  We investigate the formation and control of stationary optical patterns in a
cold Rydberg atomic gas via double electromagnetically induced transparency. We
show that, through the modulational instability of plane-wave state of a laser
field with two polarization components, the system undergoes a spontaneous
symmetry breaking and hence the emergence of plentiful self-organized spatial
optical structures, which can be manipulated by the ratio between the cross-
and self-Kerr nonlinearities, the nonlocality degree of the Kerr
nonlinearities, and the populations initially prepared in the two atomic ground
states. Interestingly, a crossover from mixture to separation in space (optical
phase separation) of the two polarization components occurs when the ratio
between the cross- and self-Kerr nonlinearities exceeds a critical value. We
also show that the system supports nonlocal two-component spatial optical
solitons and vortices when the parameters of the system are selected suitably.
The rich diversity and active controllability of the self-organized optical
structures reported here provide a way for realizing novel optical patterns and
solitons and their structural phase transitions based on Rydberg atomic gases.
