Decoherence in a system of many two--level atoms

I show that the decoherence in a system of $N$ degenerate two--level atoms interacting with a bosonic heat bath is for any number of atoms $N$ governed by a generalized Hamming distance (called ``decoherence metric'') between the superposed quantum states, with a time--dependent metric tensor that is specific for the heat bath.The decoherence metric allows for the complete characterization of the decoherence of all possible superpositions of many-particle states, and can be applied to minimize the over-all decoherence in a quantum memory. For qubits which are far apart, the decoherence is given by a function describing single-qubit decoherence times the standard Hamming distance. I apply the theory to cold atoms in an optical lattice interacting with black body radiation.