Stationary photon-atom entanglement and flow equation

A novel strategy for quantum-state engineering is presented by employing the method of flow equation. This strategy offers an optimal procedure for generating stationary entangled states of coupled systems of photons and atoms. To illustrate it, the Jaynes-Cummings model as a simple prototype example is analyzed to exhibit how stationary photon-atom entanglement is established. A nonlocal continuous unitary transformation is explicitly constructed and the associated positive operator-valued measures for the photons and atom are obtained. Then, flow of the entanglement entropy is analyzed. A comment is also made on implementing the unitary operation in the method.