第Ⅲ及第Ⅳ类两态叠加多模叠加态光场的等阶N次方Y压缩与等阶N次方H压缩——兼论“相似压缩”与“压缩简并”现象

本文根据量子力学中的线性叠加原理,分别构造了由多模(即q模)相干态|{Z_j}>_q与多模真空态|{0_j}>_q以及由多模相干态的相反态|{-Z_j}>_q与多模真空态|{0_j}>_q等的线性叠加所组成的第及第类两态叠加多模叠加态光场|ψ_+,3⁽²⁾>_q和|ψ_-,4⁽²⁾>_q.利用新近建立的多模压缩态理论,首次对态|ψ_+,3⁽²⁾>_q及态|ψ_-,4⁽²⁾>_q的广义非线性等阶N次方Y压缩和等阶N次方H压缩特性进行了详细研究.结果发现:1)态|ψ_+,3⁽²⁾>_q及态|ψ_-,4⁽²⁾>_q是两种典型的多模非经典光场,当各模的初始相位φ_j(j=1,2,3,…,q)或者各模的初始相位和 =φ_j以及态间的初始相位差(θ_±^(R)-θ^(0)_±)等分别满足一些特定的量子化条件时,态|ψ_+,3⁽²⁾>_q及态|ψ_-,4⁽²⁾>_q均可呈现出周期性变化的、任意阶的等阶N次方Y压缩效应和等阶N次方H压缩效应;2)当组成态|ψ_+,3⁽²⁾>_q及态|ψ_-,4⁽²⁾>_q的各对应复几率幅不相等亦即C₊^(R)≠C_-^(R)和C₊⁽⁰⁾≠C_-⁽⁰⁾时,态|ψ_+,3⁽²⁾>_q及态|ψ_-,4⁽²⁾>_q这两者的压缩条件和压缩特征虽然相同,但其压缩幅度(即压缩程度和压缩深度)却不相等,这种现象称为“相似压缩”;3)当组成态|ψ_+,3⁽²⁾>_q及态|ψ_-,4⁽²⁾>_q的各对应复几率幅相等亦即C₊^(R)=C_-^(R)和C₊⁽⁰⁾=C_-⁽⁰⁾时,态|ψ_+,3⁽²⁾>_q及态|ψ_-,4⁽²⁾>_q这两种截然不同的多模叠加态光场不仅具有完全相同的压缩条件和压缩特征,而且还具有完全相等的压缩幅度,这种现象就称为“压缩简并”.

STUDY ON THE PROPERTIES OF BOTH GENERALIZED NONLINEAR EQUAL-ORDER N-TH POWER Y-SQUEEZING AND GENERALIZED NONLINEAR EQUAL-ORDER N-TH POWER H-SQUEEZING IN THE THIRD AND THE FOURTH KINDS OF MULTIMODE SUPERPOSITION STATE LIGHT FIELD WITH THE SUPE

According to the linear superposition principle of quantum mechanics in this paper,it is constructed respectively the third kind of multimode superposition state light field |ψ_+,3⁽²⁾>_q composed of the linear superposition of multimode (or q-mode) coherent state |{Z_j}>_q and multimode vaccum state |{0_j}>_q,and the fourth kind of multimode superposition state light field |ψ_-,4⁽²⁾>_q made of the linear superposition of the contrary state |{-Z_j}>_q of the multimode coherent state |{Z_j}>_q and the multimode vaccum state |{0_j}>_q mentioned above.By utilizing the theory of multimode squeezed states established recently by Yang Zhiyong and Hou Xun and published in Acta Photonica Sinica,the properties of both generalized nonlinear equal-order N-th power Y-squeezing and generalized nonlinear equal-order N-th power H-squeezing of the state |ψ_+,3⁽²⁾>_q and the state |ψ_-,4⁽²⁾>_q mentioned are studied firstly in detail.It is found that 1) if some certain quantization conditions are satisfied respectively by the initial phase φ_j(here j=1,2,3,…,…,q) of each mode,or by the initial phase sum =φ_j,and by the initial phase difference (θ_±^(R)-θ^(0)_±) between the two components |{±Z_j}>_q and |{0_j}>_q,the state |ψ_+,3⁽²⁾>_q and the state |ψ_-,4⁽²⁾>_q can always display any order generalized nonlinear equal-order N-th power Y-squeezing and N-th power H-squeezing that changes periodically,these show that the state |ψ_+,3⁽²⁾>_q and the state |ψ_-,4⁽²⁾>_q are two kinds of typical nonclasical multimode light fields;2)if the corresponding complex probability amplitudes between the state |ψ_+,3⁽²⁾>_q and the state |ψ_-,4⁽²⁾>_q are not equal to each other,the state |ψ_+,3⁽²⁾>_q and the state |ψ_-,4⁽²⁾>_q can always present the ‘similitude squeezing’ of both equal-order N-th power Y-squeezing and equal-order N-th power H-squeezing;and 3)if the corresponding complex probability amplitudes mentioned above are equal to each other,the state |ψ_+,3⁽²⁾>_q and the state |ψ_-,4⁽²⁾>_q can always present the‘degenerate squeezing’of both equal-order N-th power Y-squeezing and equal-order N-th power H-squeezing.