Transverse pattern formation in an optical cavity containing a cloud of cold
two-level atoms is discussed. We show that density modulation becomes the
dominant mechanism as the atomic temperature is reduced. Indeed, for low but
achievable temperatures the internal degrees of freedom of the atoms can be
neglected, and the system is well described by treating them as mobile
dielectric particles. A linear stability analysis predicts the instability
threshold and the spatial scale of the emergent pattern. Numerical simulations
in one and two transverse dimensions confirm the instability and predict
honeycomb and hexagonal density structures, respectively, for the blue and red
detuned cases.Comment: submitted to Physical Review Letter
