参数化玻色湮灭算符高次幂的本征态及其量子起伏规律

The Eigenstates of High Power of Parametrization Boson Annihilation Operator and Their Quantum Fluctuation Law

以参数化方式［ｙ］＝（ｑｙ－１）／（ｑ－１）定义ｑ玻色湮灭算符ａｑ，生成相应的ｑ相干态，找出能产生并保持这类ｑ相干态的体系的哈密顿量。研究ａｑｋ（ｋ≥１）的正交归一本征态的数学结构和量子起伏性质，发现这些本征态中只有偶ｑ相干态存在通常的压缩效应，并且当ｑ＜１时，场的两个正交分量在各态中的量子起伏可以同时有小于相干态的最小不确定度（１／４），有ｑ压缩效应。

By using a new parametrization way, =(q y-1)/(q-1), the q Boson annihilation operator was defined, and a new q coherent state was constructed. The system Hamiltonian that can produce and maintain the q coherent state was found. We studied the mathematical construction and the quantum fluctuation characteristic of the orthonormalization eigenstates of a q k (k≥1). It is found that the only even q coherent states have usual squeezing effect, and when the parameter q<1, the quantum fluctuation of both quadrature components of the field for each state may be simultaneouly smaller than the minimum uncertainly value (1/4) of the coherent state. These eigenstates have q squeezing.