Abstract The methods developed formanipulating atomic motion with laser light, briefly described in Chapters 5 and 6, have led naturally to the creation of atom optics.
Abstract A century ago Einstein introduced the notion of the linear momentum of a photon, h k, and analyzed its transfer to an atom (and back) in the establishment of thermodynamic equilibrium between black-body radiation and matter. In addition to a linear momentum, the photon also possesses an angular momentum, ħ, directed parallel (or antiparallel) to its propagation direction (the OZ axis in Fig. 4.1), depending on its polarization direction (left- or right-handed). This angular momentum is due to the spin of the photon, equal to 1. Half a century later, Kastler (1950) considered the use of the transfer of the angular momentum of a polarized photon to the angular momentum of an atom as a method of optical orientation of atoms. In essence, this was the first method to control atomic motion by means of low-intensity light, developed even before the advent of the laser; it which found widespread application in investigating and then using spin polarization effects in atomic physics. But even after lasers had made their appearance, the method of optical orientation of atoms (or pumping of certain magnetic sublevels in atoms) proved very important, specifically in the laser cooling of atoms (Chapter 5).
With the creation of the laser in the 1960s, optics research gained a whole new type of coherent, well-behaved light with which to experiment. Later, similar matter was created; first in the form of super-fluids and then Bose-Einstein condensates (BECs).A BEC as a whole behaves in many ways analogous to a monochromatic laser beam; the ultra-cold atoms in a BEC are the matter equivalent of photons in the laser beam. Researchers have built the BEC analogs of a number of optical components, including lenses and beam splitters. The work described in this thesis was inspired by the aim to investigate theoretically BEC analogs of effects known from laser physics and by developing a BEC analog of Fourier holography.After introductions into lasers and BECs (chapter 1) and numerical methods for solving the differential equations governing the behaviour of both light and BECs (chapter 2), this thesis comes in two parts.The first part is concerned with the BEC analogs of the formation of transverse laser modes (chapter 3) and an interferometer for sorting optical vortices (chapter 5), and a non-destructive method of Fourier-transforming a BEC (chapter 4).The second part is about optical holography and optical tweezers. It starts with a review of hologram-design algorithms (chapter 6). Originally inspired by optical Fourier holography, discussions about BEC Fourier holography counter-inspired a new algorithm for optical Fourier holography, namely a Gerchberg-Saxton algorithm for 3-dimensional light shaping (chapter 7). My work on the improvement of hologram-calculation software for optical tweezers is described in chapter 8.
In the previous chapters, we have seen that the cause of the mechanical effects of light on atoms is nothing more than the momentum exchanged between photons and atoms. This exchange determines both the forces exerted on atoms and, ultimately, the atoms’ translational motion. But now things become even more interesting. In this chapter we present to a new generation of laser beams that have been developed over the last few decades. These beams have quite unusual properties and even more exotic and fascinating applications. They contain optical vortices, as do many other physical systems, and, thus, are known as optical vortex beams.