  It is shown that the Fizeau drag can be used to cause nonreciprocity. We
propose the use of a nanostructured toroid cavity made of $\chi^{(2)}$
nonlinear materials to achieve nonreciprocal photon blockade (PB) through the
Fizeau drag. Under the weak driving condition, we discuss the origins of the PB
based on the doubly resonant modes with good spatial overlap at the fundamental
and second-harmonic frequencies. We also find that for the fundamental mode,
the PB happens when we drive the system from one side but the photon-induced
tunneling happens when we drive the system from the other side. However, there
is no such phenomenon in the second-harmonic mode. Remarkably, the PB
phenomenon occurs with a reasonably small optical nonlinearity thus bringing
the system parameters closer to the reasonably achievable realm by the current
technology.
