Superposition of coherent states prepared in one mode of a dissipative   bimodal cavity
  We solve the problem of the temporal evolution of one of two-modes embedded in a same dissipative environment and investigate the role of the losses after the preparation of a coherent state in only one of the two modes. Based on current cavity QED technology, we present a calculation of the fidelity of a superposition of coherent states engineered in a bimodal high-Q cavity. Our calculation demonstrates that the engineered superposition retains coherence for large times when the mean photon number of the prepared mode is on the order of unity. 
Iara P. de Queiros, W. B. Cardoso, and N. G. de Almeida