The properties of both N-TH power Y-squeezing and N-TH power H-squeezing in the multi-mode even-coherent state light field

In this paper, the properties of N-th power Y-squeezing, N-th power H-squeezing, N-Y minimum uncertainty state and N-H minimum uncertainty state in the multi-mode even-coherent state light field |Ψ, e>_q is studied in detail, that is based upon utilizing the theory of generalized nonlinear equal-order higher-order squeezing of multi-mode radiative light field, which is proposed by Yang Zhiyong and Hou Xun recently, It is found that, 1), When N, the number of squeezing-order, is even number, the state |Ψ, e >_q is always stayed in N-Y minimum uncertainty state; and when N is odd number, the state |Ψ, e>_q, under some certain conditions, can present any order N-th power Y-squeezing which changes periodically; 2) When q • N, the products of cavity modes number and squeezing-order number, is even number, the state |Ψ, e >_q is also always stayed in N-H minimum uncertainty state, and when q • N is odd number under some other conditions the state |Ψ, e >_q, can also present any order N-th power H-squeezing that changes periodically too; and 3) the squeezing depth and degree of both N-th power Y-squeezing and N-th power H-squeezing are related nonlinearly to the probability amplitude mathamatical equation presented, to the squeezing parameter R_j;, to the initial phase of each mode mathamatical equation presented(or to the sum of the initial phase of each mode mathamatical equation presented), to the squeezing order number N and to the cavity-mode number q, the later is more intensive than the former.