Finite 1D-Lattice Physics as Induced by Dirac–Markov Operators

Finite 1D-lattice physics as induced by Dirac operators was examined. We identified the Dirac operators with Bi-Graded Markovian matrices. The Dirac operators dictate the time evolution of states in Markovian-like processes. By applying these Dirac operators to finite 1D-lattices, we find differences between the vacuum physical spinorial states over lattices with an even number of sites as compared to an odd number of sites. Solitonic states that are created by particle pairing appear on lattices with an even number of sites. On lattices with an odd number of sites, we find global solitonic states and global spin wave states, as well as a global steady oscillation of the spinorial wave function. This demonstrates how the lattice world, in a few number of sites, dramatically affects the vacuum physical states. All these vacuum states can be realized as entangled local particles over the lattice.     

Expectation Value Theorem for Thermo Vacuum States of Optical Chaotic Field and Negative-Binomial Field

For the density operator (mixed state) describing chaotic light and negative-binomial field there exist the corresponding thermal vacuum state (pure state) in the real-fictitious space. Using the method of integration within ordered product of operators we find the expectation value theorem in these two thermo vacuum states respectively. The thermal average theorem of translation operator is also deduced. Application of the new thermo vacuum state in calculating photon number disturibution and fluctuation and thermal average is presented.     

Quantum mechanical pure states with gaussian wave functions

This paper examines single-mode and two-mode Gaussian pure states (GPS), quantum mechanical pure states with Gaussian wave functions. These states are produced when harmonic oscillators in their ground states are exposed to potentials, or interaction Hamiltonians, that are linear or quadratic in the position and momentum variables (i.e., annihilation and creation operators) of the oscillators. The physical and group theoretical properties of these Hamiltonians and the unitary operators they generate are discussed. These properties lead to a natural classification scheme for GPS. Important properties of single-mode and two-mode GPS are discussed. An efficient vector notation is introduced, and used to derive many of the important properties of GPS and of the Hamiltonians and unitary operators associated with them.     

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.     

增光子压缩真空态的反群聚效应

本文讨论了压缩真空态在玻色湮灭算符的逆算符及玻色产生算符作用下的光子反群聚性质. 结果表明, 在两种情况下所得到的增光子压缩真空态都呈现出反群聚效应, 但前者呈现的反群聚效应与所增加的光子数k以及压缩参数的取值区间有关, 而后者则在相同的压缩参数取值区间内呈现出反群聚效应, 与增加的光子数k无关.     

Husimi Functions of Excited Squeezed Vacuum States

Based on the Husimi operator in pure state form introduced by Fan et al., which is a squeezed coherent state projector, and the technique ofintegration within an ordered product (IWOP) of operators, as well as theentangled state representations, we obtain the Husimi functions of theexcited squeezed vacuum states (ESVS) and two marginal distributions of theHusimi functions of the ESVS.     

Complete entanglement transfer between light and qubits

Using the two-mode two-photon Jaynes-Cummings model, entanglement transfer between atoms and field is studied. It is found that when the field is in state constructed from the two-mode photon number states |00〉,|11〉 or the two-mode squeezed vacuum states, full entanglement exchange can be attained no matter the atoms are initially in pure or mixed states. These investigations show that CV entangled states can act as perfectly as the entangled number states in entangling initially separable atoms. The two-mode two-photon atom-field interaction also provides a simple way for the quantum teleportation of atomic or field states.     

Degree of Entanglement for Some Bipartite Entangled Bosonic Systems

We calculate the degree of entanglement for some bipartite entangled states of continuous variables.These states include common two-mode squeezed vacuum state, thermal vacuum state of a free single particle (where theh fictitious tilde system is regarded as another particle), and the squeezed vacuum state of two coupling harmonic oscillators.The degree of entanglement for these quantum systems are shown clearly by using the technique of integration within an ordered product of operators.     

Degree of Entanglement for Some Bipartite Entangled Bosonic Systems

We calculate the degree of entanglement for some bipartite entangled states of continuous variables.These states include common two-mode squeezed vacuum state, thermal vacuum state of a free single particle (where the fictitious tilde system is regarded as another particle), and the squeezed vacuum state of two coupling harmonic oscillators.The degree of entanglement for these quantum systems are shown clearly by using the technique of integration within an ordered product of operators.     

Quantum uncertainty relations of two generalized quantum relative entropies of coherence

In this paper, we consider the quantum uncertainty relations of two generalized relative entropies of coherence based on two measurement bases. First, we give quantum uncertainty relations for pure states in a d-dimensional quantum system by making use of the majorization technique; these uncertainty relations are then generalized to mixed states. We find that the lower bounds are always nonnegative for pure states but may be negative for some mixed states. Second, the quantum uncertainty relations for single qubit states are obtained by the analytical method. We show that the lower bounds obtained by this technique are always positive for single qubit states. Third, the lower bounds obtained by the two methods described above are compared for single qubit states.     

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。     

压缩真空态的激发态及其在非耗散介观含源电路的应用

借助逆算符的性质,提出了压缩真空态激发态的概念,作为应用,导出了非耗散介观含源电路在该激发态下其电荷和电流的量子零点涨落,数值计算表明,在不同的激发量子数下,电荷和电流均存在压缩效应,它们的不确定度之积分别趋向于一个最小值。     

Quantum entanglement and nonlocality properties of two-mode Gaussian squeezed states

Quantum entanglement and nonlocality properties of a family of two-mode Gaussian pure states have been investigated. The results show that the entanglement of these states is determined by both the two-mode squeezing parameter and the difference of the two single-mode squeezing parameters. For the same two-mode squeezing parameter, these states show larger entanglement than the usual two-mode squeezed vacuum state. The violation of Bell inequality depends strongly on all the squeezing parameters of these states and disappears completely in the limit of large squeezing. In particular, these states can exhibit much stronger violation of local realism than two-mode squeezed vacuum state in the range of experimentally available squeezing values.     

Time-Symmetric Quantization in Spacetimes with Event Horizons

The standard quantization formalism in spacetimes with event horizons implies a non-unitary evolution of quantum states, as initial pure states may evolve into thermal states. This phenomenon is behind the famous black hole information loss paradox which provoked long-standing debates on the compatibility of quantum mechanics and gravity. In this paper we demonstrate that within an alternative time-symmetric quantization formalism thermal radiation is absent and states evolve unitarily in spacetimes with event horizons. We also discuss the theoretical consistency of the proposed formalism. We explicitly demonstrate that the theory preserves the microcausality condition and suggest a “reinterpretation postulate” to resolve other apparent pathologies associated with negative energy states. Accordingly as there is a consistent alternative, we argue that choosing to use time-asymmetric quantization is a necessary condition for the black hole information loss paradox.     

General Formalism for Mapping of Two-Mode Classical Canonical Transformations to Quantum Unitary operators

Two types of canonical transformations in two-mode classical phase space are mapped into the quantum mechanical Hilbert space to produce some new normally ordered unitary operators. These operators are evaluated in the coordinate (momentum) representations using the "integration within ordered product technique, and the mapping is maniferrtly apparent in the derivation. New generalixed coherent states are constructed in terms of these operators, and the uncertainty relations for these states are analysed.     

Coherent States for the Asymmetric Penning Trap

After identifying the appropriate ladder operators, the coherent states for the asymmetric Penning trap are derived as common eigenstates of the annihilation operators. They will be compared with the ones obtained by acting the displacement operator onto the extremal state, as well as with those which minimize some Heisenberg uncertainty relationships. The time evolution and relevant mean values for some operators in these states will be evaluated.     

Phase properties of squeezed states of light

Recently introduced unitary and hermitian phase operators are used to examine the phase properties of squeezed states of light with particular reference to the squeezed vacuum. The results differ markedly from previous calculations involving the Susskind and Glogower operators. The new formalism allows the construction of a phase probability density which, on a polar diagram, is a circle for the vacuum state, becomes elliptical with gentle squeezing and collapses to a line through the origin for full squeezing. This probability density together with the calculation of expectation values of various trigonometrical functions of phase show how squeezing impresses phase information onto the vacuum.     

测不准关系和最小不确定态

利用力学量算符的厄密性和希尔伯特状态矢量模的非负性，重新给出了关于测不准关系的数 学证明.简单的证明过程不仅揭示了测不准关系某些经常被忽视的特征，而且还可以直接给 出最小不确定态的充要条件.在此基础上，我们提出了对易子为非零常数的任意一对力学量 的最小不确定态问题，并且采用玻色型产生和湮没算符给出了它们的压缩态的明显表达式. 关键词： 海森堡测不准原理 最小不确定态 压缩态     

Dissipative squeezed vacuum in non-equilibrium thermo field dynamics

Degenerate parametric amplification accompanied by dissipation is analyzed within the canonical operator formalism for quantum dissipative systems named non-equilibrium thermo field dynamics. The vacuum of the system is subject to both dissipation and breaking of phase symmetry due to squeezing. The annihilation-creation operators for the vacuum are derived and the structure of the vacuum is examined. The effects of dissipation on squeezing and uncertainty relation are estimated.     

Uncertainty relation for the discrete Fourier transform

We derive an uncertainty relation for two unitary operators which obey a commutation relation of the form UV=e(i phi) VU. Its most important application is to constrain how much a quantum state can be localized simultaneously in two mutually unbiased bases related by a discrete fourier transform. It provides an uncertainty relation which smoothly interpolates between the well-known cases of the Pauli operators in two dimensions and the continuous variables position and momentum. This work also provides an uncertainty relation for modular variables, and could find applications in signal processing. In the finite dimensional case the minimum uncertainty states, discrete analogues of coherent and squeezed states, are minimum energy solutions of Harper's equation, a discrete version of the harmonic oscillator equation.