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The Phase of a Bose-Einstein Condensate

Stephan Dürr

Published Nov 30, 2006• 0 citations
Publisher

Abstract

If two Bose-Einstein condensates are prepared independently and then overlapped, a spatial interference pattern is observed. This prompts the question what determines the phase of the fringe pattern, and whether a condensate has a well-defined value of the phase. This problem has been studied in the literature in detail. The objective of this article is, to present an introduction to the subject and to summarize the discussion for a wider audience.

DOI
10.17877/de290r-1228

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If two Bose-Einstein condensates are prepared independently and then overlapped, a spatial interference pattern is observed. This prompts the question what determines the phase of the fringe pattern, and whether a condensate has a well-defined value of the phase. This problem has been studied in the literature in detail. The objective of this article is, to present an introduction to the subject and to summarize the discussion for a wider audience.
We consider the interference of two overlapping ideal Bose-Einstein condensates. The usual description of this phenomenon involves the introduction of a condensate wave function with a definite phase. We investigate the origin of this phase and the theoretical basis of treating interference. It is possible to construct a phase state for which the particle number is uncertain, but the phase is known. How such a state would be prepared before an experiment is not obvious. We show that a phase can also arise from experiments using condensates with known particle numbers. The analysis of measurements in such states also gives us a prescription for preparing phase states. The connection of this procedure to questions of spontaneously broken gauge symmetry and to hidden variables is discussed.
Interference is observed when two independent Bose–Einstein condensates expand and overlap. This phenomenon is typical, in the sense that the overwhelming majority of wave functions of the condensates, uniformly sampled out of a suitable portion of the total Hilbert space, display interference with maximal visibility. We focus here on the phases of the condensates and their (pseudo) randomization, which naturally emerges when two-body scattering processes are considered. Relationship to typicality is discussed and analyzed.