Quantum statistical properties of orthonormalized eigenstates of the operator (â f ($\hat n$))k
Ji‐Suo Wang, Jian Feng, Tang-Kun Liu, Mingsheng Zhan · Journal of Physics B Atomic Molecular and Optical Physics · 2002
The completeness of the k orthonormalized eigenstates of the operator (â f ( )) k ( k ⩾3) is investigated. We introduce a new kind of higher-order squeezing and an antibunching. The properties of the M th-order squeezing and the antibunching effect of the k states are studied. The result shows that these states may form a complete Hilbert space, and the M th-order ( M = ( n + 1/2) k ; n = 0,1,...) squeezing effects exist in all of the k states when k is even. There is an antibunching effect in all of the states. An alternative method for constructing the k states is proposed, and the result shows that all of them can be generated by linear superposition of the time-dependent nonlinear coherent states at different instants.