Quantum leakage of collective excitations of atomic ensemble induced by spatial motion

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We generalize the conception of quantum leakage for the atomic collective excitation states. By making use of the atomic coherence state approach, we study the influence of the atomic spatial motion on the symmetric collective states of 2-level atomic ensemble due to inhomogeneous coupling. In the macroscopic limit, we analyze the quantum decoherence of the collective atomic state by calculating the quantum leakage for a very large ensemble at a finite temperature. Our investigations show that the fidelity of the atomic system will not be good in the case of atom number N →∞. Therefore, quantum leakage is an inevitable problem in using the atomic ensemble as a quantum information memory. The detailed calculations shed theoretical light on quantum processing using atomic ensemble collective qubit.