Nth-powered amplitude squeezing in fan-states

Squeezing properties of the Hillery-type N-powered amplitude are investigated in the fan-state vertical bar xi; 2k, f> sub F which is linearly superposed by 2k 2k-quantum nonlinear coherent states in the phase-locked manner. The general expression of squeezing is derived analytically for arbitrary xi, k, N and f showing a multi-directional character of squeezing. For a given k, squeezing may appear to the even power N=2k if f ident to 1 and N>=2k if f not =1 and the number of directions along with the Nth-powered amplitude is squeezed is exactly equal to N, for both f ident to 1 (the light field) and f not =1 (the vibrational motion of the trapped ion). Discussions are also given elucidating the qualitative difference between the cases of f ident to 1 and f not =1.