Spontaneous crystallization of light and ultracold atoms

Coherent scattering of light from ultracold atoms involves an exchange of energy and momentum introducing a wealth of non-linear dynamical phenomena. As a prominent example particles can spontaneously form stationary periodic configurations which simultaneously maximize the light scattering and minimize the atomic potential energy in the emerging optical lattice. Such self-ordering effects resulting in periodic lattices via bimodal symmetry breaking have been experimentally observed with cold gases and Bose-Einstein condensates (BECs) inside an optical resonator. Here we study a new regime of periodic pattern formation for an atomic BEC in free space, driven by far off-resonant counterpropagating and non-interfering lasers of orthogonal polarization. In contrast to previous works, no spatial light modes are preselected by any boundary conditions and the transition from homogeneous to periodic order amounts to a crystallization of both light and ultracold atoms breaking a continuous translational symmetry. In the crystallized state the BEC acquires a phase similar to a supersolid with an emergent intrinsic length scale whereas the light-field forms an optical lattice allowing phononic excitations via collective back scattering, which are gapped due to the infinte-range interactions. The studied system constitutes a novel configuration allowing the simulation of synthetic solid state systems with ultracold atoms including long-range phonon dynamics.