Semiclassical Calculations of Autoionization Rate for Lithium Atoms in Parallel Electric and Magnetic Fields

By using a semiclassical method, we present theoretical computations of the ionization rate of Rydberg lithium atoms in parallel electric and magnetic fields with different scaled energies above the classical saddle point. The yielded irregular pulse trains of the escape electrons are recorded as a function of emission time, which allows for relating themselves to the terms of the recurrence periods of the photoabsorption. This fact turns to illustrate the dynamic mechanism how the electron pulses are stochastically generated. Comparing our computations with previous investigation results, we can deduce that the complicated chaos under consideration here consists of two kinds of seff-similar fractal structures which correspond to the contributions of the applied magnetic feld and the core scattering events. Furthermore, the effect of the magnetic field plays a major role in the profile of the autoionization rate curves, while the contribution of the core scattering is critical for specifying the positions of the pulse peaks.     

Limitations of the strong field approximation in ionization of the hydrogen atom by ultrashort pulses

We present a theoretical study of the ionization of hydrogen atoms as a result of the interaction with an ultrashort external electric field. Doubly-differential momentum distributions and angular momentum distributions of ejected electrons calculated in the framework of the Coulomb-Volkov and strong field approximations, as well as classical calculations are compared with the exact solution of the time dependent Schr ödinger equation. We show that in the impulsive limit, the Coulomb-Volkov distorted wave theory reproduces the exact solution. The validity of the strong field approximation is probed both classically and quantum mechanically. We found that classical mechanics describes the proper quantum momentum distributions of the ejected electrons right after a sudden momentum transfer, however pronounced the differences at latter stages that arise during the subsequent electron-nucleus interaction. Although the classical calculations reproduce the quantum momentum distributions, it fails to describe properly the angular momentum distributions, even in the limit of strong fields. The origin of this failure can be attributed to the difference between quantum and classical initial spatial distributions.     

Reduction of multi-photon ionization in dielectrics due to collisions

The collisional effect due to the multi-photon ionization process in dielectric material has been studied. We found that the breakdown threshold of fused silica is the same for both linearly and circularly polarized light at 55 fs and 100 fs, which we believe is an indication of the suppression of multi-photon ionization in solids. By numerically solving the time-dependent Schrödinger equation with scattering, for the first time, we have observed substantial reduction of the multi-photon ionization rate in dielectrics due to collisions.     

Relativistic version of the imaginary-time formalism

A relativistic version of the quasiclassical imaginary-time formalism is developed. It permits calculation of the tunneling probability of relativistic particles through potential barriers, including barriers lacking spherical symmetry. Application of the imaginary-time formalism to concrete problems calls for finding subbarrier trajectories which are solutions of the classical equations of motion, but with an imaginary time (and thus cannot be realized in classical mechanics). The ionization probability of an s level, whose binding energy can be of the order of the rest energy, under the action of electric and magnetic fields of different configuration is calculated using the imaginary-time formalism. Besides the exponential factor, the Coulomb and pre-exponential factors in the ionization probability are calculated. The Hamiltonian approach to the tunneling of relativistic particles is described briefly. Scrutiny of the ionization of heavy atoms by an electric field provides an additional argument against the existence of the “Unruh effect.” Zh. éksp. Teor. Fiz. 114, 798–820 (September 1998)     

Classical Effects of Carrier--Envelope Phase on Nonsequential Double Ionization

A classical microcanonical 1＋1-dimensional model is used to investigate the ion momentum distributions in nonsequential double ionization with linearly polarized few-cycle pulses. We find that the ion momentum distribution has a strong dependence on the carrier-envelope phase of the few-cycle pulse, which is consistent with the experimental results qualitatively. Back analysis shows that the ionization probability of the first electron at different phases and its returning kinetic energy play the main role on the ion momentum distributions.     

Semiclassical calculation of ionization rate for Rydberg hydrogen atoms near a metal surface

The ionization of Rydberg hydrogen atoms near a metal surface at different scaled energies above the classical saddle point energy has been discussed by using the semiclassical method. The results show that the atoms ionize by emitting a train of electron pulses. In order to reveal the chaotic and escape dynamical properties of this system in detail, the sensitive dependence of the ionization rate upon the scaled energy is discussed. As the scaled energy is close to the saddle point energy, the ionization process of the hydrogen atom is nearly the same as the case of hydrogen atom in an electric field. There is only a single pulse of electrons, with an exponentially decaying tail. With the increase of the scaled energy, the ionization rates are similar to the case of the hydrogen atom in parallel electric and magnetic field, a series of electron pulses appear in the ionization process. This is caused by classical chaos, which occurs for the metal surface. Our studies also suggest that the metal surface can play the role of both the electric and the magnetic fields. Our theoretical analysis will be useful for guiding experimental studies of the ionization of atoms near the metal surface.     

Ionization of atoms in electric and magnetic fields and the imaginary time method

A semiclassical theory is developed for the ionization of atoms and negative ions in constant, uniform electric and magnetic fields, including the Coulomb interaction between the electron and the atomic core during tunneling. The case of crossed fields (Lorentz ionization) is examined specially, as well as the limit of a strong magnetic field. Analytic equations are derived for arbitrary fields ℰ and ℋ that are weak compared to the characteristic intraatomic fields. The major results of this paper are obtained using the “imaginary time” method (ITM), in which tunneling is described using the classical equations of motion but with purely imaginary “time.” The possibility of generalizing the ITM to the relativistic case, as well as to states with nonzero angular momentum, is pointed out. Zh. éksp. Teor. Fiz. 113, 1579–1605 (May 1998)     

Isotope selective loading of an ion trap using resonance-enhanced two-photon ionization

We have demonstrated that resonance-enhanced two-photon ionization of atomic beams provides an effective tool for isotope selective loading of ions into a linear Paul trap. Using a tunable, narrow-bandwidth, continuous wave (cw) laser system for the ionization process, we have succeeded in producing Mg⁺ and Ca⁺ ions at rates controlled by the atomic beam flux, the laser intensity, and the laser frequency detuning from resonance. We have observed that with a proper choice of control parameters, it is rather easy to load a specific number of ions into a string. This observation has direct applications in quantum optics and quantum computation experiments. Furthermore, resonant photo-ionization loading facilitates the formation of large isotope-pure Coulomb crystals. Received: 21 December 1999 / Published online: 11 May 2000     

Sub-Half-Wavelength Atom Localization via Coherent Control of Autler-Townes Spontaneous Spectrum

We show that it is possible to localize an atom in a half-wavelength region by relaxing the strict condition that the atom is prepared in a specific excited state as in the recently proposed scheme [Phys. Rev. A 65 （2002） 043819]. In particular, we consider a four-level atom, for which a weak exciting field transfers population from the ground state to the excited state and three control fields （one standing-wave field while two travelling-wave fields） couple the excited state and two auxiliary states. By tuning the exciting field and by varying the collective phase of the control fields, the atom is localized in one of the two half-wavelength regions with 50% detecting probability. The main advantage of the scheme is the experimental accessibility and controllability.     

Ionization of Rydberg atoms in THz-laser fields at the transition from low to high scaled frequencies

We have studied the ionization of Rydberg-excited xenon atoms in THz-laser fields and by quantum dynamical calculations. The experimental threshold laser field strength for 10% ionization probability follows an n^*-1.68 (1.04 THz) dependence (n^* effective principal quantum number) with additional weak resonance structures and shows that ionization does not occur by a Landau-Zener mechanism. At scaled frequencies of to 5.6 the simulated threshold fields for ionization in oscillatory fields show a dependence on the principal quantum number n of n^-4.1 to n^-1.35. Received: 17 February 1998 / Revised: 20 April 1998 / Accepted: 21 April 1998     

The quantum acousto-optic effect in Bose-Einstein condensate

We investigate the interaction between a single mode light field and an elongated cigar shaped Bose-Einstein condensate (BEC), subject to a temporal modulation of the trap frequency in the tight confinement direction. Under appropriate conditions, the longitudinal sound like waves (Faraday waves) in the direction of weak confinement acts as a dynamic diffraction grating for the incident light field analogous to the acousto-optic effect in classical optics. The change in the refractive index due to the periodic modulation of the BEC density is responsible for the acousto-optic effect. The dynamics is characterised by Bragg scattering of light from the matter wave Faraday grating and simultaneous Bragg scattering of the condensate atoms from the optical grating formed due to the interference between the incident light and the diffracted light fields. Varying the intensity of the incident laser beam we observe the transition from the acousto-optic effect regime to the atomic Bragg scattering regime, where Rabi oscillations between two momentum levels of the atoms are observed. We show that the acousto-optic effect is reduced as the atomic interaction is increased.     

Dynamics of localized wave packets of rotational states of a molecule in a strong laser field

Numerical simulations are performed to examine the rotational dynamics of a molecule in a strong laser field when the molecular axis is initially oriented in a certain direction. The results obtained by solving the quantum-mechanical problem are compared with those computed in the framework of classical mechanics. It is found that certain characteristics of rotational motion cannot be described by classical theory, particularly for light molecules. It is demonstrated that the axis of a heteronuclear molecule can be reversed by tunneling.     

Semiclassical Dirac theory of tunnel ionization

We present analytic tunnel ionization rates for hydrogenlike ions in ultrahigh intensity laser fields, as obtained from a semiclassical solution of the three-dimensional Dirac equation. This presents the first quantitative determination of tunneling in atomic ions in the relativistic regime. Our theory opens the possibility to study strong laser field processes with highly charged ions, where relativistic ionization plays a dominant role.     

Angular momentum distribution in strong-field frustrated tunneling ionization

Using the classical-trajectory Monte Carlo model, we have theoretically studied the angular momentum distribution of frustrated tunneling ionization(FTI) of atoms in strong laser fields. Our results show that the angular momentum distribution of the FTI events exhibits a double-hump structure. With this classical model, we back traced the tunneling coordinates, i.e., the tunneling time and initial transverse momentum at tunneling ionization. It is shown that for the events tunneling ionized at the rising edge of the electric field,the final angular momentum exhibits a strong dependence on the initial transverse momentum at tunneling.While for the events ionized at the falling edge, there is a relatively harder recollision between the returning electron and the parent ion, leading to the angular momentum losing the correlation with the initial transverse momentum. Our study suggests that the angular momentum of the FTI events could be manipulated by controlling the initial coordinates of the tunneling ionization.     

Quasiclassical dynamics of resonantly driven Rydberg states

We present a semiclassical analysis of the dynamics of Rydberg states of atomic hydrogen driven by a resonant microwave field of linear polarization. The semiclassical quasienergies of the atom in the field are found to be in very good agreement with the exact quantum solutions. The ionization rates of individual eigenstates of the atom dressed by the field reflect their quasiclassical dynamics along classical periodic orbits in the near integrable regime, but exhibit a transition to nonspecific rates when global chaos takes over in phase space. We concentrate both on the principal resonance where the unperturbed Kepler frequency is equal to the driving field frequency and on the higher primary resonance The latter case allows for the construction of nondispersive wave packets which propagate along Kepler ellipses of intermediate eccentricity. Received: 23 June 1998 / Accepted: 10 November 1998     

Ionization of a hydrogen atom from its ground state by a coherent bichromatic laser field

We study the “coherent phase control” between the three-photon ionization by a fundamental laser field and the one-photon ionization by its third harmonic for a hydrogen atom in its ground state. The relative phase δ of the harmonic field with respect to the fundamental laser radiation “modulates” the interference between the two ionization channels, which is important near the crossing points between the ionization rates of the two individual processes. Numerical results for the total ionization rate and for the angular distribution of the photoelectrons as a function of the phase δ are presented for frequencies located in the vicinity of the atomic resonances corresponding to the absorption of two laser photons. Received 31 August 2000 and Received in final form 6 February 2001     

Quantum chaotic scattering in atomic physics: Ericson fluctuations in photoionization

We report the first experimental investigation of quantum chaotic scattering in an atomic system: in strong crossed magnetic and electric fields in an energy regime beyond the ionization threshold, where the classical dynamics is an example of chaotic scattering. We find Ericson fluctuations in the spectra for photo excitation into this regime. This result constitutes the first observation of Ericson fluctuations in atomic and molecular physics. Furthermore, we confirm the prediction that chaotic scattering in the underlying classical dynamics implies Ericson fluctuations.     

Deep impurity-center ionization by far-infrared radiation

An analysis is made of the ionization of deep impurity centers by high-intensity far-infrared and submillimeter-wavelength radiation, with photon energies tens of times lower than the impurity ionization energy. Within a broad range of intensities and wavelengths, terahertz electric fields of the exciting radiation act as a dc field. Under these conditions, deep-center ionization can be described as multiphonon-assisted tunneling, in which carrier emission is accompanied by defect tunneling in configuration space and electron tunneling in the electric field. The field dependence of the ionization probability permits one to determine the defect tunneling times and the character of the defect adiabatic potentials. The ionization probability deviates from the field dependence e(E) ∝ exp(E ²/E _c ² ) (where E is the wave field, and E _c is a characteristic field) corresponding to multiphonon-assisted tunneling ionization in relatively low fields, where the defects are ionized through the Poole-Frenkel effect, and in very strong fields, where the ionization is produced by direct tunneling without thermal activation. The effects resulting from the high radiation frequency are considered and it is shown that, at low temperatures, they become dominant. Fiz. Tverd. Tela (St. Petersburg) 39, 1905–1932 (November 1997)     

Non-adiabatic quantum molecular dynamics: General formalism and case study H<Subscript>2</Subscript><Superscript>+</Superscript> in strong laser fields

In Rydberg atoms subject to static and harmonic collinear electric fields, intrashell transition can be induced by the first order perturbation from a small perpendicular electric or magnetic field, or by effects of the second order in the major fields. Both mechanisms lead to resonances that are suppressed under certain conditions, and high-frequency interference oscillations in case of non-adiabatic field switching. Recent measurements of microwave ionization signals show very rich and fascinating structures similar to the ones predicted for intrashell mixing. We show that the observed ionization structures may be explained by diabatic electric-field ionization and the consistent use of perturbation theory for intrashell mixing. In particular, the dominant oscillation frequency is successfully interpreted in terms of interference between first and second order transition amplitudes. New predictions are provided. The present approach gives a comprehensive picture of intrashell transitions, which may be tested in future experiments designed to observe such transitions directly. Received 2 May 2002 / Received in final form 23 September 2002 Published online 21 January 2003 RID="a" ID="a"e-mail: Valentin.Ostrovsky@pobox.spbu.ru RID="b" ID="b"e-mail: horsdal@ifa.au.dk     

Study on Non-Sequential Double Ionization of Aligned Diatomic Molecules in Strong Laser Fields

We develop a semiclassical model to describe the non-sequential double ionization of aligned diatomic molecules in an intense linearly polarized field. It is found that in the tunnelling regime, the oriented molecule shows geometric effects on double ionization process when aligned parallel and perpendicular to the external field. Our results are qualitatively consistent with the recent experimental observations.