Abstract

Wave packets (WPs) has recently emerged as a very active research field in quantum optics. We show here that the evolution of WPs may result in new class of large-scale interference effects: the formation of highly regular spatiotemporal patterns in the QM probability, |Ψ|², with the key mechanism for this being pair interference between the eigen-modes of the system and the degeneracy of this interference. The new patterns have been discovered in the probability density |Ψ|²(x, t) of a particle in an infinitely deep square well, by numerical simulations of the evolution of a Gaussian WP¹; later work by a few groups used other initial conditions and media (e.g. Bose-Einstein condensate and angular WPs). In all these cases, the QM distribution shows a net of “canals” (minima), and “ridges” (maxima), running as straight lines in space-time (x, t). Similar patterns in the near field of a diffraction grating, and in matter waves in atom optics² reveals a new aspects of the Talbot effect. So far the numerical exploration of these patterns has relied on the specific choice (i) of the initial conditions and (ii) of the square well; no physical explanation of the patterns has been suggested. Recently, we observed³ a “quantum carpet” under more general conditions, offered its universal explanation, and predicted distinct “curved” patterns in general case of an anharmonic potentials.

© 1999 Optical Society of America