Phase difference and the squeezing property of the superpositions of the q-deformed generalized coherent states

It is shown that the possible higher squeezing order of the superposition state |β> + e iφ |βeiδ > of the generalized coherent states of the q-deformed non-harmonic oscillator can be expressed as k ≠ 2πn/δ, with n an integer and δ the phase difference between the two generalized coherent states. When δ = π, the order of squeezing can only be odd, which is just the result of the generalized even and odd coherent states of the q-deformed non-harmonic oscillator; when δ takes other values, the squeezing order can be even. These results show that the parameter phase difference δ plays the key role in determining the possible squeezing order