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Spontaneous symmetry breaking and formation of self-organized structures innonlinear systems are intriguing and important phenomena in nature. Advancingsuch research to new nonlinear optical regimes is of much interest for bothfundamental physics and practical applications. Here we propose a scheme torealize optical pattern formation in a cold Rydberg atomic gas viaelectromagnetically induced transparency. We show that, by coupling two Rydbergstates with a microwave field (microwave dressing), the nonlocal Kerrnonlinearity of the Rydberg gas can be enhanced significantly and may be tunedactively. Based on such nonlocal Kerr nonlinearity, we demonstrate that aplane-wave state of probe laser field can undergo a modulation instability (MI)and hence spontaneous symmetry breaking, which may result in the emergence ofvarious self-organized optical patterns. Especially, we find that a hexagonallattice pattern (which is the only optical pattern when the microwave dressingis absent) may develop into several types of square lattice ones when themicrowave dressing is applied; moreover, as a outcome of the MI the formationof nonlocal optical solitons is also possible in the system. Different fromearlier studies, the optical patterns and nonlocal optical solitons found herecan be flexibly manipulated by adjusting the effective probe-field intensity,nonlocality degree of the Kerr nonlinearity, and the strength of the microwavefield. Our work opens a route for versatile controls of self-organizations andstructural phase transitions of laser light, which may have potentialapplications in optical information processing and transmission.

Structural Phase Transitions of Optical Patterns in Atomic Gases with Microwave Controlled Rydberg Interactions