Cold Atom Interferometry in Optical Potentials

Abstract

This thesis describes recent advances in ultra-cold atom interferometry. A common theme in the work described here is that the experiments are conducted on a Bose-Einstein condensate in an optical waveguide. This optical potential confines the atoms against gravity in the vertical dimension, guiding them to freely propagate along one horizontal dimension. Being supported against gravity enables long expansion times of hundreds of milliseconds, which facilitates techniques such as delta-kick cooling.

There are two main advantages of using ultra-cold atoms, rather than simply cold atoms, as a source for interferometry. Firstly, the coherence of an ensemble of atoms (as measured by either coherence length or coherence time) increases with a reduction in temperature. This means that a larger signal-to-noise may be obtained for a greater perturbation to ideal conditions, such as imperfect beam alignment, vibrations, intensity fluctuations etc. Conversely, this also means that such perturbations must be better understood so as to remove their systematic shift from a measurement of a quantity of interest. The second advantage to using an ultra-cold source cloud is its small size and small momentum width, as compared with a thermal source. Their small positional width means that clouds separated by only a small amount in momenta can easily be spatially separated and separately counted without the need for (magnetic) state labelling. Their small momentum width (and thus low spatial dispersion) means that better mode-matching is possible at the end of the interferometer, and that less-imperfect beam-splitter pulses are able to be used over the whole cloud.

The beamsplitters themselves would ideally impart a large momentum splitting between the interfering states as the signal of the interferometer is proportional to this splitting. The effective use of such a large momentum splitting, however, requires both an even narrower momentum width source and a system free of vibrations to at least a certain level. Otherwise such confounding factors can prevent any useful signal from being measured in such a device. Three such techniques were investigated in this thesis: reflection from a repulsive light potential barrier, Bragg transitions from an optical lattice (which are effectively bouncing atoms off a moving grating), and Bloch-acceleration by loading the atoms into such an optical lattice and then accelerating the combined system. It is found that a combination of both Bragg and Bloch provides the most promising route to truly large momentum transfer in a system which is sensitive only to acceleration. Lastly, large-momentum transfer techniques can be used to effectively increase the way in which the output signal scales with time, creating interferometers which generate the same sensitivity faster (increasing the bandwidth of a sensor), or generate a much better sensitivity in the same time.

The atom chosen for use in such a system depends largely upon what is easy to condense in a given lab, but it also depends upon which knobs one would like to be able to play with. A BEC of Rubidium-87 is comparatively easy to produce thanks to favourable collisional properties and the availability of diode lasers at the correct wavelength. However if one would like more control over the properties of the condensed cloud, including its collisional self-interaction strength, one must move to a different species. Conveniently also present in natural-abundance Rubidium sources, the collisional properties of Rubidium-85 can be modified by applying an external magnetic field, at an easy-to-experimentally-reach value of between 150-170G. Inconveniently, it is difficult (although not impossible) to condense by itself, so a sympathetic cooling technique in which 87Rb is used as an expendable coolant to acquire a cold sample of 85Rb is used in this thesis. This technique works surprisingly well thanks to yet more fortunate coincidences of the atomic properties of each atom. One benefit of requiring cold 87Rb to produce cold 85Rb is that it is easy to then produce a condensate of each species simultaneously in the same trap. It turns out that this combination of atomic isotopes is ideal for an interferometric test of the weak equivalence principle, one of the underpinnings of General Relativity. In fact, space missions are currently being proposed and funded on this combination of isotopes. This thesis also presents the results of the first Bose-condensed version of such a dual-species interferometer. As could well be expected, inter-atomic interactions play a large role in determining the output of such an interferometer and much further study is required before such a system could be deployed in space.

By ensuring there is no 87Rb left after condensation, we have created a pure 85Rb BEC. Using this we can now explore how the inter-atomic interactions affect the phase shift of a condensed atom interferometer, as we have complete control over the interaction strength. Two especially interesting cases are the following. Firstly, a condensate with no inter-particle interactions should not exhibit this effect at all, allowing a clean comparison point. Secondly, with a small attractive interaction between atoms, it is possible to create a self-trapped cloud of atoms which propagates dispersionlessly, even in the presence of a repulsive trapping potential. This cloud is known as a soliton, and it is predicted to have even more interesting quantum mechanical properties. For example it is predicted that by colliding two such solitons, an entangled state can be generated. Our results indicate that the dispersionless character of the soliton out-performs all other interaction strengths in an atom interferometer, including even the non-interacting cloud.

Throughout this thesis I have gained a better understanding of how ultra-cold atom interferometers work and what can be done to improve and extend their capabilities into new and exciting directions, and hopefully after reading this thesis, you will too.

Type
Publication
PhD Thesis
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