Optomechanical self-structuring in a cold atomic gas

The rapidly developing field of optomechanics aims at the com- bined control of optical and mechanical modes1–3. In cold atoms, the spontaneous emergence of spatial structures due to opto- mechanical back-action has been observed in one dimension in optical cavities3–8 or highly anisotropic samples9. Extensions to higher dimensions that aim to exploit multimode configurations have been suggested theoretically10–16. Here, we describe a simple experiment with many spatial degrees of freedom, in which two continuous symmetries—rotation and translation in the plane orthogonal to a pump beam axis—are spontaneously broken. We observe the simultaneous long- range spatial structuring (with hexagonal symmetry) of the density of a cold atomic cloud and of the pump optical field, with adjustable length scale. Being based on coherent phenom- ena (diffraction and the dipole force), this scheme can poten- tially be extended to quantum degenerate gases.