Special Issue: Coherent Matter Waves

P. G. Kevrekidis, D. J. Frantzeskakis, R. Carretero-González

Rakesh Kumar Pandey

Ever since behavior of photons were explained in terms of the matter-wave duality, mystery about the size of such a photon as it behaves like a particle has never slipped out from the scientific discussions. It is normally believed that the size of the photons is of the order of the wavelength of the electromagnetic wave. This paper addresses this scientific concern and attempts at opening the issue up for discussion after making a completely theoretical but consistent proposition. The argument presented here borrows the idea from the way particles have been conceptualized in quantum mechanics. In quantum mechanics it is argued that a particle gets represented not by a single wave but a group of waves in a way that the group velocity of such a group of waves exactly gives the velocity of the particle. Based on the same argument it is explained how the coherence length instead of the wavelength of the electromagnetic wave, must estimate the linear dimension of a photon. In the end, the discussion on the size of a photon in view of the special theory of relativity is also initiated in this paper.

F. S. Cataliotti, I. Herrera, Saverio Bartalini +3 more

W. Vassen, Andreas Hemmerich, E. Arimondo

This Special Issue of Journal of Optics B: Quantum and Semiclassical Optics brings together the contributions of various researchers working on theoretical and experimental aspects of cold quantum gases. Different aspects of atom optics, matter wave interferometry, laser manipulation of atoms and molecules, and production of very cold and degenerate gases are presented. The variety of subjects demonstrates the steadily expanding role associated with this research area. The topics discussed in this issue, extending from basic physics to applications of atom optics and of cold atomic samples, include: •Bose--Einstein condensation •Fermi degenerate gases •Characterization and manipulation of quantum gases •Coherent and nonlinear cold matter wave optics •New schemes for laser cooling •Coherent cold molecular gases •Ultra-precise atomic clocks •Applications of cold quantum gases to metrology and spectroscopy •Applications of cold quantum gases to quantum computing •Nanoprobes and nanolithography. This special issue is published in connection with the 7th International Workshop on Atom Optics and Interferometry, held in Lunteren, The Netherlands, from 28 September to 2 October 2002. This was the last in a series of Workshops organized with the support of the European Community that have greatly contributed to progress in this area. The scientific part of the Workshop was managed by A Hemmerich, W Hogervorst, W Vassen and J T M Walraven, with input from members of the International Programme Committee who are listed below. The practical aspects of the organization were ably handled by Petra de Gijsel from the Vrije Universiteit in Amsterdam. The Workshop was funded by the European Science Foundation (programme BEC2000+), the European Networks 'Cold Quantum Gases (CQG)', coordinated by E Arimondo, and 'Cold Atoms and Ultraprecise Atomic Clocks (CAUAC)', coordinated by J Henningsen, by the German Physical Society (DFG), by the Dutch Foundation for Fundamental Research on Matter (FOM) and by the Dutch Gelderland province. We thank all these sponsors and the members of the International Programme Committee for making the Workshop such a success. At this point we take the opportunity to express our gratitude to both authors and reviewers, for their efforts in preparing and ensuring the high quality of the papers in this special issue. Wim Vassen Vrije Universiteit, Amsterdam Andreas Hemmerich Universität Hamburg Ennio Arimondo Università di Pisa Guest Editors International Programme Committee A Aspect Orsay, France E Cornell Boulder, USA W Ertmer Hannover, Germany T W Haensch Munich, Germany A Hemmerich Hamburg, Germany W Hogervorst Amsterdam, The Netherlands D Kleppner Cambridge, USA C Salomon Paris, France G V Shlyapnikov Amsterdam, Paris, Moscow S Stringari Trento, Italy W Vassen Amsterdam, The Netherlands J T M Walraven Amsterdam, The Netherlands

Jun Chen, Qiang Lin

Gintautas Kamuntavičius

The free relativistic particle, by definition, has to move in an inertial reference frame with uniform velocity less than the speed of light. The corresponding movement of a material quantum particle describes a wave packet, composed of matter waves—solutions of the Schr?dinger equation. The maximum of packet, corresponding to the largest probability to find the particle, has to move with the same uniform velocity, defined by the initial condition. It has been shown that the traditional definition of the quantum momentum operator i.e. taking it to correspond to the special relativity theory, relativistic momentum, cannot produce precise description of a relativistic matter particle. Different definitions are investigated and one that solves this issue is found. Obtained original expression of relativistic kinetic energy operator creates new possibilities for relativistic quantum systems theory.