The properties of both generalized nonlinear equal-order N-th power Y-squeezing and generalized nonlinear equal-order N-th power H-squeezing in a new type of multimode imaginary-even coherent state light field

In this paper, the properties of both generalized nonlinear equal-order N-th power Y-squeezing and generalized nonlinear equal-order N-th power H-squeezing in a new type of multimode imaginary-even coherent state light field mathematical equation presented are studied in detail, by utilizing the theory of multimode squeezed state constructed by Yang Zhiyong and Hon Xun and published in Acta Photonica Sinica recently. It is found that 1). if the squeezed order number N is an odd number, the state mathematical equation presented mentioned above can always present any order generalized nonlinear equal-order N-th power Y-squeezing which changes periodically under some certain conditions; and if q • N, the products of the cavity-mode number q and the squeezed order number N, is an odd number, the state mathematical equation presented mentioned can also display any order generalized nonlinear equal-order N-th power H-squeezing which changes periodically too. 2) the squeezed degree and the squeezed depth of both the generalized nonlinear equal-order N-th power Y-squeezing and the generalized nonlinear equal-order N-th power H-squeezing of the state mathematical equation presented are all related intensively and nonlinearly to the probability amplitude r_(e)^q, to the squeezing parameter R_j, to the initial phase mathematical equation presented each mode for equal-order N-th power Y-squeezing, to 1 the sum mathematical equation presented of the initial phase of all the modes for equal-order N-th power H-squeezing, to the squeezed order number N, and to the cavity-mode number q, and so on. The related nonlinear degree of equal-order N-th power H-squeezing is more intensive than that of equal-order N-th power Y-squeezing. and 3), the squeezing conditions and the squeezing features of both equal-order N-th power Y-squeezing and equal-order N-th power H-squeezing of the multimode imaginary-even coherent state mathematical equation presented are just contrary to that of the multimode even coherent state mathematical equation presented and the multimode complex-conjugation even coherent state mathematical equation presented this phenomenon is so-called contrary squeezing.