On the cutoff law of laser induced high harmonic spectra

The currently well accepted cutoff law for laser induced high harmonic spectra predicts the cutoff energy as a linear combination of two interaction energies, the ponderomotive energy U_p and the atomic biding energy I_p, with coefficients 3.17 and 1.32, respectively. Even though, this law has been there for twenty years or so, the background information for these two constants, such as how they relate to fundamental physics and mathematics constants, is still unknown. This simple fact, keeps this cutoff law remaining as an empirical one. Based on the cutoff property of Bessel functions and the Einstein photoelectric law in the multiphoton case, we show these two coefficients are algebraic constants, 9 - 42≈ 3.34 and 22- 1 ≈ 1.83, respectively. A recent spectra calculation and an experimental measurement support the new cutoff law.     

线偏振激光场中原子的多光子电离的光电子角分布研究

非微扰量子电动力学的发展使我们可以利用精确的波函数和非微扰的散射理论来研究多光子电离问题.文章作者及其合作者发展了光电子角分布的处理方法,利用复合相位Bessel函数来表征光电子的跃迁几率幅,将光电子的角分布与复合相位Bessel函数直接联系起来.研究发现,复合相位Bessel函数的性质决定了光电子角分布的主要特点及其随激光强度、频率以及光电子能量的演化.该理论不但证实了实验上已经观测到的各种光电子角分布,而且还预言了实验上尚未观测到的光电子角分布,确立了光电子角分布的标度定律.     

A nonperturbative quantum electrodynamic approach to the theory of laser induced high harmonic generation

Using nonperturbative quantum electrodynamics, we develop a scattering theory for high harmonic generation (HHG). A transition rate formula for HHG is obtained. Applying this formula, we calculate the spectra of high harmonics generated from different noble gases shined by strong laser light. We study the cutoff property of the spectra. The data show that the cutoff orders of high harmonics are greater than that predicted by the “3.17” cutoff law. As a numerical experiment, the data obtained from our repeated calculations support the newly derived theoretical expression of the cutoff law. The cutoff energy of high harmonics described by the new cutoff law, in terms of the ponderomotive energy U_p and the ionization potential energy I_p, is 3.34U_p+ 1.83I_p. The higher cutoff orders predicted by this theory are due to the absorption of the extra photons, which participate only the photon-mode up-conversion and do nothing in the photoionization process.     

Even-odd harmonics generated from above-threshold ionization

We are reporting a theoretical prediction： The photoelectrons forming above-threshold-ionization （ATI） peaks emit both even and odd harmonics. These harmonics exhibit plateau and cut-off features similar to those odd-only harmonics observed in ATI experiments.     

Efimov effect in Dirac semi-metals

The Efimov effect is defined as a quantum state with discrete scaling symmetry and a universal scaling factor. It has attracted considerable interests from nuclear to atomic physics communities. In a Dirac semi-metal, when an electron interacts with a static impurity through a Coulombic interaction, the same kinetic scaling and the interaction energy results in the Efimov effect. However, even when the Fermi energy lies exactly at the Dirac point, the vacuum polarization of the electron-hole pair fluctuation can still screen the Coulombic interaction, which leads to deviations from the scaling symmetry and eventually breaks down of the Efimov effect. This energy distortion of the Efimov states due to vacuum polarization is a relativistic electron analogy of the Lamb shift for the hydrogen atom. Motivated by the recent experimental observations in two- and three-dimensional Dirac semi-metals, we herein investigate this many-body correction to the Efimov effect and the conditions that allow some of the Efimov-like quasi-bound states to be observed in these condensed matter experiments.     

Dirac光子晶体

Dirac费米子作为粒子物理中的基本粒子之一,其理论在近年来蓬勃发展的拓扑电子理论领域中被广泛提及并用来刻画具有Dirac费米子性质的电子态.这种特殊的能态通常被称为Dirac点,在能谱上表现为两条不同能带之间的线性交叉点.由于Dirac点往往是发生拓扑相变的转变点,因而也被视为实现各种拓扑态的重要母态.作为可与拓扑电子体系类比的拓扑光子晶体因其独特的潜在应用价值也受到人们的广泛关注,实现包含Dirac点的光子能带已成为研究拓扑光子晶体的核心课题.本文基于电子的拓扑理论,简要地回顾了Dirac点在光子系统中的研究进展,特别介绍了如何在光子晶体中利用不同晶格对称性实现在高对称点/线上的Dirac点,以及由Dirac点衍生的Weyl点.     

Dirac Equation and Some Quasi-Exact Solvable Potentials in the Turbiner’s Classification

In this paper quasi-exact solvability (QES) of Dirac equation with some scalar potentials based on sl(2) Lie algebra is studied. According to the quasi-exact solvability theory, we construct the configuration of the classes II, IV, V, and X potentials in the Turbiner's classification such that the Dirac equation with scalar potential is quasi-exactly solved and the Bethe ansatz equations are derived in order to obtain the energy eigenvalues and eigenfunctions.     

Environment induced quantum Zeno effect in coupled microwave cavities

We model a feasible experiment involving two interacting microwave cavities with very different quality factors. An excitation is initially present in the high Q cavity. Modeling the environment as linearly coupled oscillators, we find a Zeno-like behavior which should occur when the dissipation constant is large enough as compared to the unitary coupling.     

A spin observable for a Dirac particle

We discuss the form of the spin operator in relativistic quantum mechanics. We derive the form of the spin operator in the case when the states with negative energies are admitted. It appears that for a Dirac particle the spin operator reduces to the so called mean-spin operator introduced by Foldy and Wouthuysen. We show that the spin operator transforms under Lorentz group action according to an operator Wigner rotation, analogously as a Bloch vector describing polarization of a particle in momentum representation.     

Nodal theorems for the Dirac equation in d ≥ 1 dimensions

A single particle obeys the Dirac equation in spatial dimensions and is bound by an attractive central monotone potential that vanishes at infinity. In one dimension, the potential is even, and monotone for The asymptotic behavior of the wave functions near the origin and at infinity are discussed. Nodal theorems are proven for the cases and , which specify the relationship between the numbers of nodes n₁ and n₂ in the upper and lower components of the Dirac spinor. For , whereas for if and if where and This work generalizes the classic results of Rose and Newton in 1951 for the case Specific examples are presented with graphs, including Dirac spinor orbits      

On non‐equilibrium photon distributions in the Casimir effect

The electromagnetic field in a typical geometry of the Casimir effect is described in the Schwinger–Keldysh formalism. The main result is the photon distribution function (Keldysh Green function) in any stationary state of the field. A two‐plate geometry with a sliding interface in local equilibrium is studied in detail, and full agreement with the results of Rytov fluctuation electrodynamics is found.     

Dirac Equation and Some Quasi-Exact Solvable Potentials in the Turbiner's Classification

In this paper quasi-exact solvability(QES)of Dirac equation with some scalar potentials based on sl(2)Lie algebra is studied.According to the quasi-exact solvability theory,we construct the configuration of the classes II,IV,V,and X potentials in the Turbiner’s classification such that the Dirac equation with scalar potential is quasi-exactly solved and the Bethe ansatz equations are derived in order to obtain the energy eigenvalues and eigenfunctions.     

Level spacing statistics for two-dimensional massless Dirac billiards

Classical-quantum correspondence has been an intriguing issue ever since quantum theory was proposed. The searching for signatures of classically nonintegrable dynamics in quantum systems comprises the interesting field of quantum chaos. In this short review, we shall go over recent efforts of extending the understanding of quantum chaos to relativistic cases. We shall focus on the level spacing statistics for two-dimensional massless Dirac billiards, i.e., particles confined in a closed region. We shall discuss the works for both the particle described by the massless Dirac equation(or Weyl equation)and the quasiparticle from graphene. Although the equations are the same, the boundary conditions are typically different,rendering distinct level spacing statistics.     

Spontaneous Edge Currents for the Dirac Equation in Two Space Dimensions

Spontaneous edge currents are known to occur in systems of two space dimensions in a strong magnetic field. The latter creates chirality and determines the direction of the currents. Here we show that an analogous effect occurs in a field-free situation when time reversal symmetry is broken by the mass term of the Dirac equation in two space dimensions. On a half plane, one sees explicitly that the strength of the edge current is proportional to the difference between the chemical potentials at the edge and in the bulk, so that the effect is analogous to the Hall effect, but with an internal potential. The edge conductivity differs from the bulk (Hall) conductivity on the whole plane. This results from the dependence of the edge conductivity on the choice of a selfadjoint extension of the Dirac Hamiltonian. The invariance of the edge conductivity with respect to small perturbations is studied in this example by topological techniques Mathematics Subject Classification (2000). 81Q10, 58J32     

On how the (1+1)-dimensional Dirac equation arises in classical physics

We demonstrate how the (1+1)-dimensional Dirac equation can be derived from the equation for the probability distribution governing a stochastic process when particles are permitted to propagate both backwards and forwards in time. This derivation uses a real transfer matrix and does not require a formal analytic continuation from classical physics. The physical significance of the quantity we interpret as being the wave function is discussed.     

Integration method for the Dirac equation

An integration method for the Dirac equation is proposed. The method, based on diagonalization, reduces the problem to one of integration of independent second-order differential equations.     

强激光场中真空极化效应

 通过求解狄拉克方程,对强激光场下真空极化问题进行了研究。理论计算结果表明：在仅随时间变化的电场下,要激发狄拉克海中负能级的电子,需要两个阈值条件,即激光场的电场强度大于等于10¹⁶ V/cm和激光场的持续时间大于等于10^-21 s。前者主要保证负能态电子有足够的能量跃迁到正能态,后者主要是保证电子在跃迁过程中动量亏损得以补偿。     

Wigner function for the Dirac oscillator in spinor space

The Wigner function for the Dirac oscillator in spinor space is studied in this paper.Firstly,since the Dirac equation is described as a matrix equation in phase space,it is necessary to define the Wigner function as a matrix function in spinor space.Secondly,the matrix form of the Wigner function is proven to support the Dirac equation.Thirdly,by solving the Dirac equation,energy levels and the Wigner function for the Dirac oscillator in spinor space are obtained.     

Wigner function for the Dirac oscillator in spinor space

The Wigner function for the Dirac oscillator in spinor space is studied in this paper. Firstly, since the Dirac equation is described as a matrix equation in phase space, it is necessary to define the Wigner function as a matrix function in spinor space. Secondly, the matrix form of the Wigner function is proven to support the Dirac equation. Thirdly, by solving the Dirac equation, energy levels and the Wigner function for the Dirac oscillator in spinor space are obtained.