Self-induced modulation and compression of an ultracold atomic cloud in a nonlinear atomic cavity

We consider a sample of ultracold atoms inside an atomic cavity and driven by a laser field. We show that this field acts effectively as a nonlinear ''light crystal'' for the intracavity atomic wave, which in turn can cause self-modulation and compression of ultracold atomic wave packets. The analogy to the conventional compression technique of optical pulses in a nonlinear optical cavity is discussed.