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Chinese Journal of Physics

The phase of a bose-einstein condensate by the interference of matter waves

Wen-Hsuan Kuan, Tsin-Fu Jiang

Published Oct 1, 2005• 0 citations
OpenAlex

Abstract

We present a calculation which produces the additional phase of a matter wave by applying an adiabatically changing optical field to a double-well Bose-Einstein condensate. An examination of the additional quantum phase is proposed through the comparison of the free expansion interference patterns of the perturbed double-well condensate and the pure double-well condensate. PACS numbers: 03.75.Dg, 07.05.Tp I.

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We present a calculation which produces the additional phase of a matter wave by applying an adiabatically changing optical field to a double-well Bose-Einstein condensate. An examination of the additional quantum phase is proposed through the comparison of the free expansion interference patterns of the perturbed double-well condensate and the pure double-well condensate. PACS numbers: 03.75.Dg, 07.05.Tp I.
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.
Bose–Einstein condensates of particles behave in many ways like coherent radiation fields, and the realization of Bose–Einstein condensation in dilute gases has opened up the experimental study of interactions between coherent matter waves. In addition, the existence of these dilute trapped quantum gases has prompted a re-examination of a number of theoretical issues. In Sec. 13.1 we discuss Josephson tunnelling of a condensate between two wells and the role of fluctuations in particle number and phase. The number and phase variables play a key role in the description of the classic interference experiment, in which two clouds of atoms are allowed to expand and overlap (Sec. 13.2). Rather surprisingly, an interference pattern is produced even though initially the two clouds are completely isolated. Density fluctuations in a Bose gas are studied in Sec. 13.3, where we relate atomic clock shifts to the two-particle correlation function. The ability to manipulate gaseous Bose–Einstein condensates by lasers has made possible the study of coherent matter wave optics and in Sec. 13.4 we describe applications of these techniques to observe solitons, Bragg scattering, and non-linear mixing of matter waves. How to characterize Bose–Einstein condensation in terms of the density matrix is the subject of Sec. 13.5, where we also consider fragmented condensates.
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.
Understanding the effect of interactions in the phase evolution of expanding atomic Bose-Einstein condensates is fundamental to describing the basic phenomenon of matter wave interference. Many theoretical and experimental works tackled this problem, always with the implicit assumption that the mutual interaction between two expanding condensates rigidly modifies the phase evolution through an effective force. In this paper, we present a combined experimental and theoretical investigation of the interference profile of expanding 87Rb^{87}\mathrm{Rb}87Rb condensates, with a specific focus on the effect of interactions. We come to the different conclusion that the mutual interaction produces local modifications of the condensate phase only in the region where the wave packets overlap.
Bose–Einstein condensates of particles behave in many ways like coherent radiation fields, and the realization of Bose–Einstein condensation in dilute gases has opened up the experimental study of many aspects of interactions between coherent matter waves. In addition, the existence of these dilute trapped quantum gases has prompted a re-examination of a number of theoretical issues. This field is a vast one, and in this chapter we shall touch briefly on selected topics. In Sec. 13.1 we describe the classic interference experiment, in which two clouds of atoms are allowed to expand and overlap. Rather surprisingly, an interference pattern is produced even though initially the two clouds are completely isolated. We shall analyse the reasons for this effect. The marked decrease in density fluctuations in a Bose gas when it undergoes Bose–Einstein condensation is demonstrated in Sec. 13.2. Gaseous Bose–Einstein condensates can be manipulated by lasers, and this has made possible the study of coherent matter wave optics. We describe applications of these techniques to observe solitons, Bragg scattering, and non-linear mixing of matter waves in Sec. 13.3. The atom laser and amplification of matter waves is taken up in Sec. 13.4. How to characterize Bose–Einstein condensation microscopically is the subject of Sec. 13.5, where we also consider fragmented condensates. Interference of two condensates One of the striking manifestations of the wave nature of Bose–Einstein condensates is the observation of an interference pattern when two condensed and initially separated clouds are allowed to overlap. An example is shown in Fig. 13.1.
A trapped >(87)Rb Bose-Einstein condensate is initially put into a superposition of two internal states. Under the effect of gravity and by means of a second transition, we prepare two vertically displaced condensates in the same internal state. These constitute two coherent sources of matter waves with adjustable spatial separation. Fringe patterns, observed after free expansion, are associated with the interplay between internal and external degrees of freedom and substantially agree with those for a double-slit experiment.