Hillery-type amplitude squeezing in linear and nonlinear fan-states

Squeezing properties of the Hillery-type N-powered amplitude are investigated in the linear and nonlinear fan-state. For a given k, squeezing may appear to the even power N = 2k and the number of directions along which the Nth-powered amplitude is squeezed is exactly equal to N, in both linear (the light field) and nonlinear (the vibrational motion of the trapped ion) fan-states.