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.     

奇偶相干态中测量相位算符的涨落及其压缩

利用Ｂａｒｎｅｔｔ和Ｐｅｇｇ提出的测量相位算符讨论了奇偶相干态中的相位涨落及其高阶涨落，在测不准关系和高阶测不准关系基础上给出了测量相位压缩和高阶压缩的二类定义，并用这二类定义研究了奇偶相干态中测量相位的二阶和高阶压缩情况。     

非简谐振子湮灭算符三次幂的本征态及其性质

构造了非简谐振子湮灭算符３次幂的正交归一本征态，证明它是光场振幅的３ｎ次幂的最小测不准态，无压缩效应，并研究了它的反聚束性质。     

混合态的不确定关系与压缩效应

在关于混合态的海森堡不确定关系的基础上，研究了纯态和混合态的最小不确定性和压缩效应.虽然最小不确定态必定是纯态，但在某些并非最小不确定态的纯态或混合态中，依然可 以实现力学量不确定度的压缩.还给出了普通统计学的不确定关系，它们不涉及量子相干性却与量子力学的海森堡不确定关系具有相似的数学结构. 关键词： 混合态 最小不确定性 压缩效应     

介观电路压缩态的热动力学研究

利用信息理论和密度矩阵，分析研究了频率随时间变化的介观LC电路中的相干态及压缩态。通过与密度矩阵相关算符，我们将相干态、压缩态的出现与电路的初始条件联系起来。结果显示：系统量子态的演化和初始状态密切相关。一般来说，由于环境温度的影响，初始处于某一激发态的介观LC电路系统会演化到压缩态；在低温下，让电路参数作阶跃变化，如果跃变前后电路的谐振频率不变，则能够制备出压缩最小测不准态。     

第Ⅰ类两态叠加多模叠加态光场的非线性高阶压缩特性研究

本文在文献２０的基础上进一步提出了多模辐射场的Ｎ－Ｙ最小测不准态、Ｎ－Ｈ最小测不准态、Ｎ－Ｙ压缩最小测不准态以及Ｎ－Ｈ压缩最小测不准态等的定义．构造了由多模（ｑ模）相干态｜｛Ｚｊ｝＞ｑ及其相反态｜｛－Ｚｊ｝＞ｑ的线性叠加所组成的第Ⅰ类两态叠加多模叠加态光场｜ψ（２）１＞ｑ，利用文献２０新近提出的有关多模辐射场的两种非线性高阶压缩的定义，首次对态｜ψ（２）１＞ｑ的Ｎ次方Ｙ压缩及Ｎ次方Ｈ压缩效应进行了详细研究．结果表明，１）当Ｎ为偶数时，态｜ψ（２）１＞ｑ恒处于Ｎ－Ｙ最小测不准态；当Ｎ为奇数时，态｜ψ（２）１＞ｑ在一定条件下可呈现出周期性变化的、任意阶的Ｎ次方Ｙ压缩效应．２）当ｑ·Ｎ为偶数时，态｜ψ（２）１＞ｑ恒处于Ｎ－Ｈ最小测不准态；当ｑ·Ｎ为奇数时，在另外的条件下，态｜ψ（２）１＞ｑ则可呈现出周期性变化的、任意阶的Ｎ次方Ｈ压缩效应．３）Ｎ次方Ｙ压缩及Ｎ次方Ｈ压缩效应的压缩深度与腔模总数ｑ、压缩参数Ｒｊ以及压缩阶数Ｎ等非线性相关，后者与上述参量的非线性关联程度要比前者的更强．     

二次型含时间的谐振子系统的压缩态和压缩相干态

利用演化算符方法研究了最一般的二次型含时间的谐振子系统的时间演化和压缩态问题,进一步讨论了脉动质量的受迫谐振子系统的压缩态和高n压缩态.最后,构造了在时间演化过程中保持最小测不准关系的压缩相干态和高n压缩相干态. 关键词：     

相量的q形变相干态及其压缩性质

研究位相正交算符在相量的q形变相干态中的压缩性质和二能级系统中粒子数-位相压缩及其不确定关系，进而得到了一些新的粒子数-位相不确定态. 关键词：     

Q形变的非简谐振子广义相干态

利用变换算符导出了Q形变的非简谐振子代数,由此得到Q形变的非简谐振子广义相干态.这些状态具有过完备性,是Q形变的自然算符的极小测不准状态.在主压缩区间中偶相干态的相对压缩率随形变程度的增大而增大.     

一种新型的两态叠加多模Schrdinger猫态光场的等阶N次方Y压缩

本文根据量子力学的线性叠加原理,构造了由多模（即q模时目平态的相反态|｛｛－Zj｝〉q及多模虚相干态|｛｛－Zj｝〉q这两者的线性叠加所组成的一种新型的多模Schrodinger猫态光场利用新近建立的多模压缩态理论,研究了态的N次方Y压缩效应,结果发现：①当压缩阶数N＝Zp且p＝2m（m＝1,2,3,…,…）时,态。总是恒处于N－Y最小测不准态;②当压缩阶数N＝2p且p＝2m＋1（m＝0,1,2,3,…,…）时,如果各模的初始相位,态间的初始相位差以及各单模相干态光场的平均光子数之总和等满足一定的量子化条件,则态可呈现出周期性变化的、任意阶的N次方Y压缩效应;③当压缩阶数N＝2P＇＋1时,无论p＇＝2m（m＝0,1,2,…,…）还是p＇＝2m＋1（m＝0,1,2,3,…,……）,只要各模的初始相位满足一定的量子条件,则当两态叠加几率幅满足时,态就恒处于N－Y测不准态,始终不呈现N－Y最小测不准态和N次方Y压缩;而当时,态始终不呈现N－Y测不准态、N－Y最小测不准态和N次方Y压缩效应．     

Gaussian states as minimum uncertainty states

In bosonic fields, Gaussian states, which consist of a rather wide family of states including coherent states, squeezed states, thermal states, etc., have many classical-like features, and are usually defined from the mathematical perspective in terms of characteristic functions. It is well known that some special Gaussian states, such as coherent states, are minimum uncertainty states for the conventional Heisenberg uncertainty relation involving canonical pair of position and momentum observables. A natural question arises as whether all Gaussian states can be characterized as minimum uncertainty states. In this work, we show that indeed Gaussian states coincide with minimum uncertainty states for an information-theoretic refinement of the conventional uncertainty relation established in Luo (2005) [40]. This characterization puts Gaussian states on a novel basis of physical significance.     

Extremum uncertainty product and sum states

We consider the states with extremum products and sums of the uncertainties in non-commuting observables. These are illustrated by two specific examples of harmonic oscillator and the angular momentum states. It shows that the coherent states of the harmonic oscillator are characterized by the minimum uncertainty sum 〈(Δq)²〉 + 〈(Δp)²〉. The extremum values of the sums and products of the uncertainties of the components of the angular momentum are also obtained.     

On the role of the uncertainty principle in superconductivity and superfluidity

We discuss the general interplay between the uncertainty principle and the onset of dissipationless transport phenomena such as superconductivity and superfluidity. We argue that these phenomena are possible because of the robustness of many-body quantum states with respect to the external environment, which is directly related to the uncertainty principle as applied to coordinates and momenta of the carriers. In the case of superconductors, this implies relationships between macroscopic quantities such as critical temperature and critical magnetic field, and microscopic quantities such as the amount of spatial squeezing of a Cooper pair and its correlation time. In the case of ultracold atomic Fermi gases, this should be paralleled by a connection between the critical temperature for the onset of superfluidity and the corresponding critical velocity. Tests of this conjecture are finally sketched with particular regard to the understanding of the behaviour of superconductors under external pressures or mesoscopic superconductors, and the possibility to mimic these effects in ultracold atomic Fermi gases using Feshbach resonances and atomic squeezed states.     

Entanglement conditions for four-mode states via the uncertainty relations in conjunction with partial transposition

From the Heisenberg uncertainty relation in conjunction with partial transposition, we derive a class of inequalities for detecting entanglements in four-mode states. The sufficient conditions for bipartite entangled states are presented. We also discuss the generalization of the entanglement conditions via the Schrödinger-Robertson indeterminacy relation, which are in general stronger than those based on the Heisenberg uncertainty relation.     

Higher-order squeezing of quantum electromagnetic fields and higher-order uncertainty relations in two-mode squeezed states

It is found that the two-mode output quantum electromagnetic field in two-mode squeezed states exhibits higherorder squeezing to all even orders, and the degree of higher-order squeezing is greater than that of the second-order.The higher-order squeezed parameter and squeezed limit due to the modulation frequency are investigated. The smaller the modulation frequency is, the stronger the degree of higher-order squeezing becomes. Furthermore, the higher-order uncertainty relations in two-mode squeezed states are presented for the first time. The product of higher-order noise moments is related to even order number N and the squeeze factor r.     

Multimode uncertainty relations and separability of continuous variable states

A multimode uncertainty relation (generalizing the Robertson-Schr?dinger relation) is derived as a necessary constraint on the second moments of n pairs of canonical operators. In turn, necessary conditions for the separability of multimode continuous variable states under (m+n)-mode bipartitions are derived from the uncertainty relation. These conditions are proven to be necessary and sufficient for (1+n)-mode Gaussian states and for (m+n)-mode bisymmetric Gaussian states.     

A rigorous uncertainty relation (Cauchy Inequality) for an electromagnetic field in quantum superpositions of coherent states and in a two-photon coherent state

It is shown that the Heisenberg uncertainty relation (or soft uncertainty relation) determined by the commutation properties of operators of electromagnetic field quadratures differs significantly from the Robertson–Schrödinger uncertainty relation (or rigorous uncertainty relation) determined by the quantum correlation properties of field quadratures. In the case of field quantum states, for which mutually noncommuting field operators are quantum-statistically independent or their quantum central correlation moment is zero, the rigorous uncertainty relation makes it possible to measure simultaneously and exactly the observables corresponding to both operators or measure exactly the observable of one of the operators at a finite measurement uncertainty for the other observable. The significant difference between the rigorous and soft uncertainty relations for quantum superpositions of coherent states and the two-photon coherent state of electromagnetic field (which is a state with minimum uncertainty, according to the rigorous uncertainty relation) is analyzed.