The amplitude-kth power characters of the superposition state |ψ=a|β+be~(iφ)|mβe~(iδ) of the generalized coherent states are studied, the results show that the possible kth-power squeezing can be expressed as k≠2nπ/δ when m=i, with n an integer and δthe phase difference between the two generalized coherent states; When m≠1, the kth-power can be even and odd; when δ=π the power of the squeezing can only be odd; when δ=π/2, the power of squeezing can be even and odd. These results show that the parameter phase difference δ plays the key role in determining the possible power of squeezing.
We have defined a new nonclassical effect: amplitude kth-power squeezing. We have analyzed the squeezing properties of the k-photon coherent states as defined by D'Ariano, Rasetti, and Vadacchio [Phys. Rev. D 32, 1034 (1985)]; Katriel et al. [Phys. Rev. D 34, 332 (1986)]; and D'Ariano and Sterpi [Phys. Rev. A 39, 1810 (1989)]. It has been shown that, due to the interaction with the nonlinear nonabsorbing medium modeled as an anharmonic oscillator, these states become amplitude kth power squeezed.