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Interference in a Bose-Einstein Condensate

Ambrosius Thomas Vermeulen

Published Jan 1, 2016• 0 citations
OpenAlex

Abstract

A BEC can be viewed as a giant matter wave, this means that it can show interference. By creating a double-well potential we can split a BEC into two parts. After turning off the potential the BEC will start to expand because of its chemical potential. As the BEC's expand and the two matter waves superpose they show an interference pattern. In this thesis it is described how to succesfully create such a double-well potential. The potential created is stable, however not symmetric. The reason why it is not symmetric is investigated and it can be concluded that for a symmetric potential an optical dipole potential with a crosssection of around 10 micrometer is preferable. A description is given of the interference pattern that arises from different expansion time and different height of the potential barrier. Because the potential is not symmetric a dependence arises that causes the interference pattern not to be constant in space as observed in previous experiments. This might be an advantage for determining the phase difference between two BEC's.

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A BEC can be viewed as a giant matter wave, this means that it can show interference. By creating a double-well potential we can split a BEC into two parts. After turning off the potential the BEC will start to expand because of its chemical potential. As the BEC's expand and the two matter waves superpose they show an interference pattern. In this thesis it is described how to succesfully create such a double-well potential. The potential created is stable, however not symmetric. The reason why it is not symmetric is investigated and it can be concluded that for a symmetric potential an optical dipole potential with a crosssection of around 10 micrometer is preferable. A description is given of the interference pattern that arises from different expansion time and different height of the potential barrier. Because the potential is not symmetric a dependence arises that causes the interference pattern not to be constant in space as observed in previous experiments. This might be an advantage for determining the phase difference between two BEC's.
Interference between two freely expanding Bose-Einstein condensates has been observed. Two condensates separated by approximately 40 micrometers were created by evaporatively cooling sodium atoms in a double-well potential formed by magnetic and optical forces. High-contrast matter-wave interference fringes with a period of approximately 15 micrometers were observed after switching off the potential and letting the condensates expand for 40 milliseconds and overlap. This demonstrates that Bose condensed atoms are "laser-like"; that is, they are coherent and show long-range correlations. These results have direct implications for the atom laser and the Josephson effect for atoms.
A trapped-atom interferometer was demonstrated using gaseous Bose-Einstein condensates coherently split by deforming an optical single-well potential into a double-well potential. The relative phase between the two condensates was determined from the spatial phase of the matter wave interference pattern formed upon releasing the condensates from the separated potential wells. Coherent phase evolution was observed for condensates held separated by 13 microm for up to 5 ms and was controlled by applying ac Stark shift potentials to either of the two separated condensates.
Quantum interference is ubiquitous to many (if not all) quantum processes and phenomena, for it is a direct manifestation of their inherent coherence. Experiments based on matter wave interferometry [1] constitute very nice empirical evidences of this property. Though the first diffraction experiments were carried out with electrons [2], nowadays the (matter) particles utilized range from large atoms and single molecules [3-6] to very complex, large molecules [7] and Bose-Einstein condensates (BECs) [8]. This kind of experiments, apart from confirming the wave nature of matter, has also given rise to important practical applications. For example, sensing, metrology or quantum information processing are potential applications which have motivated in the last few years the remarkable development of BEC interferometry [9-11]. This can be observed in the increasing amount of (theoretical and T&F Cat # K11224, Chapter 13, Page 198, 15-9-2010 experimental) work appearing in the literature [12-18] since the first experimental evidence of interference between two freely expanding BECs [19]. The basic scheme upon which this type of interferometry is based is depicted in Figure 13.1. In the first stage (left), the atomic cloud is cooled down in a magnetic trap until condensation takes place. Then (right), the BEC is split up coherently by means of radio-frequency [16] or microwave fields [17]. Finally, the double-well-like trapping potential [20] is switched off, releasing the two resulting BECs, which will interfere by free expansion (e.g., see Figure 6 of Ref. [18] as an illustration of a real experimental outcome).
We have used a microfabricated atom chip to split a single Bose-Einstein condensate of sodium atoms into two spatially separated condensates. Dynamical splitting was achieved by deforming the trap along the tightly confining direction into a purely magnetic double-well potential. We observed the matter wave interference pattern formed upon releasing the condensates from the microtraps. The intrinsic features of the quartic potential at the merge point, such as zero trap frequency and extremely high field-sensitivity, caused random variations of the relative phase between the two split condensates. Moreover, the perturbation from the abrupt change of the trapping potential during the splitting was observed to induce vortices.
The interference pattern of two Bose—Einstein condensates released from a double-well potential for different holding times is theoretically investigated using a decoupled two-mode Bose—Hubbard model. For two coherently separated condensates, the interference displays a periodic behavior, which is closely related to the atomic interaction. A remarkable parity effect is found in the interference patterns. For certain holding times, the even/odd total number of atoms would result in different interference fringes. The influences of different initial conditions on the evolution of interference and the observation of parity effects are discussed.