In this paper, the squeezing properties of orthonormal eigenstates of high order power of photon annihilation operator αk (k≥3) are studied. It is shown that the amplitude Nth-power squeezing (k=2N) can exist in the eigenstates when k is even.
The characteristics of the k th-power squeezing of a class of superposition states which involving two orthonormalized eigenstates of photon annihilation operator aN are studied.The result show that the characteristics of the k th-power squeezing of a class of superposition states which involving two orthonormalized eigenstates of photon annihilation operator aN are different from the characteristics of the k th-power squeezing of the orthonormalized eigenstates of photon annihilation operator aN clearly.No matter what N is an odd number or even number,the superposition states own 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 that,when phase difference δ=2mπ/t(m is integer),the superposition states don′t own amplitude k th-power squeezing;when δ=π,only N and t are odd number simultaneously,the superposition states may own amplitude k th-power squeezing;when δ=π/2,t≠4m,the superposition states own amplitude k th-power squeezing;thus the phase difference of parameter has key effect on amplitude k th-power squeezing.
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.
We have studied the orthonormalized eigenstates of the higher powers ak (k\ensuremath{\ge}3) of the annihilation operator a and their properties. Our conclusions are as follows: (1) The orthonormalized eigenstates of ak construct a complete representation with respect to \ensuremath{\alpha}. (2) None of the orthonormalized eigenstates of ak shows the squeezing effect in the usual sense. (3) All of the eigenstates of ak show the antibunching effect.