Spin self-organization in an optical cavity facilitated by inhomogeneous broadening

We study the onset of collective spin self-organization in a thermal ensemble of driven two-level atoms confined in an optical cavity. The atoms spontaneously form a spin pattern above a critical driving strength that sets a threshold and is determined by the cavity parameters, the initial temperature, and the transition frequency of the atomic spin. Remarkably, we find that inhomogeneous Doppler broadening facilitates the onset of spin self-organization. In particular, the threshold is nonmonotonic when increasing the spin transition frequency and reaches a minimum when the Doppler broadening is of similar magnitude. This feature emerges due to Doppler-induced resonances. Above the threshold, we find cooperative dynamics of spin, spatial, and momentum degrees of freedom leading to density modulations, fast reduction of kinetic energy, and the emergence of nonthermal states. More broadly, our work demonstrates how broadening can facilitate strong light-matter interactions in many-body systems.