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In this article, we consider a quantum model constructed using N two-level atoms within a photonic band-gap material, and interacting with a single photon mode under suitable nonequilibrium boundary conditions. We solved the eigenvalue problem of the Hamiltonian by using a projection approach, and found that the behavior of the total system is like that of a two-level system with the eigenvectors existing in a dual pair of spaces. Furthermore, we constructed the operators for a quantum logic gate using the entangled states, the eigenvectors of the system. Therefore the interaction between the atoms and the single photon mode cannot introduce any decoherence over the constructed quantum logic gates. Since this approach necessitates solving the eigenvalue problem of the Hamiltonian from first principles, it represents a general formulation for obtaining the spectral decomposition of the Hamiltonian as well as the evolution of the density operator for N two-level atoms interacting with multimode photonic fields; this will be the case independent of whether the system is under equilibrium or not. © 1999 American Institute of Physics.
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