Motion of Atomic Objects.

Gunther K. Wertheim

Elmer A. Ogryzlo

It is the object of this paper to describe the classical motion which is compatible with the exact distribution functions for atomic orbitals.

A. N. Tupolev

The paper introduces a method of V-function, from which it follows that the trajectory motion of an object is connected with the wave motion. We formulate a local variational principle (LVP) and the basic theorems of the method of V-function, which allow a new statement of the direct and inverse dynamics problems. Based on the method of V-function, we consider the optical-mechanic analogy, which is presented in a new extended version and investigate the properties of the wave nature of electron motion in a hydrogen-like atom and the motion of an object (particle) for a harmonic oscillator. We demonstrate that in a physical sense, the wave V(x,t) characterizes the properties of an action showing itself in the motion of an object (particle). By its node, the wave is connected with the position of the particle and so leads it. The particle (trajectory) in its turn generates a wave propagating along it. We establish that the energy levels of a hydrogen-like atom, obtained using the method of V-function, correspond entirely to the classical results of quantum physics, while the energy levels of a harmonic oscillator do not contradict the known Schrodinger's results.

Patricia Daukantas

Thierry Botter

An exciting scientific goal, common to many fields of research, is the development of ever-larger physical systems operating in the quantum regime. Relevant to this dissertation is the objective of preparing and observing a mechanical object in its motional quantum ground state. In order to sense the object's zero-point motion, the probe itself must have quantum-limited sensitivity. Cavity optomechanics, the interactions between light and a mechanical object inside an optical cavity, provides an elegant means to achieve the quantum regime. In this dissertation, I provide context to the successful cavity-based optical detection of the quantum-ground-state motion of atoms-based mechanical elements; mechanical elements, consisting of the collective center-of-mass (CM) motion of ultracold atomic ensembles and prepared inside a high-finesse Fabry-P'erot cavity, were dispersively probed with an average intracavity photon number as small as 0.1. I first show that cavity optomechanics emerges from the theory of cavity quantum electrodynamics when one takes into account the CM motion of one or many atoms within the cavity, and provide a simple theoretical framework to model optomechanical interactions. I then outline details regarding the apparatus and the experimental methods employed, highlighting certain fundamental aspects of optical detection along the way. Finally, I describe background information, both theoretical and experimental, to two published results on quantum cavity optomechanics that form the backbone of this dissertation. The first publication shows the observation of zero-point collective motion of several thousand atoms and quantum-limited measurement backaction on that observed motion. The second publication demonstrates that an array of near-ground-state collective atomic oscillators can be simultaneously prepared and probed, and that the motional state of one oscillator can be selectively addressed while preserving the near-zero-point motion of neighboring oscillators.

Pieter Kok