Quantum control of atomic systems by homodyne detection and feedback

We investigate the possibilities of preserving and manipulating the coherence of atomic two-level systems by ideal projective homodyne detection and feedback. For this purpose, the photon emission process is described on time scales much shorter than the Lifetime of the excited state using a model based on Wigner-Weisskopf theory. The backaction of this emission process is analytically described as a quantum diffusion of the Bloch vector. It is shown that the evolution of the atomic wave function can be controlled completely using the results of homodyne detection. This allows the stabilization of a known quantum state or the creation of coherent states by a feedback mechanism. However, the feedback mechanism can never compensate the dissipative effects of quantum fluctuations even though the coherent state of the system is known at all times.