Rotating and spiralling optomechanical cavity solitons

Optomechanical forces in a cloud of cold atoms under the action of a coherent beam of light lead to self-structuring in single mirror feedback configurations [1] and optical cavities (see left panel in Fig. 1 ) [2] . Orbital angular momentum (OAM) in the input laser beam can induce rotational dynamics and atomic transport in the transverse light-atom structures [3] , [4] . Here we consider an optical cavity containing a thermal cloud of two-level atoms at constant low temperature T where the atomic motion is overdamped by means of optical molasses beams. In this regime, the medium dynamics is described by a Smoluchowski equation describing the dipole force and spatial diffusion for an atomic density distribution n ( r , t ) where t is the time and r is in the plane perpendicular to the direction of propagation. This equation is coupled to that of an electric field ℇ( r , t ) propagating inside a ring cavity under the action of the external pump ℇ 0 ( r ).