Hillery-type Amplitude Squeezing in Linear and Nonlinear Fan-states

Abstract

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.