Properties of nonlinear higher-order squeezing effects in a new type of multi-mode light field state of superposition state with distinguishable two quantum states in the kind (I)

In this paper, a series of new definitions, such as N - Y minimum uncertainty state, N - H minimun uncertainty state, N - Y squeezed minimum uncertainty state and N - H squeezed minimum uncertainty state of multi - mode radiative light field is further suggested by Hou Xun and Yang Zhiyong firstly, that is based upon the definition of both N th power Y - squeezing and N th power H - squeezing proposed in reference 2 0. According to the linear superposition principle in quantum mechanics, it is constructed the multi-mode light field state of superposition state with distinguishable two quantum states in the kind ( I ) | φ⁽²⁾ >_q, which is made of linear superposition of multi - mode coherent state. | {Z_j,} >_q, and its contrary state | {- Z_j}>_q.,So the two kinds of nonlinear higher-order squeezing effects, both Nthe power Y-squeezing and Nth power H-squeezing, of the state | ψ₁ ⁽²⁾>_q,therefore studied in detail by using the definition of nonlinear higher - order squeezing of multi - mode radiative light field which is proposed recently in reference 20. The result shows that l), when iV. the number of squeezing order, is even mumber, the state |ψ₁⁽²⁾>_q is alway in NrY minimum uncertainty state? when N is odd number, the state ψ₁ ⁽²⁾>_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 |ψ₁⁽²⁾>_q is always in,N - H minimum uncertainty statejwhen q · N is odd number,under some other conditions the state |ψ₁⁽²⁾>_q can also present any order N-th power H-squeezing that changes periodically ; and 3) the depth and degree of both Nth power Y-squeezing and Nth power H-squeezing are related nonlinearly to the cavity modes number q, to the squeezed parameter R_j, and to the squeezing order number N ; the later is more intensive than the former.