一种新型的两态叠加多模叠加态光场的广义非线性等阶N次方H压缩

本文根据量子力学中的线性叠加原理,构造了由多模(即 q模)相干态的相反态 | {-Z_j}〉_q及多模虚相干态的相反态 | {-iZ_j}〉_q 这两者的线性叠加所组成的一种新型的两态叠加多模叠加态光场 | ψ_msc⁽²⁾〉_q 利用新近建立的多模压缩态理论,详细研究了态 | ψ_msc⁽²⁾〉_q 的广义非线性等阶N次方H压缩特性 结果发现:1)当压缩阶数N与腔模总数q这两者之积为偶数,亦即当q·N =2p且p =2m(m =1,2,3,…,…)时,态 | ψ_msc⁽²⁾〉_q恒处于等阶N-H最小测不准态;2)当q·N =2p且 p =2m′+ 1(m′ =0,1,2,3,…,…)时,如果各模的初始相位之和 、态间的初始相位差(θ_nq^(I)-θ_nq^(R))、各多模相干态光场的总的平均光子数 以及 (θ_nq^(I)-θ_nq^(R))+ ]等满足一定的量子化条件时,态 | ψ_msc⁽²⁾〉_q 总可呈现出周期性变化的、任意阶的等阶N次方H压缩效应;3)当压缩阶数N与腔模总数 q这两者之积为奇数时,亦即当 q·N =2p + 1时,无论 p =2m(m =0,1,2,3,…,…)还是 p =2m′ + 1(m′ =0,1,2,3,…,…),只要各模初始相位之和 满足一定的量子化条件,则当两态叠加几率幅满足r_nq^(R) =r_nq^(I) 时,态 | ψ_msc⁽²⁾〉_q 就恒处于N-H测不准态

THE PROPERTY OF GENERALIZED NONLINEAR EQUAL-ORDER N-TH POWER H-SQUEEZING IN A NEW TYPE OF MULTI-MODE LIGHT FIELD STATE WITH THE SUPERPOSITION OF MACROSCOPICALLY DISTINCT TWO QUANTUM STATES

According to the linear superposition principle in quantum mechanics in this paper,it is constructed a new type of multi-mode superposition light field state | ψ_msc⁽²⁾〉_q,which is made of the linear superposition of macroscopically distinct two quantum states named the contrary state | {-Z_j}〉_q of multi-mode(q mode)coherent state | {Z_j}〉_q and the contrary state | {-iZ_j}〉_q of multi-mode imaginary coherent state | {-iZ_j}〉_q repectively.By using the theory of multi-mode squeezed states established recently by Yang Zhiyong and Hou Xun,which was published in Acta Photonica Sinica from April 1998 to May 1999,the property of generalied nonlinear equal-order N-th power H-squeezing of the state | ψ_msc⁽²⁾〉_q mentioned above is studied in detail.It is found that:1)if q·N=2p and p=2m(m=1,2,3,…,…),the state | ψ_msc⁽²⁾〉_q is always stayed in the N-H minimum uncertainty state;2)If q·N=2p and p=2m′+1(m′=0,1,2,3,…,…)when some certain quantization conditions are satisfied by the sum of initial phase of each mode (j=1,2,3,…,q),by the initial phase difference(θ_nq^(I)-θ_nq^(R))between the two components in the state | ψ_msc⁽²⁾〉_q,by qj= the average photon numbers of all the single mode coherent state light field and by (θ_nq^(I)-θ_nq^(R))+ ],the state | ψ_msc⁽²⁾〉_q can presents any order N-th power H-squeezing effect which changes periodically;3)if q·N=2p+1,whether p=2m(m=0,1,2,3,…,…)or p=2m′+1(m′=0,1,2,3,…,…),when the sum of initial phase of each mode satisfy some certain quantization conditions,and while the probability amplitudes satisfy r_nq^(I) =r_nq^(R), the state | ψ_msc⁽²⁾〉_q is only stayed in the N-H uncertainty state.