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The Casimir-Polder interaction between a single neutral atom and a nearby surface, arising from the (quantum and thermal) fluctuations of the electromagnetic field, is a cornerstone of cavity quantum electrodynamics (cQED), and theoretically well established. Recently, Bose-Einstein condensates (BECs) of ultracold atoms have been used to test the predictions of cQED. The purpose of the present thesis is to upgrade single-atom cQED with the many-body theory needed to describe trapped atomic BECs. Tools and methods are developed in a second-quantized picture that treats atom and photon fields on the same footing. We formulate a diagrammatic expansion using correlation functions for both the electromagnetic field and the atomic system. The formalism is applied to investigate, for BECs trapped near surfaces, dispersion interactions of the van der Waals-Casimir-Polder type, and the Bosonic stimulation in spontaneous decay of excited atomic states. We also discuss a phononic Casimir effect, which arises from the quantum fluctuations in an interacting BEC.
With ongoing miniaturization of electronic devices, the need for individually addressable, switchable molecules arises. An example are azobenzenes on surfaces which have been shown to be switchable between trans and cis forms. Here, we examine the "direct" (rather than substrate-mediated) channel of the trans -> cis photoisomerization after pi pi* excitation of tetra-tert-butyl-azobenzene physisorbed on surfaces mimicking Au(111) and Bi(111), respectively. In spirit of the direct channel, the electronic structure of the surface is neglected, the latter merely acting as a rigid platform which weakly interacts with the molecule via Van-der-Waals forces. Starting from thermal ensembles which represent the trans-form, sudden excitations promote the molecules to pi pi*-excited states which are non-adiabatically coupled among themselves and to a n pi*-excited and the ground state, respectively. After excitation, relaxation to the ground state by internal conversion takes place, possibly accompanied by isomerization. The process is described here by "on the fly" semiclassical surface hopping dynamics in conjunction with a semiempirical Hamiltonian (AM1) and configuration-interaction type methods. It is found that steric constraints imposed by the substrate lead to reduced but non-vanishing, trans -> cis reaction yields and longer internal conversion times than for the isolated molecule. Implications for recent experiments for azobenzenes on surfaces are discussed.