Eigenstates of squeeze operators do not exist

Xin Ma, William Rhodes

Zhou-Fei Wang

The characteristics of the kth-power squeezing of a class of superposition states which involing two orthonormalized eigenstates of photo annihilation operator aN are studied,the result show that the characteristics of the kth-power squeezing of a class of superposition states which involving two orthonormalized of photon annihilation operator aN are different from the characteristics of the kth-power squeezing of the orthonormalized eigenstates of photo annihilation operator aN clearly.No matter what N is odd number or even number,the superposition states exist amplitude k(k=Nt or Nt/2)th-power squeezing,but for the orthonormalized eigenstates of aN,only when N is even number there exist amplitude k(k=(2p+1)N/2)th-power squeezing.Owing to,when phase difference δ=2mπ/t(m is integer),the superposition states don't exist amplitude k th-power squeezing,when δ=π,only N and t are odd number together,the superposition states may exist amplitude kth-power squeezing,…,thus the phase difference of paramter takes key effect for amplitude kth-power squeezing.The research result also show that j,N,δ, and α play a not be ignored part in squeezing and squeezing region.

Anthony F. J. Levi

Ji‐Suo Wang

The squeezing and higherorder squeezing properties of k orthonormalized eigenstates of the higher powers akqs(k≥3) of the annihilation operator of twoparameter deformed harmonic oscillator are investigated. It is found that the Nthpower squeezing [N=(m+1/2)k, m=0,1,2,…] can exist in the all of them when k is even.

Marian J. R. Gilton

Jian‐Sheng Wang, TK Liu, Zhan Zhan

The eigenstates of the Kth powers (K greater than or equal to3) of the annihilation operator of the Q-deformed non-harmonic oscillator are constructed, and their completeness and higher-order squeezing properties are investigated. The results show that they form a complete Hilbert space, and the Mth order [M = (n + 1/2) K; n = 0,1,2,...] squeezing effects exist in all of the eigenstates when K is even.