Bifurcation phenomena of photodetached electron flux in parallel external fields

A semiclassical method based on the closed-orbit theory is applied to analysing the dynamics of photodetached electron of H- in the parallel electric and magnetic fields. By simply varying the magnetic field we reveal spatial bifurcations of electron orbits at a fixed emission energy, which is referred to as the fold caustic in classical motion. The quantum manifestations of these singularities display a series of intermittent divergences in electronic flux distributions. We introduce semiclassical uniform approximation to repair the electron wavefunctions locally in a mixed phase space and obtain reasonable results. The approximation provides a better treatment of the problem.

Asymmetry in the Strong-field Photodetachment of H- by Linearly Polarized Few-cycle Pulses

Photodetachment of H- irradiated by linearly polarized few-cycle laser field is investigated by time-dependent SchrSdinger equation numerically. The photo-electron left-right asymmetry parameter as a function of carrier-envelop （CE） phase of few-cycle pulses is attained. We confirm the asymmetry of photoelectron distribution in H- photodetachment and find that the maximal asymmetry parameter of H- is equal to that of H atom under the same conditions but the corresponding CE phases are quite different. Thus a CE phase shift appears. Compared to that of H atom and field free electron, the zero asymmetry CE phase shift is sensitively affected by Coulomb field. The Coulomb effect on the asymmetry of H- photodetachment mainly behaves in the CE phase shift of H- instead of the amplitude of asymmetry parameter curve.

Collinear Velocity-map Photoelectron Imaging Spectrometer for Cluster Anions

We describe a collinear velocity-map photoelectron imaging spectrometer, which combines a Wiley-McLaren time-of-flight mass analyzer with a dual-valve laser vaporization source for investigating size-selected cluster and reaction intermediate anions. To generate the reaction anions conveniently, two pulsed valves and a reaction channel are employed instead of premixing carrier gas. The collinear photoelectron imaging spectrometer adopts modified velocity-map electrostatic lens, and provides kinetic energy resolution better than 3%. The performance of the instrument is demonstrated on the photodetachment of Si4^- at 532 and 355 nm, and SiaC^- at 532 nm, respectively. In both cases, photoelectron spectra and anisotropy parameters are obtained from the images. For Si4^-, the spectra show two well- resolved vibrational progressions which correspond to the ground state and the first excited state of the neutral Si4 with peak spacing of 330 and 312 cm^-1, respectively. Preliminary results suggest that the apparatus is a powerful tool for characterizing the electronic structure and photodetachment dynamics of cluster anions.

Double—Pulse Spectra and Closed—Orbits：Photodetachment of H^— in parallel Electric and Magnetic Fields

We derive a formula for double-pulse spectra from closed-orbit theory. We then calculate the double-pulse photodetachment spectra of H? in the presence of parallel electric and magnetic fields. We analyze the spectra in terms of closed-orbits of the system. We suggest a method for the measurement of a phase associated with each closed-orbit.

The influence of electric field on the photodetachment of H^- near a metal surface

The influence of electric field on the photodetachment of H- near a metal surface is investigated based on the closed-orbit theory. It is found that the photodetachment of H- near a metal surface is not only related to the electric field strength but also to the electric field direction. If the electric field is along the ＋z axis, it can strengthen the oscillation in the photodetachment cross section. However, if the electric field is along the -z axis, since the direction of electric field force is opposite to that of static-image force caused by the metal surface, the situation becomes much more complicated. When the electric field is very weak, its influence can be neglected. The photodetachment cross section is nearly the same as that when a single metal surface exists. When the electric field strength is strong enough, the electric field force is able to counteract the metallic attraction, therefore no closed orbit is formed. If the electric field continues to increase until its influence becomes dominant, the photodetachment cross section approaches the case of the photodetachment of H^- in an electric field. Our results may be useful for guiding future experimental studies on the photodetachment of negative ions near surfaces.

Magnetic field effect in photodetachment from negative ion in electric field near metal surface

Based on the closed-orbit theory, the magnetic field effect in the photodetachment of negative ion in the electric field near a metal surface is studied for the first time. The results show that the magnetic field can produce a significant effect on the photodetachment of negative ion near a metal surface. Besides the closed orbits previously found by Duet al. for the H in the electric field near a metal surface （J. Phys. B 43 035002 （2010））, some additional closed orbits are produced due to the effect of magnetic field. For a given ion surface distance and an electric field strength, the cross section depends sensitively on the magnetic field strength. As the magnetic field strength is very small, its influence can be neglected. With the increase of the magnetic field strength, the number of the closed orbits increases greatly and the oscillation in the cross section becomes much more complex. Therefore we can control the photodetachment cross section of the negative ion by changing the magnetic field strength. We hope that our results may guide future experimental studies for the photodetachment process of negative ion in the presence of external fields and surfaces.

Photodetachment of hydrogen negative ion inside a circular microcavity

The photodetachment of a hydrogen negative ion inside a circular microcavity is studied based on the semiclassical closed orbit theory. The closed orbit of the photo-detached electron in a circular microcavity is investigated and the photodetachment cross section of this system is calculated. The calculation result suggests that oscillating structure appears in the photodetachment cross section, which is caused by the interference effects of the returning electron waves with the outgoing waves traveling along the closed orbits. Besides, our study suggests that the photodetachment cross section of the negative ions depends on the laser polarization sensitively. In order to show the correspondence between the cross section and the closed orbits of the detached electron clearly, we calculate the Fourier transformation of the cross section and find that each peak corresponds to the length of one closed orbit. We hope that our results will be useful for understanding the photodetachment process of negative ions or the electron transport in a microcavity.

Recurrence Spectra of the Rydberg Hydrogen Atom near Two Parallel Metal Surfaces

Using closed orbit theory, we study the influence of the two parallel metal surfaces on the recurrence spectra of a hydrogen atom placed in the region between the two surfaces. The results show that the metal surfaces have significant effect on the photoabsorption process. Each resonance peak in the recurrence spectra is associated with one electronic closed orbit. In our work, we put the first metal surface at the critical value dc and vary the second metal surface. The results show that when the distances between the hydrogen atom and the two metal surfaces are close to the critical valuedc, the number of the closed orbits is the greatest and there are more peaks in the recurrence spectra. When the distance between the atom and the second metal surface is larger or smaller than dc, the number of the closed orbits decreases and there are fewer peaks in the recurrence spectra. The agreement between the semiclassical calculation spectra and the quantum calculation spectra suggests that our analysis is correct.

Photodetachment of H^- Near a Dielectric Surface

Using the closed orbit theory, the photodetachment cross section of H- near a dielectric surface has been derived and calculated. The results show that the dielectric surface has great influence on the photodetachment process of negative ion near the ionization threshold. Above the ionization threshold, the photodetachment cross section starts to oscillate. With the increase of the energy, the oscillating amplitude decreases and the oscillating frequency increases. The oscillation in the photodetachment cross section of H- in the presence of a dielectric surface is either larger or smaller than the photodetachment of H- without the surface. As the photon energy is larger than the critical value Epc, the oscillatory structure disappeared and the cross section approaches to the case of the photodetachment of H- without any external fields. For a given detached-electron energy, the photodetachment cross section becomes decreased with the increase of the ion-surface distance. Besides, the dielectric constant has great influence on the photodetachment of H-. With the increase of the dielectric constant, the oscillation in the cross section becomes increased. As the dielectric constant increases to infinity, the cross section is the same as the photodetachment of H- near a metal surface. This study provides a new understanding on the photodetachment process of H- in the presence of a dielectric surface.

Interferences in Photodetachment of a Negative Molecular Ion Model

By employing a two-center model, the total and differential cross sections in the photodetachment of ＂a negative molecular ion＂ are studied theoreticedly and obtained for the case of light polarization paredlel to the molecular axis. We find that in contrast to the smooth behavior of the total cross section for perpendicular polarized light, the cross section for parallel polarized light shows an interesting oscillatory structure. The oscillations in the toted cross section may provide a method to determine the distance between the two centers. We explain the oscillation in the toted cross section as an interference effect using closed-orbit theory. We also cedculated the detached-electron flux distributions on a screen placed at a large distance from the negative molecular ion. The distributions display multiple-ring-like interference patterns. Such interference patterns are similar to those in the photodetachment microscopy experiments.

Photodetachment of negative ion in a gradient electric field near a metal surface

Based on closed-orbit theory, the photodetachment of H- in a gradient electric field near a metal surface is studied. It is demonstrated that the gradient electric field has a significant influence on the photodetachment of negative ions near a metal surface. With the increase of the gradient of the electric field, the oscillation in the photodetachment cross section becomes strengthened. Besides, in contrast to the photodetachment of H- near a metal surface in a uniform electric field, the oscillating amplitude and the oscillating region in the cross section of a gradient electric field also become enlarged. Therefore, we can use the gradient electric field to control the photodetachment of negative ions near a metal surface. We hope that our results will be useful for understanding the photodetachment of negative ions in the vicinity of surfaces, cavities, and ion traps.

Quantum calculations for photodetachment cross sections of H^- in an inhomogeneous electric field

We calculate the photodetachment cross sections of H- in a gradient electric field based on traditional quantum approach. The system provides a rare example that the formulas for the cross sections can be explicitly derived by both the quantum approach and closed-orbit theory. The quantum results are compared with those of the closed-orbit theory. The correct phase values in the closed-orbit theory are essential and necessary to produce accurate cross sections. Our quantum results remove some previous ambiguities in assigning the phase values in the closed-orbit theory （G. C. Yang and M. L. Du 2007 Phys. Rev. A 75 029904E）.

Photodetachment microscopy of a hydrogen negative ion in an electric field near a metal surface

According to the semi-classical theory, we study the photodetachment microscopy of H- in the electric field near a metal surface. During the photodetachment, the electron is photo-detached by a laser and the electron is drawn toward a position-sensitive detector. The electron flux distribution is measured as a function of position. Two classical paths lead the ion to any point in the classically allowed region on the detector, and waves traveling along these paths produce an interference pattern. If the metal surface perpendicular to the electric field is added, we find that the interference pattern is related not only to the electron energy and the electric-field strength, but also to the ion surface distance. In addition, the laser polarization also has a great influence on the electron flux distribution. We present calculations predicting the interference pattern that may be seen in experiment. We hope that our study can provide a new understanding of the electron flux distribution of negative ions in an external field and surface, and can guide future experimental research on negative ion photo-detachment microscopy.

Interferences in Photodetachment of a Negative Molecular Ion

The photodetachment of a negative molecular ion is studied theoretically using a two-center model. The detached electron wave function is obtained as a superposition of two coherent waves originating from each center. The photo-detached electron flux is evaluated on a screen placed at a large distance from the negative molecular ion. The electron flux on the screen displays strong interferences, the peak positions are related to the distance between the two centers in the negative molecular ion. We a/so obtained a simple analytical formula for the total photodetachment cross section. It approaches one and two times of the cross section for the one-center system in the high and lowphoton energy limits respectively.

Photodetachment of H^- in an electric field between two parallel interfaces

By using the closed orbit theory, the photodetachment cross section of H- in a static electric field between two parallel elastic interfaces is derived and calculated. It is found that the photodetachment cross section depends on the electric field and the distance between the ion and the elastic interface. The oscillation of the cross section becomes more complicated than in the case of H- near one elastic interface. The results show that near the detachment threshold, the influence of the additional interface can be neglected. But with the increase of the energy, its influence becomes great. At some energies, the cross sections display sharp peaks, contrasting with the staircase structure when only one interface exists. This study provides a new understanding of the photodetachment process of H- in the presence of external field and interfaces.

Autocorrelation Function of Hydrogen Atoms in Magnetic Fields

The autocorrelation function is an important quantity that can reflect the dynamical properties of the Rydberg wave packet and can be measured in experiments. Applying time-dependent perturbation theory and rotating wave approximation, we derive the autocorrelation function of the double-pulse laser describing the evolution of a Rydberg wave packet of hydrogen atoms in magnetic fields. The resulting expression is written as a sum of the modified Caussian terms. Each Caussian term comes from a parent semiclassical closed orbit. It provides a direct explanation and experimentally controllable measurement scheme, which allows us therefore to recognize the closed orbit and to determine its returning time in high precision.

Photodetachment of H^-near an elastic surface in a magnetic field

This paper investigates the photodetachment of the negative hydrogen ion H- near an elastic wall in a magnetic field. The magnetic field confines the perpendicular motion of the electron, which results in a real three-dimensional well for the detached electron. The analytical formulas for the cross section of the photodetachment in the three-dimensional quantum well are derived based on both the quantum approach and closed-orbit theory. The magnetic field and the elastic surface lead to two completely different modulations to the cross section of the photodetachment. The oscillation amplitude depends on the strength of the magnetic field, the ion-wall distance and the photon polarization as well. Specially, for the circularly polarized photon-induced photodetachment, the cross sections display a suppressed （E - Eth）1/2 threshold law with energy E in the vicinity above Landau energy Eta, contrasting with the （E - Eta）-1/2 threshold law in the presence of only the magnetic field. The semiclassical calculation fits the quantum result quite well, although there are still small deviations. The difference is attributed to the failure of semiclassical mechanics.

Electric flux distribution in photodetachment of heteronuclear diatomic molecular negative ion

The photodetachment of a hetero-nuclear diatomic molecular negative ion is studied by using a two-centre model. An analytic formula is presented for the electron flux distribution of a heteronuclear diatomic molecular negative ion. Taking HF- as an example, we calculated the electron flux distributions of this ion for various detached electron energies. The results show that the electron flux distributions exhibit oscillatory structures, which are caused by the interference effect between the two nuclei. Besides, the laser light polarization also has a great influence on the electron flux distribution. The oscillation amplitude is the largest when the laser polarization is parallel to the z-axis; when the laser polarization is perpendicular to the z-axis, the oscillation almost vanishes. This study provides a new understanding of the photodetachment of a heteronuclear diatomic molecular negative ion.

Photodetachment of H^- near a hard wall with arbitrary laser polarization direction

The photodetachment of H-near a hard wall is investigated with linear polarized laser light travelling in arbitrary direction θL with respect to the z axis. An analytical formula for the total cross section is derived using semi-classical closed orbit theory, which consists of two terms, i.e., the smooth background term and the oscillatory term with an extra factor 2(θL). This factor controls oscillations in the total photodetachment cross section. The amplitude of oscillation is maximum at θL = 0 when the laser polarization direction is perpendicular to the wall and it approaches zero at θL = π /2when the laser polarization direction is parallel to the wall. It is also observed that the total cross section depends on the source–wall distance and it reduces to a free space case when the wall is at infinite distance from the source.

The influence of interface modifier on photodetachment of negative ions in an electric field near a metal surface

Based on closed-orbit theory, the influence of an interface modifier on the photodetachment of H^- in an electric field near a metal surface is studied. It is demonstrated that the interface strengthens the oscillations in the photodetachment cross section. However, when the electric field environments are different, the strengthening oscillations are caused by different sources. When the electric field direction is upward, the interface enhances the oscillations by shortening the period and the action of the closed orbit. When the electric field direction is downward, the interface strengthens the oscillations either by extending the coherent energy range or by increasing the total number of the closed orbits. We hope that our results will be conducive to the understanding of the photodetachment process of negative ions near interfaces, cavities and ion traps.