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Sculpturing of a non-spreading wave packet in imaginary potentials

R. Stuetzle, M. C. Goebel, T. Hoerner, E. Kierig, I. Mourachko, Markus K Oberthaler, Maxim A. Efremov, Mikhail Vladimirovich Fedorov, Valery P. Yakovlev, K. A. H. van Leeuwen, W. P. Schleich

Published Dec 17, 2004• 0 citations
OpenAlex

Abstract

We propose and experimentally demonstrate a method to prepare a non-spreading atomic wave packet. Our technique relies on a spatially modulated absorption constantly chiselling away from an initially broad de-Broglie wave. Heisenberg's uncertainty principle puts a limit to this contraction and determines the final complex Gaussian form of the packet. Experimentally we confirm the predicted formation process of the wave packet by observing the evolution of the momentum distribution. Moreover by employing interferometric techniques we measure the predicted quadratic phase across the wave packet.

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We propose and experimentally demonstrate a method to prepare a non-spreading atomic wave packet. Our technique relies on a spatially modulated absorption constantly chiselling away from an initially broad de-Broglie wave. Heisenberg's uncertainty principle puts a limit to this contraction and determines the final complex Gaussian form of the packet. Experimentally we confirm the predicted formation process of the wave packet by observing the evolution of the momentum distribution. Moreover by employing interferometric techniques we measure the predicted quadratic phase across the wave packet.
We propose and experimentally demonstrate a method to prepare a nonspreading atomic wave packet. Our technique relies on a spatially modulated absorption constantly chiseling away from an initially broad de Broglie wave. The resulting contraction is balanced by dispersion due to Heisenberg's uncertainty principle. This quantum evolution results in the formation of a nonspreading wave packet of Gaussian form with a spatially quadratic phase. Experimentally, we confirm these predictions by observing the evolution of the momentum distribution. Moreover, by employing interferometric techniques, we measure the predicted quadratic phase across the wave packet. Nonspreading wave packets of this kind also exist in two space dimensions and we can control their amplitude and phase using optical elements.
We discuss four general features of the force-free evolution of wave packets: (1) The spatial spread of a packet changes with time in a simple way. (2) For sufficiently short durations (related to the spread in the momentum of the packet) the probability distribution will move with uniform speed and little change in shape. (3) After a sufficiently long time (related to the initial spatial spread) the wave function converges to a simple form that is simply related to the momentum distribution of the packet. In this asymptotic regime the shape of the probability distribution no longer changes, and its scale increases linearly with the time. (4) There is an infinite denumerable set of simple wave packets (the Hermite-Gauss packets) that do not change shape at any time during their evolution.