  The optical nondestructive method for in situ detection of the bound states
of ultracold polar molecules is developed. It promises a minimally destructive
measurement scheme up to a physically exciting quantum non-demolition (QND)
level. The detection of molecular complexes beyond simple pairs of quantum
particles (dimers, known, e.g., from the BEC-BCS theory) is suggested,
including three-body (trimers) and four-body (tertramers) complexes trapped by
one-dimensional tubes. The intensity of scattered light is sensitive to the
molecule number fluctuations beyond the mean-density approximation. Such
fluctuations are very different for various complexes, which leads to radically
different light scattering. This type of research extends "quantum optics of
quantum gases" to the field of ultracold molecules. Merging the quantum optical
and ultracold gas problems will advance the experimental efforts towards the
study of the light-matter interaction at its ultimate quantum level, where the
quantizations of both light and matter are equally important.
