  Dispersive shock waves (DSWs) are fascinating wave phenomena occurring in
media when nonlinearity overwhelms dispersion (or diffraction). Creating DSWs
with low generation power and realizing their active controls is desirable but
remains a longstanding challenge. Here, we propose a scheme to generate
weak-light DSWs and realize their manipulations in an atomic gas involving
strongly interacting Rydberg states under the condition of electromagnetically
induced transparency (EIT). We show that for a two-dimensional (2D) Rydberg gas
a weak nonlocality of optical Kerr nonlinearity can significantly change the
edge speed of DSWs and induces a singular behavior of the edge speed and hence
an instability of the DSWs. However, by increasing the degree of the Kerr
nonlocality, the singular behavior of the edge speed and the instability of the
DSWs can be suppressed. We also show that in a 3D Rydberg gas, DSWs can be
created and propagate stably when the system works in the intermediate
nonlocality regime. Due to the EIT effect and the giant nonlocal Kerr
nonlinearity contributed by the Rydberg-Rydberg interaction, DSWs found here
have extremely low generation power. In addition, an active control of DSWs can
be realized; in particular, they can be stored and retrieved with high
efficiency and fidelity through switching off and on a control laser field. The
results reported here are useful not only for unveiling intriguing physics of
DSWs but also for finding promising applications of nonlinear and nonlocal
Rydberg media.
