In this chapter we discuss the effects of losses on quantum optical systems. We discuss quantum jumps and master equations. We introduce the notion of using fictitious beam splitters to model losses. We introduce the decoherence of pure quantum mechanical states into a statistical mixture.

Appendix G: interaction between a monochromatic field and two-level atom. The problem is treated first in the case of a classical field and a quantum two-level system (semiclassical approach): It is characterised by a rotation of the Bloch vector (Rabi ocillation) and allows us to generate any qubit state by applying a field of well-controlled duration and amplitude. One then includes spontaneous emission to the model, and finally obtains the set of Bloch equations that are used in many different problems of light–matter interaction. One then considers the full quantum case of cavity quantum electrodynamics (CQED), where the field is single mode and fully quantum: this is the Jaynes–Cummings Hamiltonian approach, which is fully solvable when one negelcts spontaneous emission: quantum oscillations and revivals are predicted. Damping is then introduced in the model, and two regimes of strong and weak couplings are predicted in this case.