  Magnetic-free optical isolators are critical components for the realization
of integrated optical systems. The underlying physics of passive nonlinear
optical isolators is not solely about breaking the Lorentz reciprocity without
requiring any external bias. Indeed, one major obstacle to the operation of
Kerr-type nonlinear optical isolators was found to be the so-called dynamic
reciprocity, of which the serious outcome is that a backward signal cannot be
isolated in the presence of a forward strong signal. In this work, we advocate
the novel concept of velocity-selective nonlinearity to bypass such dynamic
reciprocity. Using a proof-of-principle platform with warm rubidium atoms in an
asymmetric cavity, we experimentally achieve the isolation of a backward signal
in the presence of a strong forward signal, with experimental observations in
agreement with our theoretical simulations. This work has thus made one
essential step towards functioning Kerr-type passive optical isolators.
