量子体系中的时域压缩-频域展宽正、逆效应及其非经典性

本文利用全量子理论,对连续能谱量子体系和分立能谱量子体系中的时域压缩-频域展宽以及频域压缩-时域展宽效应进行了详细研究.在文献17构造时间算符的基础上给出频率算符ω∧的定义,根据时间算符t∧与频率算符ω∧之间的对易关系并利用Cauchy-Schwartz不等式导出t∧和ω∧所满足的测不准关系式.给出时域压缩和频域压缩的定义,并对时域/频域上的最小测不准态、压缩最小测不准态和压缩态等进行了详细讨论,指出了时域压缩和频域压缩的非经典性质.给出时域上的拟量子产生算符τ∧+(t)、拟量子湮没算符τ∧(t)和拟量子数算符N∧τ(t)的定义,首次建立了时域量子化的形式理论,并由此进一步提出了时域量子化的基本观点.

THE EFFECTS OF TIME/FREQUENCY SQUEEZING——FREQUENCY/TIME EXPANDING IN QUANTUM SYSTEMS AND THEIR NONCIASSICAL PROPERTIES

In this paper,the complete quantum theory is used to study the effects of both time squeezing-frequency expanding and frequency squeezing-time expanding in the quantum systems of both continuous energy spectrum and discrete energy spectrum in detail.Based on the reference 17 in which the time operator t∧ is constructed,it is given the definition of frequency operator ω∧.According to the commutative relation for time operator t∧ and frequency operator ω∧,the Cauchy Schwartz inequality is used to deduce the uncertainty relation satisfied by both time operator t∧ and frequency operator ω∧,and then the definitions of both time squeezing and frequency squeezing are given,the minimumuncertainty state,the squeezed minimum uncertainty state and the squeezed state of time/frequency are therefore discussed in detail.So the nonclassical properties of both time squeezing-frequency expanding and frequency squeezing-time expanding are revealed.Finally,based upon defining the time quantum like creation operator τ∧ +(t),the time quantum like destruction operator τ∧(t) and the time quantum like number operator N∧ τ(t),the formulated theory of the time quantization originated by Yang Zhiyong and Hou Xun is established,and the basic point of view on the time quantization is further presented.