Phase and number fluctuation of the orthonormalization eigenstates of α~k

• 出 处: Chinese Journal of Lasers
• 发表日期: 1992年05期
• 关键词: fluctuation coherent operators uncertainty cosine uncertain attractive deviation

In this paper,the phase fluctuations of the orthonormalization eigenstates ofa~k(k>3)were calculated in coherent state representation.The results show that the fluctuat-ing properties of cosine and sine operators are the same,the phase fluctuations of│ψ_j〉_k(j ≠0)are always equal to 1/2,and the phase fluctuations of │ψ_0〉_k are the increasing function of│a│~2.When │a│~2→0 and │a│~2→∞,the limit values of phase fluctuations are 1/4 and 1/2respectively.The uncertainty relation between the particle number and the phase was dis-cussed.

In this paper, the phase fluctuations of the orthonormalization eigenstates ofa ~ k (k> 3) were calculated in coherent state representation. The results show that the fluctuating-ing properties of cosine and sine operators are the same, the phase fluctuations of ψψj > _k (j ≠ 0) are always equal to 1/2, and the phase fluctuations of │ψ_0> _k are the increasing function of│a│ ~ 2.When │a│ ~ 2 → 0 and │a│ ~ 2 → ∞, the limit values ​​of phase fluctuations are 1/4 and 1/2 respectively. The relationship between the particle number and the phase was dis-cussed.