Decoherence is considered a main ingredient in the transition from quantum to classical mechanics. While decoherence is well understood for systems with few degrees of freedom, the long term goal of constructing a large scale quantum computer has lead to the necessity to understand decoherence of true many particle states in a quantitative manner. Indeed, the construction of quantum processors with even a few ten qubits shall allow to test quantum mechanics in a direction in which it has never been tested before experimentally.

I discuss in this talk the decoherence of N two-level atoms interacting with a bosonic heat bath. I show that the initial decoherence of a superposition of two arbitrary quantum code words is governed by a decoherence metric specific to the heat bath, which introduces a natural distance between quantum code words, generalizing the well-known Hamming distance. The metric tensor is calculated explicitly for neutral atoms in optical lattices and atomic gases interacting with thermal black body radiation, and allows a detailed understanding of the time dependent decoherences for all possible superpositions.

Laboratoire de Physique Théorique IRSAMC Université Paul Sabatier, Toulouse