  Spontaneous symmetry breaking and formation of self-organized structures in
nonlinear systems are intriguing and important phenomena in nature. Advancing
such research to new nonlinear optical regimes is of much interest for both
fundamental physics and practical applications. Here we propose a scheme to
realize optical pattern formation in a cold Rydberg atomic gas via
electromagnetically induced transparency. We show that, by coupling two Rydberg
states with a microwave field (microwave dressing), the nonlocal Kerr
nonlinearity of the Rydberg gas can be enhanced significantly and may be tuned
actively. Based on such nonlocal Kerr nonlinearity, we demonstrate that a
plane-wave state of probe laser field can undergo a modulation instability (MI)
and hence spontaneous symmetry breaking, which may result in the emergence of
various self-organized optical patterns. Especially, we find that a hexagonal
lattice pattern (which is the only optical pattern when the microwave dressing
is absent) may develop into several types of square lattice ones when the
microwave dressing is applied; moreover, as a outcome of the MI the formation
of nonlocal optical solitons is also possible in the system. Different from
earlier studies, the optical patterns and nonlocal optical solitons found here
can be flexibly manipulated by adjusting the effective probe-field intensity,
nonlocality degree of the Kerr nonlinearity, and the strength of the microwave
field. Our work opens a route for versatile controls of self-organizations and
structural phase transitions of laser light, which may have potential
applications in optical information processing and transmission.
