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arXiv:quant-ph/9806033

Quantum Carpets made simple

Irene Marzoli, Farhan Saif, Iwo Białynicki‐Birula, O. M. Friesch, A. E. Kaplan, Wolfgang P. Schleich

Published Jun 10, 1998• 39 citations
arXivHTMLPDF

Abstract

We show that the concept of degeneracy is the key idea for understanding the quantum carpet woven by a particle in the box.
DOI
10.48550/arxiv.quant-ph/9806033

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Fortschritte der Physik•May 27, 2009•0 citations
Abstract We analyze the structures emerging in the spacetime representation of the probability density woven by a slightly relativistic particle caught in a one‐dimensional box. In particular, we evaluate the relativistic effects on the revival time and the specific changes produced in the intermode traces, which quantum carpets consist of. Moreover, we present a detailed mathematical analysis of such quantum carpets pursuing the approach of a kernel. Here we represent the probability distribution as a superposition of interfering Airy function‐type structures along straight world lines. We also show that this phenomenon can be enhanced by many orders of magnitude in semiconductors with narrow band‐gap (e.g. as in InSb) and small effective mass of the electron, whereby due to the strong nonparabolicity of the semiconductor conduction band, the electron energy vs momentum dispersion relation behaves in a pseudo‐relativistic way.
The cover page of 2009 shows high-resolution interference “quantum carpet” patterns for the momentum wave function of an interacting Bose-Einstein condensate (BEC). As time progresses (from back to front), the many-body mean field interaction of the BEC first leads to a broadening of the wave function, but then also to a time-varying interference structure by inducing site-dependent nonlinear phase shifts when the BEC is confined in a spatially periodic potential. Imaging the wave function in momentum space for different times leads to a pattern that one reminds of a carefully woven carpet and is hence termed “quantum carpet”. Quantum carpets beautifully demonstrate the surprisingly high matter wave coherence of particle-particle interactions in the zero-temperature limit.
The cover page of 2009 shows high-resolution interference “quantum carpet” patterns for the momentum wave function of an interacting Bose-Einstein condensate (BEC). As time progresses (from back to front), the many-body mean field interaction of the BEC first leads to a broadening of the wave function, but then also to a time-varying interference structure by inducing site-dependent nonlinear phase shifts when the BEC is confined in a spatially periodic potential. Imaging the wave function in momentum space for different times leads to a pattern that one reminds of a carefully woven carpet and is hence termed “quantum carpet”. Quantum carpets beautifully demonstrate the surprisingly high matter wave coherence of particle-particle interactions in the zero-temperature limit.