  Quantum optics with quantum gases represents a new field, where the quantum
nature of both light and ultracold matter plays equally important role. Only
very recently this ultimate quantum limit of light-matter interaction became
feasible experimentally. In traditional quantum optics, the cold atoms are
considered classically, whereas, in quantum atom optics, the light is used as
an essentially classical axillary tool. On the one hand, the quantization of
optical trapping potentials can significantly modify many-body dynamics of
atoms, which is well-known only for classical potentials. On the other hand,
atomic fluctuations can modify the properties of the scattered light.
