in their intrinsic restriction to different asymptotic time scales. In the last part of this dissertation, we apply our method towards the prediction of spectral signatures of quantum friction in frequency-modulated selective reflection spectroscopy of cesium atoms in a sapphire assisted field on the one hand and rota- tional spectroscopy of carbon monoxide quantum rotors in an indium-antimonide assisted field on the other hand. In the former setup we employ the enhancement of such signatures for non-parallel motion whereas in the second setup we make use of the amended sensitivity with respect to motion-induced corrections of ro- tational decay rates due to the dense spacing of rotational energy levels. In both cases we arrive at an experimental signal which significantly differs with respect to a purely static signal. We thereby present first experimental testbeds for signa- tures of the quantum friction force. viii ZUSAMMENFASSUNG Im Quantenvakuum findet kontinuierlich spontane Erzeugung und Vernichtung von Materie und Strahlung statt. Dementsprechend wird ein Atom im Vakuum permanent durch die Interaktion mit solchen Fluktuationen gestört. In Folge des- sen verschieben sich die atomaren Energieniveaus um die Lamb-Verschiebung und spontane Übergänge zwischen den atomaren Zuständen werden ermöglicht — das Vakuum veändert die Eigenschaften des Atoms. Wenn wiederum das Vaku- um verändert wird, so schlägt sich dies in der Erscheinung und Dynamik eines in diesem Vakuum befindlichen Atoms wider. Ein prominentes Beispiel ist der Casimir-Polder Effekt. Dort begründet ein makroskopischer Körper, platziert im Vakuum, eine Ortsabhängigkeit in der Lamb-Verschiebung. Folglich erfährt das Atom eine Kraft und wird von dem Körper angezogen. Die vorgelegte Dissertationsschrift hat nicht-stationäre Aspekte dieses Effektes zum Thema. In Konfigurationen wie beispielsweise der eines angeregten Atoms und eines makroskopischen Körpers, oder aber eines sich in Relativbewegung zu einem solchen Körper befindlichen Atoms, acquiriert das Casimir-Polder Potential eine nicht-triviale Zeit- und Geschwindigkeitsabhängigkeit. Erstere führt zu aus- geprägten Transienten und letztere zum Auftreten von Quantenreibungskräften. Bisher entwickelte Methoden zur Beschreibung des Casimir-Polder Effektes las- sen sich vornehmlich in Fluktuationale Elektrodynamik, Störungstheoretische An- sätze, und Semigruppen-Markov’sche Quantenmastergleichungen einteilen. Ers- tere ist grundsätzlich nicht zur Untersuchung nicht-stationärer Systeme geeignet, zweitere setzt klare Grenzen bezüglich der behandelbaren Zeitskalen, und letztere erlauben zwar ein näherungsweises Erfassen der Dynamik obengenannter nicht- stationärer Konfigurationen — jedoch bleiben sowohl transiente Verhalten als auch der asymptotische Zusammenbruch exponentieller Relaxation, welcher Sys- temen von beschränkter Spektraldichte inherent ist, dieser Methode verborgen. In der vorgelegten Thesis präsentieren wir eine Annäherung an den Casimir-Polder Effekt und Quantenreibung, welcher auf nicht-Markov’schen Quantenmasterglei- chungen basiert. Unsere Formulierung dieser Phänomene gilt über alle Zeit- ska- len hinweg. Sie beschreibt transiente, post-transiente, sowie asymptotische atoma- re Dynamik. Unser Ansatz erlaubt Zugang zu Nichtgleichgewichts-Korrelations- funktionen eines Atoms welches schwach an ein Körper-assistiertes Vakuum ge- koppelt ist. Dies ermöglicht uns neben der internen Dynamik angeregter oder in Relativbewegung befindlicher Atome, auch die Casimir-Polder und Quanten- reibungskräfte welche auf jene Atome wirken, zu erfassen. In einem ersten Schritt untersuchen wir ein Atom welches sich bezüglich des be- nachbarten Körpers in Ruhe befindet. Wir kombinieren Zeitfaltungsfreie Projek- tionsoperatortechniken
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