Self-ordering dynamics of ultracold atoms in multicolored cavity fields

We study light-induced spatial crystallization of ultracold quantum particles confined along the axis of a high-Q linear cavity via a transverse multicolor pump using numerical simulations. Whenever a pump frequency is tuned close to resonance with a longitudinal cavity mode, the dynamics favors bistable spatial particle ordering into a Bragg grating at a wavelength distance. Simultaneous pumping at several resonant frequencies fosters competition between the different spatial lattice orders, exhibiting complex nonlinear field dynamics involving several metastable atom-field states. For few particles, even superpositions of different spatial orders entangled with different light-mode amplitudes appear. By a proper choice of trap geometry and pump frequencies, a broad variety of many-particle Hamiltonians with a nontrivial long-range coupling can be emulated in such a setup. When applying quantum Monte Carlo wave-function simulations to study time evolution, we find simultaneous superradiant scattering into several light modes and the buildup of strong nonclassical atom-field correlations.