Two kinds of different generalized nonlinear equal-order minimum uncertainty states in a new type of multimode imaginary-odd coherent state light field

In this paper, the properties of two kinds of different generalized nonlinear equal-order minimum uncertainty states, or both equal-order N-Y minimum uncertainty state, and equal-order N - H minimum uncertainty state, in a new type of multimode imaginary-odd coherent state light field lΨ⁽²⁾_i.0>)_q, are studied in detail, by utilizing the theory of multimode squeezed state constructed by Yang Zhiyong and Hou Xun and published in Acta Photonica Sinica recently, It is found that:1)if N, the number of squeezed-order, is an even number, the state |ψ_i.0⁽²⁾ >_q, is always staid in equal - order N-Y minimum uncertainty state ; if N is an odd number, the state |ψ_i.0⁽²⁾ >_q, is neither staid in equal-order N-Y minimum uncertainty state nor stayed in equal-order N-th. power Y-squeezing state; 2) if q middot; N, the products of cavity-modes mumber and squeezed-order number, is an even number, the state I ψ_i.0 ⁽²⁾ >_q, is always staid in equal-order N-H minimum uncertainty state;if q · N is an odd number, the state |ψ_i.0⁽²⁾ >_q, is neither staid in equal-order N.-H minimum uncertainty state nor staid in equal-order N-th power H-squeezing state too;3)There exist the strict and important differences between equal-order N-Y minimum uncertainty state and equal-order N-H minimum uncertainty state of multimode imaginary-odd coherent state | ψ_i.0⁽²⁾ >_q, under the same condition of their occuring;and 4)just as the multimode odd-coherent state |ψ_i.0⁽²⁾ >_q, and the multimode complex conjugation odd-coherent state |ψ_i.0⁽²⁾ >_q, reported in References 13 - 14, the multimode imaginary-odd coherent state |ψ_i.0⁽²⁾ >_q, considered in this paper can never display any generalized nonlinear equal-order N-th power Y-squeezing and generalized nonlinear equal-order N-th power Pi- squeezing, but they can always display the generalized nonlinear equal-order N-Y minimum uncertainty state and the generalized nonlinear equal-order N-H minimum uncertainty state under the same condition of their occuring.