Abstract: It is constructed that the two kinds of three state superposition multimode superposition state light field |(3)>q and |(3)>2q which are composed of the linear superposition ofmacroscopically distinguish three quantum states named multimode complex conjugation imaginary coherent state, the contrary state of multimode complex conjugation imaginary coherent state and multimode complex conjugation coherent state based upon linear superposition principle of states in quantum mechanics. By utilizing the multimode squeezed states theory established recently by Yang Zhiyong and Hou Xun and published in Acta Photonica Sinica, the properties of generalized nonlinear equal-power N-th power Y-squeezing and N-th power H-squeezing of the state ,the properties of generalizednonlinear equal-power N-th power X-squeezing of the state |Ψ(3)>2q ,the properties of generalized nonlinear unequal-power Nj -th power Y-squeezing and Nj -th power H-squeezing of the state ,and the properties of generalized nonlinear unequal-power Nj -th power X-squeezing of the state are studied firstly and systematically in detail.The major research contents of this thesis are drawn as follows:1.It is constructed that the first new kind of three state superposition multimodesuperposition state light field which is made of the linear superposition ofmacroscopically distinguish three quantum states that are called multimode (q-modes) complex conjugation imaginary coherent state |{iZ*j}>q , the contrary state of multimode (q-modes)complex conjugation imaginary coherent state |{- iZ*j }>q and multimode (q-modes) complex conjugation coherent state |{iZ*j}>q . It is also constructed that the second new kind of threestate superposition multimode superposition state light field |Ψ(3)>2q which consists of thelinear superposition of macroscopically distinguish three quantum states that is so-called multimode(2q-modes) complex conjugation imaginary coherent state|{iZ*j}>q , the contrarystate of multimode(2q-modes) complex conjugation imaginary coherent state {- iZ*j }) andmultimode(2q-modes) complex conjugation coherent state [Z'j }) .2.The properties of generalized nonlinear equal-power N-th power Y-squeezing, equal-power N-th power H-squeezing of the state |Ψ(3)>q, and the properties of generalizednonlinear equal-power N-th power X-squeezing of the state|Ψ(3)>2q are studied. It is found thatfor any squeezing-power-number, if some fixed conditions are satisfied respectively by the initial phase of each mode in the state |Ψ(3)>q, by the initial phase difference between any twocomponents in the state |Ψ(3)>q ,and by the sum of mean photon-numbers of all the singlemode coherent states light field, the state |Ψ(3)>q can always display the effects ofgeneralized nonlinear equal-power N-th power Y-squeezing ,equal-power N-th power H-squeezing that changes periodically and alternatively; also for any squeezing-power-number, if another fixed conditions are satisfied respectively by the initial phase of each mode in thestate|Ψ(3)>2q , by the initial phase difference between any two components in the stateby the sum of mean photon-numbers of all the single mode coherent states light field, and bythe probability amplitudes of the three components in the state |Ψ(3)>2q , the state |Ψ(3)>q canrespectively display the effects of generalized nonlinear equal-power N-th power X-squeezing, "half squeezing state-half coherent state" and "completely equal-power N-th power X-squeezing state" that also changes periodically and alternatively.3. The properties of generalized nonlinear unequal-power Nj -th power Y-squeezing,unequal-power Nj -th power H-squeezing of the state |Ψ(3)>q , and the properties ofgeneralized nonlinear unequal-power Ni -th power X-squeezing of the state |Ψ(3)>q arefurther studied. The major results and conclusions are shown as follows:(l)For any squeezing-power-number, if some certain conditions are satisfied respectively by the initial phase of eac…

Key words: Three state superpositions; Multimode superposition state light field; Equal-power N-th power Y-squeezing; equal-power N-th power H-squeezing; equal-power N-th power X-squeezing; unequal-power N_j -th power Y-squeezing; unequal-power N_j -th power H-squeezing; unequal-power N_j -th power X-squeezing

# Study on the Properties of Generalized Nonlinear Equal-Power and Unequal-Power Higher-Power Squeezing in a New Kind of Multimode Superposition State Light Field with Macroscopically Distinct Three Quantum States

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