Correlation of momenta of electrons and the nucleus in atoms

The process of resonant multiphoton ionization of a hydrogen atom in the ground 1s state is studied by direct numerical integration of the nonstationary Schrödinger equation for a quantum system in an electromagnetic field. The dependence of photoionization probability on the radiation intensity is found to be nonmonotonic. It is established that the minima of ionization correspond to multiphoton resonances between the ground state and one of the excited (Rydberg) atomic states perturbed by the laser field. It is shown that ionization is suppressed due to rearrangement of Rydberg states in a strong electromagnetic field and is accompanied by efficient Raman Λ transitions, which connect a set of closely lying Rydberg states via the continuum.     

Calculation of Resonance Parameters for Atomic Hydrogen in a Static Electric Field

A mapped Fourier grid method for the Schrödinger equation is implemented in cylindrical coordinates. The complex absorbing potential method with Padé extrapolation and Riss–Meyer iteration is applied to calculate resonance parameters for the ground state of the hydrogen atom in a strong static electric field. The obtained values are compared with known results from the literature.     

Numerical modeling of the photoionization of Rydberg atoms by the field of an electromagnetic wave

The ionization of excited hydrogen-like atoms in a femtosecond laser pulse is studied by direct numerical integration of the time-dependent Schrödinger equation for a quantum system in the field of an electromagnetic wave. Expressions are obtained for the ionization probability of the system as a function of the parameters of the laser pulse and the initial state of the atom. Ionization suppression is found, confirming the basic premises of the theory of interference stabilization of Rydberg atoms.     

The influence of an electric field on a hydrogen atom confined to boxes of different shapes

The ground state energy of a hydrogen atom confined to a box, in the presence of an electric field is calculated. Boxes of various shapes are applied in order to demonstrate the shape's influence on that energy level. The procedure consists of numerically solving the two-dimensional Schrödinger equation using a finite element package.     

Strong-coupling limit for one-dimensional polarons in a finite box

The strong coupling limit is studied for a Pekar-Fröhlich polaron confined to a one-dimensional (1D) structure. The non-linear effective Schrödinger equation is solved exactly in the case of two different external potentials which imitate a finite size 1D sample: an infinite and a finite deep rectangular well. The ground state and excited states are calculated. We found that taking the limit of a finite size box to an infinitely large box leads to additional solutions which are not found in a treatment on an infinite axis. The additional solutions, which have a 1/n ² discrete spectrum, correspond to polaron states in which the wave function is split up in identical parts which are infinitely apart from each other.     

Strong-coupling limit for one-dimensional polarons in a finite box

The strong coupling limit is studied for a Pekar-Fröhlich polaron confined to a one-dimensional (1D) structure. The non-linear effective Schrödinger equation is solved exactly in the case of two different external potentials which imitate a finite size 1D sample: an infinite and a finite deep rectangular well. The ground state and excited states are calculated. We found that taking the limit of a finite size box to an infinitely large box leads to additional solutions which are not found in a treatment on an infinite axis. The additional solutions, which have a 1/n ² discrete spectrum, correspond to polaron states in which the wave function is split up in identical parts which are infinitely apart from each other.     

Stabilization of circular states of the hydrogen atom in a strong field

A solution of the three-dimensional time-dependent Schrödinger equation, describing the ionization dynamics of the hydrogen atom in a circular state in an electromagnetic field, is obtained by direct numerical integration. It is shown that the observed stabilization effect can be interpreted on the basis of the Kramers-Henneberger approach. A simple analytical model is proposed, which qualitatively describes the basic laws of the ionization process under the conditions of the reported calculations and laboratory experiments on ionization of the circular hydrogenlike 5g, m=4 state of the Ne atom.     

On the Energy of a “Two-Dimensional” Two-Electron Atom

With the use of the known solution of the Schrödinger equation for an electron in the nucleus field in the polar coordinates, the energy of a “two-dimensional” two-electron atom in the ground state, as well as its single ionization energy, has been calculated both in perturbation theory and with an almost century-old method of variation of the parameter Z in a trial wavefunction of the ground state. Since such two-dimensional atoms, e.g., helium atoms, can in principle be implemented in experiments by “freezing” of one degree of freedom in the phase of Bose–Einstein condensate, the conclusions made in this work can be tested. Fundamental features of the calculation of the energy of “one-dimensional” two-electron atoms and the formation of their Bose–Einstein condensate have also been discussed. The results obtained in this work coincide in a number of particular cases with the results obtained in a previous work, where some results were absent.     

Double ionization of helium studied with the multi-configuration time-dependent Hartree–Fock method

The intensity dependence of double ionization probability of helium in a strong laser field is investigated by using the multi-configuration time-dependent Hartree–Fock (MCTDHF) method. The results agree with the previous theoretical report by directly solving the time-dependent Schrödinger equation. The time evolution of electronic population on the ground state, electronic energy and dipole moment are also presented and discussed.     

Persistent currents and induced magnetization in presence of external magnetic field and transition probabilities in presence of combined laser pulse and external magnetic field for a confined hydrogen atom

In this work we propose to study an atom confined in a potential which consists of a Hulthén potential plus a ring-shaped potential. The atom is further subjected to a spherical confinement. The time-independent Schrödinger equation (TISE) of the system is solved numerically. Exact energy levels are obtained. The persistent current and induced magnetic field of such a confined atom is evaluated. Finally, the atomic system in this potential and confinement is subjected to short electromagnetic pulses, which are shown to induce enormous currents.     

Tunneling ionization of a hydrogen atom in short and ultrashort laser pulses

The ionization of a hydrogen atom in a linearly polarized low-frequency electromagnetic field is investigated by direct numerical integration of the time-dependent Schrödinger equation. The data obtained for various ionization regimes and various initial atomic states are compared with the Keldysh and Perelomov-Popov-Terent’ev (PPT) theories. The validity ranges for the quasi-static model of tunneling ionization and the PPT theory in laser intensity and frequency are determined. The tunneling ionization of the excited 2s and 2p states is discussed. The ionization of a hydrogen atom in an ultrashort (on the order of one optical period) pulse is investigated.     

Modern methods for calculating photoionization and electron-impact ionization of two-electron atoms and molecules

A number of recently developed methods for calculating multifold differential cross sections for photoionization and electron impact ionization of atoms and molecules with two active electrons are reviewed. The methods are based on unique approaches to the calculation of three-body Coulomb wave functions. The exterior scaling method and the driven Schrödinger equation formalism are considered. The effectiveness of the time-dependent approaches to the scattering problem, such as the paraxial approximation and the time-dependent scaling, is demonstrated. A novel numerical method is formulated, which has been developed by the authors to solve the six-dimensional Schrödinger equation for an atom with two active electrons on the basis of the Chang-Fano transformation and the discrete variable representation. The threshold behavior manifested by the angular distributions of the two-electron photoionization of a negative hydrogen ion and a helium atom and the multifold differential cross sections for the electronimpact ionization of hydrogen and nitrogen molecules are analyzed on the basis of numerical simulations. The Wannier law for the angular distribution of double ionization is demonstrated to be incorrect even at very low energies.     

The solution of the Schrödinger equation for coupled quadratic and quartic potentials in two dimensions

We deal with the difficulties claimed by the author of [Ann. Phys. 206, 90 (1991)] while solving the Schrödinger equation for the ground states of two-dimensional anharmonic potentials. It is shown that the ground state energy eigenvalues and eigenfunctions for the coupled quadratic and quartic potentials can be obtained by making some simple assumptions. Expressions for the energy eigenvalues and the eigenfunctions for the first and second excited states of these systems are also obtained.     

Nonlinear polarization response of a gaseous medium in the regime of atom stabilization in a strong radiation field

The nonlinear polarization response of a quantum system modeling a silver atom in the field of high-intensity radiation in the IR and UV spectral ranges has been studied by direct numerical integration of a nonstationary Schrödinger equation. The domains of applicability of perturbation theory and polarization expansion in powers of the field intensity are determined. The contribution of excited atoms and electrons in a continuum to the atomic polarization response at the field frequency, which arises due to the radiation-induced excitation and photoionization processes, is analyzed. Features of the nonlinear response to an external field under conditions of atom stabilization are considered.     

激光场中锂原子发射的电离阈值以下低阶谐波的研究

利用单电子近似下锂原子精确的模型势,通过数值求解三维含时薛定谔方程的方法,研究了锂原子在激光场中发射低阶谐波的性质,研究结果表明,对于锂原子电离阈值以下的低阶谐波,除了通常的奇次谐波外,还有侧峰结构出现,运用同步压缩变换技术(SST)分析这些低阶谐波的辐射特性,我们发现这些侧峰是由原子在激光场中的缀饰态之间的跃迁和无场下激发态到基态的跃迁组成的,如果当激光脉冲结束后,仍有发射的侧峰,其位置与主峰之间的能量差可以用来估算原子激发态在激光场中的最大Stark移动.     

Effects on the non-relativistic dynamics of a charged particle interacting with a Chern-Simons potential

The hydrogen atom in two dimensions, described by a Schrödinger equation with a Chern-Simons potential, is numerically solved. Both its wavefunctions and eigenvalues were determined for small values of the principal quantum number n. The only possible states correspond to l = 0. How the result depends on the topological mass of the photon is also discussed. In the case n = 1, the energy of the fundamental state, corresponding to different choice for the photon mass scale, are found to be comprehended in the interval ?3.5 × 10^-3 eV ≤ E ≤ ?9.0 × 10^?2 eV, corresponding to a mean radius of the electron in the range (5.637 ± 0.005) × 10^?8 cm ≤ ?r? ≤ (48.87 ± 0.03) × 10^-8 cm. In any case, the planar atom is found to be very weekly bounded showing some features similar to the Rydberg atoms in three dimensions with a Coulombian interaction.     

Quantum trajectory perspective of atom–field interaction in attosecond time scale

The ionization and high-harmonic generation in hydrogen and helium by using quantum (hydrodynamic) trajectories is analyzed theoretically. The quantum trajectories are introduced in the frame of a new time-dependent quantum Monte Carlo technique that allows a self-contained ab initio treatment of the electron correlation effects without introducing parametrized correlation potentials into the Schrödinger equation. Our approach predicts correct ionization, high-harmonic spectra, and attosecond pulses generated by a helium atom beyond the single active electron approximation. It can be used to study complex multi-electron systems in arbitrary dimensions and their interaction with laser fields of both low and high intensity.     

Chirp-dependent ionization of hydrogen atoms in the presence of super-intense laser pulses

We perform a theoretical study on dynamic interference in single photon ionization of ground state hydrogen atoms in the presence of a super-intense ultra-fast chirped laser pulse of different chirp types(equal-power and equal-FWHM laser pulses) by numerically solving the time-dependent Schr ¨odinger equation in one dimension. We investigate the influences of peak intensity and chirp parameters on the instantaneous ionization rate and photoelectron yield, respectively. We also compare the photoelectron energy spectra for the ionization by the laser pulses with different chirp types. We find that the difference between the instantaneous ionization rates for the ionization of hydrogen atom driven by two different chirped laser pulses is originated from the difference in variation of vector potentials with time.     

Nonlocality of a free atomic wave packet

A simple model allows us to study the nonclassical behavior of slowly moving atoms interacting with a quantized field. Atom and field become entangled and their joint state can be identified as a mesoscopic “Schrödinger cat”. By introducing appropriate observables for atom and field and by analyzing correlations between them based on a Bell-type inequality we can show the corresponding nonclassical behavior.     

用MCH方法研究库仑屏蔽势的高角动量能谱

以库仑屏蔽势为模型,用蒙特卡罗哈密顿方法对库仑屏蔽势束缚态进行研究,并把结果和传统的数值解一维薛定谔方程的方法相比较,在基态或激发态,都得出相一致的结果.