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arXiv:1410.1381 · International Journal of Quantum Information

Phase randomization and typicality in the interference of two condensates

Paolo Facchi A, Hiromichi Nakazato, Saverio Pascazio, Francesco Vincenzo Pepe, Golam Ali Sekh, Kazuya Yuasa

Published Nov 1, 2014• 3 citations
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Abstract

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.

DOI
10.1142/s0219749915600199

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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.
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.
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.
We study theoretically the interference patterns produced by the overlap of an array of Bose-Einstein condensates that have no phase coherence among them. We show that density-density correlations at different quasimomenta, which play an important role in two-condensate interference, become negligible for large NNN, where NNN is the number of overlapping condensates. In order to understand the physics of this phenomenon, it is sufficient to consider the periodicity of the lattice and the statistical probability distribution of a random-walk problem. The average visibility of such interference patterns decreases as ${N}^{\ensuremath{-}1∕2}$ for large NNN.