Decoherence in ion trap quantum computers

intrinsic decoherence from vibrational coupling of the ions in the Cirac-Zoller quantum computer [Phys. Rev. Lett. 74, 4091 (1995)] is considered. Starting from a state in which the vibrational modes are at a temperature T, and each ion is in a superposition of an excited and a ground state, an adiabatic approximation is used to find the inclusive probability P(t) for the ions to evolve as they would without the vibrations, and for the vibrational modes to evolve into any final state. An analytic form is found for P(t) at T = 0, and the decoherence time is found for all T. The decoherence is found to be quite small, even for 1000 ions.