Bose-Einstein condensates and precision measurements

How an interacting many-body system tunnels through a potential barrier to open space

The tunneling process in a many-body system is a phenomenon which lies at the very heart of quantum mechanics. It appears in nature in the form of α-decay, fusion and fission in nuclear physics, and photoassociation and photodissociation in biology and chemistry. A detailed theoretical description of the decay process in these systems is a very cumbersome problem, either because of very complicated or even unknown interparticle interactions or due to a large number of constituent particles. In this work, we theoretically study the phenomenon of quantum many-body tunneling in a transparent and controllable physical system, an ultracold atomic gas. We analyze a full, numerically exact many-body solution of the Schrödinger equation of a one-dimensional system with repulsive interactions tunneling to open space. We show how the emitted particles dissociate or fragment from the trapped and coherent source of bosons: The overall many-particle decay process is a quantum interference of single-particle tunneling processes emerging from sources with different particle numbers taking place simultaneously. The close relation to atom lasers and ionization processes allows us to unveil the great relevance of many-body correlations between the emitted and trapped fractions of the wave function in the respective processes.

Quantum number theoretic transforms on multipartite finite systems

A quantum system composed of p-1 subsystems, each of which is described with a p-dimensional Hilbert space (where p is a prime number), is considered. A quantum number theoretic transform on this system, which has properties similar to those of a Fourier transform, is studied. A representation of the Heisenberg-Weyl group in this context is also discussed.

Introduction: the fundamental constants of physics, precision measurements and the base units of the SI

This is a short introductory note to the texts of lectures presented at a Royal Society Discussion meeting held on 14-15 February 2005 and now published in this issue of Philosophical Transactions A. It contains a brief resumé of the papers in the order they were presented at the meeting. This issue contains the texts of all of the presentations except those of Christophe Salomon, on cold atom clocks and tests of fundamental theory, and Francis Everitt, on Gravity Probe B, which were, unfortunately, not available.