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We investigate the Nth order amplitude squeezing in the fan-state |\xi;2k,f>_F which is a linear superposition of the 2k-quantum nonlinear coherentstates. Unlike in usual states where an ellipse is the symbol of squeezing, a4k-winged flower results in the fan state. We first derive the analyticalexpression of squeezing for arbitrary k, N, f and then study in detail the caseof a laser-driven trapped ion characterized by a specific form of the nonlinearfunction f. We show that the lowest order in which squeezing may appear and thenumber of directions along which the amplitude may be squeezed depend only on kwhereas the precise directions of squeezing are determined also by the otherphysical parameters involved. Finally, we present a scheme to produce suchfan-states.

FLOWER-LIKE SQUEEZING IN THE MOTION OF A LASER-DRIVEN TRAPPED ION