Optical Pattern Formation in a Rydberg-Dressed Atomic Gas with Non-Hermitian Potentials

Spontaneous pattern formation from a spatially homogeneous background of nonlinear systems driven out of equilibrium is a widespread phenomenon in nature. However, similar phenomena and their physical realization in nonlinear systems with external potentials of gain and loss remain a challenge. We propose a scheme to realize a new type of spatial pattern formation through the self-organization of laser light in a Rydberg-dressed atomic gas with self-defocusing Kerr nonlinearity as well as non-Hermitian optical potentials. We show that by a suitable design of control and assistant laser fields, non-Hermitian optical potentials with or without parity-time (PT) symmetry for the probe laser field can be created. We find that through the nonlocal Kerr nonlinearity contributed by the long-range atom–atom interaction, a constant-intensity wave (CIW) may undergo modulation instability and induce spontaneous symmetry breaking, resulting in the emergence of various self-organized optical structures, which can be actively manipulated by tuning the nonlocality degree of the Kerr nonlinearity and by designing the non-Hermitian optical potentials. The results reported here open a door for developing non-Hermitian nonlinear optics.