The Geometric Phases and Quasienergy Spectral Series of a Hartree-Type Equation with a Quadratic Potential

Based on the ideology of the complex WKB–Maslov method, the general construction of quasiclassically concentrated solutions is given for Hartree-type equations with a quadratic potential and periodic coefficients. Exact expressions are constructed for the quasienergies and associated quasienergy states. In the construction of solutions, an important role is played by the Hamilton–Ehrenfest system of equations obtained in this work. Explicit expressions are found for the geometric phase of Aharonov–Anandan quasienergy states.     

Flexible for Multiple Equations about GHZ States and a Prototype Case

According to the peculiar entanglement and measurement properties of the three-particle GHZ state, we have systematically analyzed that two GHZ states and three GHZ states satisfy some expressions after exchanging one or two groups of particles respectively, which are described as four interesting and flexible equations. The four equations can deduce that four GHZ states or even m GHZ states still satisfy some expressions after exchanging one group and two groups of particles, and they can be summarized as two general flexible equations. Furthermore, we also investigate their application in the field of quantum key agreement based on these equations. In particular, we combine with decoy photons to propose a novel session key sharing protocol, which can guarantee the unconditional security of the protocol. It is feasible to use the existing quantum processing technology to realize the proposed protocol.

     

Investigation of interfacial states in MIS structures by a single-frequency admittance method

Two models of tunneling charge exchange on interfacial states buried in the insulator are examined. In one model the spatial distribution of these states is assumed to be uniform and in the other model the volume density of traps decreases exponentially with increasing depth. Analytical expressions are obtained for the width and position of the peak in the normalizedconductance curves in both models, and the accuracy and limitations of these expressions are indicated. A new procedure for investigating interfacial states by the admittance method is proposed, based on the use of G-V characteristics of metal-insulator-semiconductor (MIS) structures measured at a fixed frequency. Zh. Tekh. Fiz. 67, 55–59 (October 1997)     

具有n维氢原子型标量势与矢量势的Klein-Gordon方程的束缚态

研究了具有n维氢原子型标量势和矢量势的Klein-Gordon方程的束缚态性质，获得了束 缚态的精确解-给出了精确的能谱方程和归一化的解析波函数，推导出径向平均值的两个递 推关系和部分低幂次径向平均值的解析表达式- 关键词： n维氢原子势 Klein-Gordon方程 束缚态 精确解     

Radiative properties of Zeeman components of atomic multiplets: Dependence of line intensities on the magnetic field

Analytical expressions for the dependence of the intensity of Zeeman components of doublet lines on the magnetic field are obtained. Sharp changes of these function on passing from the anomalous Zeeman effect to the Paschen-Back effect lead to the disappearance of marginal lines and the equalization of intensities of remaining lines. In the region of the complete Paschen-Back effect, a strong influence on these dependences is produced by the dynamic atom-field interaction, which weakens the paramagnetic effect in the states with a positive magnetic quantum number m and enhances the effect in the states with a negative m. Simple analytical expressions are obtained that take into account the effect of the diamagnetic interaction on line intensities. The role of the diamagnetic interaction increases in Rydberg atomic states with a large spin-orbit splitting. For the states with m > 0, it can lead to the “diamagnetic reversal” of the Paschen-Back effect, i.e., the recovery of the anomalous Zeeman effect.     

Operator method for calculating the spectrum of states in the framework of the extended dicke model

A system of N two-level atoms interacting with a resonant single-mode quantum field (the Dicke model) is described using the operator method for solving the Schrödinger equation. The spectrum of states is calculated without recourse to the rotating-wave approximation and the assumption regarding smallness of the linear sizes of the system as compared to the radiation wavelength. Analytical approximate expressions are obtained for the energy spectrum. These expressions approximate the energy spectrum over the entire range of Hamiltonian parameters in the normal and collective states of the system and make it possible to calculate the thermodynamic characteristics.     

高激发态钠原子的量子拍实验的某些分析

本文推导了一个量子拍实验中观察量的解析表式,与实验对比可得n²D态钠原子的精细裂距,其它特征也与实验符合。同时还讨论了上述高激发态钠原子在弱电场中的能态变化特性,指出了观察此特性的可能实验方法。 关键词：     

Quantum freeze of fidelity decay for chaotic dynamics

We show that the mechanism of quantum freeze of fidelity decay for perturbations with a zero time average, recently discovered for a specific case of integrable dynamics [New J. Phys. 5, 109 (2003)], can be generalized to arbitrary quantum dynamics. We work out explicitly the case of a chaotic classical counterpart, for which we find semiclassical expressions for the value and the range of the plateau of fidelity. After the plateau ends, we find explicit expressions for the asymptotic decay, which can be exponential or Gaussian depending on the ratio of the Heisenberg time to the decay time. Arbitrary initial states can be considered; e.g., we discuss coherent states and random states.     

原子相干性对双光子Jaynes-Cummings模型动力学特性的影响

本文研究了双光子Jaynes-Cumming模型在初始相干光场较强的条件下(n >>1)对于不同的原子初态原子和场退耦合而形成的各种纯态的确切表达式及演化规律,并运用密度算符间的距离进行了充分的论证.     

Lower‐ and Higher‐Order Nonclassical Properties of Photon Added and Subtracted Displaced Fock States

Nonclassical properties of photon added and subtracted displaced Fock states are studied using various witnesses of lower‐ and higher‐order nonclassicality. Compact analytic expressions are obtained for the nonclassicality witnesses. Using those expressions, it is established that these states and the states that can be obtained as their limiting cases (except coherent states) are highly nonclassical as they show the existence of lower‐ and higher‐order antibunching and sub‐Poissonian photon statistics, in addition to the nonclassical features revealed through the Mandel $Q_M$ parameter, zeros of Q function, Klyshko's criterion, and Agarwal–Tara criterion. Further, some comparison between the nonclassicality of photon added and subtracted displaced Fock states have been performed using witnesses of nonclassicality. This has established that between the two types of non‐Gaussianity inducing operations (i.e., photon addition and subtraction) used here, photon addition influences the nonclassical properties more strongly. Further, optical designs for the generation of photon added and subtracted displaced Fock states from squeezed vacuum state have also been proposed.     

Positron states in alkali-halide single crystals

Detailed consideration is given to the annihilatory decay of positron states in real alkali-halide single crystals of defective structure. Representations of the exciton-positron states in the matrix of the crystal and close to a lattice defect are analyzed. On the basis of these representations, expressions are derived for the yield of the three-quantum decay process and the intensities of the components contributing to two-quantum annihilation; the expressions agree with existing experimental data. It is shown that the greatest contribution to the three-quantum decay arises from an exciton-orthopositronium state located in the vicinity of the defect.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 76–79, October, 1974.     

Si(111)理想、弛豫及2×1重构表面的声子谱研究

本文利用微扰的方法考虑了占据态与空态间的耦合对能带能量的影响,给出延展键轨道近似下半导体力常数的解析表达式.利用这些表达式求出Si(111)的理想、1×1弛豫及2×1Haneman模型重构表面的声子色散曲线及其表面振动的振幅分布.不同表面结果的比较显示弛豫及重构对表面声子性质具有决定性的影响.同时,分析表明Haneman的2×1表面重构模型不足以满意地解释有关实验结果.     

On the theory of the adsorption of atoms onto a metal surface in the presence of an external quantizing magnetic field

The Anderson-Newns model for the adsorption of atoms onto metals is generalized to the case of the presence of an external transverse quantizing magnetic field. Analytical expressions for the density of metal states in the external magnetic field are obtained. Analytical expressions for the density of adatom states are obtained in the approximation taking only the change in the density of substrate states into account. The charge exchange between the adatom and the metal is studied. The dependences of the density of adatom and transition-charge states on the magnetic field are studied for different values of the interaction constant. An analytical expression for the density of substrate states perturbed by adsorption is obtained.     

Using interference for high fidelity quantum state transfer in optomechanics

We revisit the problem of using a mechanical resonator to perform the transfer of a quantum state between two electromagnetic cavities (e.g., optical and microwave). We show that this system possesses an effective mechanically dark mode which is immune to mechanical dissipation; utilizing this feature allows highly efficient transfer of intracavity states, as well as of itinerant photon states. We provide simple analytic expressions for the fidelity for transferring both gaussian and non-gaussian states.     

Partial-wave analysis of the reactions pp → ϱ0ϱ0, ωϱ0, ϱ0f,and ωf in the T(2200) region

The helicity formalism is used to derive expressions for the joint decay distributions for ?⁰?⁰, ω?⁰, ?⁰f and ωf states in terms of the joint density matrix elements. These expressions are used to extract the density matrix elements from the data of the Rutgers- Stevens-Albany collaboration in the T(2200) region. A partial-wave analysis is then performed in an attempt to determine the dominant partial-wave amplitudes. The results are discussed and comparisons are made to the extremely limited amount of data available at neighboring energies. Finally it is pointed out that the expressions derived for this analysis could be applied without modification to e^?e⁺ annihilations into these states.     

Linestrength formulas of Hund's intermediate case multiplet transitions in diatomic molecules

Explicit expressions in fairly condensed form are obtained for the intensity distribution in the branches of quartet transitions of any type with ΔΛ = 0 and ΔΛ = ±1 where both electronic states involved in transition may belong to a coupling case intermediate between Hund's cases (a) and (b). Moreover, similar condensed expressions are given for the linestrengths already known of the doublet, triplet, and quintet transitions.     

Comparing energy difference and fidelity of quantum states

We look for upper bounds of the relative energy difference of two pure quantum states with a fixed fidelity between them or upper bounds of the fidelity for a fixed relative energy difference. The results depend on the concrete families of states chosen for the comparison. Exact analytical expressions are found for several popular sets of states: coherent, squeezed vacuum, binomial, negative binomial, and coherent phase states. Their consequence is that to guarantee, for example, a relative energy difference less than 10% for quite arbitrary (unknown) coherent states, the fidelity must exceed the level 0.995. For other kinds of states, the restrictions can be much stronger.     

On the convergence of reflectionless approximations to confining potentials

The construction of reflectionless potentials supporting a prescribed spectrum of Schrödinger bound states is discussed and related to the inverse problem for confining potentials. A simple formula is derived for the Jost solution in a one-dimensional reflection-less potential with N bound states. This leads to compact expressions for the potential and the bound-state wavefunctions in terms of the bound-state energies. For symmetric potentials, N-fold product formulas are obtained for bound-state wavefunctions and their slopes at the origin. Corresponding quantities in a confining potential are given by infinite products. Comparison of the finite-product and infinite-product expressions allows a demonstration of the convergence of the reflectionless results to the confining potential results as N → ∞. Several sum rules satisfied by the reflectionless potential at the origin are applied to numerical studies of convergence.     

Perturbation of the radiative lifetimes of rovibronic levels of the nl complex of terms of a diatomic molecule

Within the framework of a sufficiently general nonadiabatic model taking into account the interaction of an arbitrary finite number of electronic states and not requiring the smallness of a perturbation parameter, expressions have been obtained for the radiative lifetimes of the rovibronic levels of states of the nl complex of terms of a diatomic molecule. It is shown that the determination of ratios of the nonadiabatic and adiabatic radiative lifetimes for the rovibronic levels can be reduced to the solution of two independent problems (the determination of ratios of the adiabatic values of radiative lifetimes for the mutually perturbing states and determination of the expansion coefficients of the wave functions of rovibronic states in the Born-Oppenheimer basis set of wave functions) when the rovibronic states are perturbed by only a single rovibrational level of each electronic state or by an arbitrary number of rovibrational states of each electronic state provided that the potential curves of the combining states are similar and the dipole moments of electronic transitions weakly depend on the internuclear separation (which is quite a case for highly excited electronic states). To illustrate the efficiency of using the expressions obtained, the perturbations of the radiative lifetimes of rovibrational levels of the I ¹Π _g ^? and J ¹Δ _g ^? states of the 3d complex of terms of the H₂ molecule were considered.     

Unified approach to superposition states of the quantized radiation field

Summary In the recent years various and interesting superposition states of the quantized radiation field were investigated in the literature, such as that involving two number states by Wodkiewiczet al.; that involving two coherent states by Hillery and Gerryet al.; that involving two squeezed states by Xinet al., etc. Here we study a general one-parameter superposition state which unifies those states and others in the literature, all becoming a particularization of ours. General expressions characterizing the physical properties of the field are obtained. The role played by the present superposition state as an alternative interpolating state is also discussed. The authors of this paper have agreed to not receive the proofs for correction.