LA ÚNICA LIBERTAD QUE TIENEN ESTOS INFELICES ES LA DE SOLICITAR AMO

In contrast to optics, which is well established, the field of guiding matter waves and its subsequent application to practical devices is in its infancy. Many of the funda- mental properties of such a system are yet to be characterised. Early atom guiding experiments focused on the transmission properties of thermal atoms through optical fibres, magnetic potentials and dipole potentials. Optical fibre guides were created using a range of configurations. These include numerous hollow fibre configurations using both red detuned potentials [207, 208, 209], evanescent waves from blue de- tuned potentials [210, 211, 212, 213, 214, 215], optical fibres with micro-wires lining the inside [216] and (more recently) micro-structured optical fibres [217, 218, 219]. Magnetic fields produced by current carrying wires have also been used to create guides [220, 221, 222]. An advantage of this approach is the option of using micro- wires fabricated on atom chips [223, 224, 225, 226], which are a promising approach for applications that have miniaturisation and integration of components as key requirements. While these micro-fabricated chips have been used to guide ther- mal atoms [227, 228, 229], some major drawbacks exist. For instance, detrimental thermal effects can result from having a room temperature surface so close to the ultra-cold atoms [230, 231, 232] and imperfections in the manufacturing process can lead to irregularities in the current flow [233, 234, 235]. Hollow (Laguerre-Gaussian “doughnut” mode) blue detuned laser beams propagating in free space have also been used as thermal atomic waveguides [236, 237, 238, 239]. However, in all of these studies, a major limitation is the large kinetic energy of thermal atoms, which results in highly multi-mode excitation of the discrete transverse energy levels in the guiding potential1_.

In later experiments, the use of ultracold atoms and Bose-Einstein condensates (BECs) as a source greatly reduces the excitation energy when coupled into guiding structures. Here the guides were generated using blue detuned hollow optical po-

tentials [241], magnetic fields generated by microstructured wires on an atom chip configured to form waveguides [235] and conveyor belts [225], and dressed-state RF potentials [242]. Note that in all these cases the guiding was still highly multi-mode. More recently, significantly lower transverse mode occupancies have been realised with the guiding of atom laser beams output-coupled from BECs. This has been accomplished using optical waveguides to confine 87_{Rb atoms released from mag-} netic [243] and optical [43, 244] trapping fields. In both cases the output-coupled atoms were confined by far-red-detuned, focused laser beams aligned horizontally. The significance of these experiments is that the output-coupling mechanism allows the population of just a few transverse modes, with atoms ultimately being guided predominantly in a single-mode. For the first experiment, described in [243], the guide potential was overlaid on a magnetic trap and the atoms were spin-flipped into an un-trapped state, which is then guided horizontally. However, due to mis- matches in the optical and magnetic potential alignments, motion of the guide and the transfer process not being adiabatic, their transverse ground state population was only _∼14% [243]. In two separate experiments by the one group ([244] being an improvement on their orignal work [43]), most of these technical problems were overcome by using an all-optical trap and guide configuration. This ensured a more adiabatic transfer, as well as removing much of the influence of relative motion. Their out-coupling process, involving lowering the horizontal potential in one di- mension over time, was also more adiabatic and led to their reported occupancies of _∼50% [43] and _∼85% [244] in the lowest transverse mode. In all cases the mode population was inferred by observing the propagation of atoms along the waveguide via absorption imaging, which enables the transverse energy of the guided atoms to be determined and compared with that expected for various transverse mode com- binations. As such, until the present work, no direct observation of transverse mode structures has been reported. This is due in part to the differences in detection techniques between alkali atoms (used in all the previous guiding work) and He* atoms.

Freely propagating atom laser mode profiles are typically poor compared to their optical counterparts. This is mostly due to the interactions between atoms, which are not present in the optical case. When atoms are outcoupled they experience the mean-field potential of the BEC atoms which remain trapped. This causes a lensing effect on the atom laser, leading to caustics on the atom laser profile [245]. Interference fringes are also observed, due to the path differences between outcoupled atoms which were coherent in trap but follow different trajectories as they roll off the potential [246, 78]. Such effects are especially dramatic for He∗_{, whose light} mass also leads to a fountaining of the outcoupled atoms [78].

A similar case in optics is the mode profile of diode laser, which often exhibits far from ideal structure. To improve the mode quality a number of techniques can be employed, referred to as mode filtering. The beam could either be spatially filtered using a focusing lens and aperture or passed through a resonant cavity [247] (a mode cleaner). More often however, the beam is coupled into a single mode fibre which only supports the lowest mode of propagation, thus removing all higher modes [248]. In direct analogy the guiding of an atom laser in an optical potential should similarly

§6.1 Introduction 125

give a dramatically improved mode profile, although here the BEC is normally in the lowest mode, with the challenge being to minimise excitations in the outcoupling procedure. The divergence will also be greatly reduced, even after the atoms leave the guide, similar to the collimated output of an optical fibre.

From a practical standpoint, atom guiding may become an important technique for any application involving transmitting atoms over macroscopic distances. In many of these cases, knowledge of the coherence of the transmitted matter-wave is an important requirement.