We consider a moving ultra-dispersive medium and demonstrate the enhanced Fizeau effect due to dragging the light. We have shown that the enhanced Fizeau effect on a single atom in a cavity can be observed. It has been shown that the change of phase is sensitive to the motion the speed of the order of 10−15 cm/Hz1/2 and for possible displacements as small as 10−17 cm/Hz1/2. One of application can be the detection of weak forces exerted on a single atom. In particular, the Coriolis force as small as 10−42 N/Hz1/2 can be detected that would provide opportunity to detect rotation with sensitivity 10−17 s−1Hz−1/2.