Multiphoton Ionization of Atoms by Two Radiation Fields: Theory and Calculations for Hydrogen

Abstract

An approximate non-perturbative theory of multiphoton ionization of a hydrogen atom by two strong radiation fields is outlined. The special case is then considered for when one of the fields is of low intensity and high frequency and the other field is of high intensity and low frequency. A set of representative calculations has been performed for this case; that is, (a) angular distributions for given numbers of absorbed and emitted low-frequency photons and different geometries; (b) total cross-sections versus the strong-field intensity; (c) angular distributions summed over all the low-frequency photon exchanges, showing a fourfold symmetry in a geometry in which each ionization channel exhibits, instead, only a twofold symmetry; (d) the average energy gained by the ejected electrons. Calculations are performed for a strong low-frequency field of arbitrary polarization. In many respects, the present calculations are expected to complement those of single-field multiphoton ionization. It is hoped that the results of the calculations reported here may prompt systematic measurements also in this new class of processes, as the predictions are well within the state of the art of present multiphoton-ionization experiments.     

Saturation Effects in the Spatial and Energy Distributions in Short-pulse High-intensity Multiphoton Ionization

Abstract

We have calculated the spatial and electron energy structure for short-pulse high-intensity multiphoton ionization taking into account saturation. Using an avoided-crossing picture, we have modelled multiphoton resonances induced by the high-intensity a.c. Stark effect. We have explicitly considered ionization due to the rising and falling edges of the laser pulse including saturation and ground-state depletion. Using only the laser-pulse duration as the adjustable parameter, our results show the dramatic modifications both to the spatial structure and to the photoelectron energy spectrum as saturation becomes important.     

A comparison of avalanche breakdown probabilities in semiconductor materials

Abstract

Using a hard dead space impact ionization model, the dependence of breakdown probabilities on overbias ratio in single photon avalanche diodes is investigated theoretically in a variety of semiconductor materials for the simple case of constant electric field, that is, in a p⁺-i-n⁺ diode structure. By using avalanche widths of 2 μm, the effects of dead space are minimized so that the breakdown probability results are determined primarily by the enabled ionization coefficients of the materials. The results illustrate how the slope of breakdown probability with overbias ratio is affected by the enabled ionization coefficients ratio and by the field dependences of ionization coefficients, which should be taken into account when choosing semiconductor materials for single photon avalanche diodes.     

Effect of a Multimode Laser Field on Multichannel Multiphoton Ionization of Hydrogen

Abstract

The effect of the multimode structure of a laser field on multichannel multiphoton ionization is investigated, taking the hydrogen atom as a study case. It is found that at moderately high laser intensity the ionization rate into a given channel is changed by varying the number of modes in a similar way to the single-channel multiphoton ionization. At higher intensities the ionization rates saturate, reaching a maximum which is almost independent of the number of modes. In the saturation regime a peaking approximation is performed which gives the ionization rate in a given channel as a simple analytical function of the number of modes and the laser intensity, and provides a useful insight into the characteristic features of the process.     

Magnetic field effect on highly excited states near ionization potential of nitric oxide

Fluorescence excitation spectra due to the A ²∑–X ²Π transition of gaseous nitric oxide (NO) were measured in magnetic fields, H; ranging from 0 ≤ H ≤ 10 T. Lines in the observed spectra were assigned by using quantum mechanical calculations. Based on the assignment, two-color resonance-enhanced multiphoton ionization spectra via a single Zeeman sublevel in the A state were measured to observe the effect of magnetic fields on electronic states near the ionization potential (IP). Complicated structures due to strong n- and l-mixing in highly excited Rydberg states were observed below the IP. It was found that new resonance appears above the IP for H ≤ 4T. By using a semi-classical calculation, this resonance was assigned to the quasi-Landau resonance, which was observed for the first time in molecules.

© 2003 Elsevier Ltd. All rights reserved.     

Polarization recording of holograms in partially polarized recording light

A theoretical approach is considered for media whose scalar and anisotropic responses are of opposite sign. The nondiffracted beam, and the imaginary and real images formed by a polarization hologram are analyzed under these conditions. It is shown that the imaginary image has its polarization transformed compared with the object field while a pseudoscopic object field reconstructed in terms of polarization state and degree is formed in the real image. Pis’ma Zh. Tekh. Fiz. 23, 38–42 (February 12, 1997)     

On the Squeezing of Coherent States by the Multiphoton Jaynes-Cummings Hamiltonian with an Intensity-dependent Coupling

Abstract

The squeezing properties of the multiphoton Hamiltonian with intensity-dependent coupling are evaluated for the [xcirc] and [pcirc] _x quadratures, for the initial state of a coherent electromagnetic field and an atom in the ground state. Two measures of squeezing: the percentage of total squeezing and the squeezing time-period percentage, are introduced. Interesting squeezing properties with respect to [xcirc] are observed for real coherent states when the time evolution of the above measures and of the time-averaged squeezing are analysed. The multiphoton intensity-dependent coupling Hamiltonian is found to be almost independent of the specific powers of the annihilation and creation operators, as long as the sum of the powers is kept constant.     

Periodic Squeezing in the Tavis-Cummings Model

Abstract

By utilizing our previous operator solution [17], we have investigated the squeezing in the radiation field of the Tavis-Cummings model (collective N ? 1 two-level atoms interacting with a resonant single cavity quantized mode). With field and atoms initially in coherent field state strong or weak and atomic coherent state (of few excited atoms), periodic time-dependent squeezing in the field and the macroscopic polarization is expressed in terms of Jacobian elliptic functions of the first kind. The statistical investigations are carried out for the quasiprobability distribution functions (Wigner function and Q function). The distribution function of the field quadrature has a variance less (greater) than that for a coherent state if this quadrature is squeezed (unsqueezed).     

Magnetic field effect on highly excited states near ionization potential of nitric oxide

Fluorescence excitation spectra due to the A ²Σ–X ²Π transition of gaseous nitric oxide (NO) were measured in magnetic fields, H, ranging from 0≤H≤10 T. Lines in the observed spectra were assigned by using quantum mechanical calculations. Based on the assignment, two-color resonance-enhanced multiphoton ionization spectra via a single Zeeman sublevel in the A state were measured to observe the effect of magnetic fields on electronic states near the ionization potential (IP). Complicated structures due to strong n- and l-mixing in highly excited Rydberg states were observed below the IP. It was found that new resonance appears above the IP for H≥4 T. By using a semi-classical calculation, this resonance was assigned to the quasi-Landau resonance, which was observed for the first time in molecules.     

Squeezing in Multiphoton Absorption

Abstract

The conditions for obtaining squeezing by single-beam multiphoton absorption are examined. For an initial coherent light the amount of squeezing is calculated in the second order of interaction time using the master-equation formalism. A limit formula for the amount of squeezing is found in the case of an initial strong coherent beam. The results are compared with the exact numerical calculations and some remarks are made on the short-time approximation in multiphoton absorption.     

N-level Atom Interacting with Single-mode Radiation Field: An Exactly Solvable Model with Multiphoton Transitions and Intensity-dependent Coupling

Abstract

We study the dynamics of an N-level atom coupled in a lossless cavity to a single-mode near-resonant quantized field. The atomic levels are coupled by the multiphoton transitions and the coupling constants between the field and the atomic levels are supposed to be intensity dependent. We find the exact solution for the state vector describing the dynamics of the atom-plus-field system. As an illustration we use the model for studying (i) the time evolution of the atomic occupation probability with the initially coherent field and (ii) the light squeezing, when the cavity field is initially in the vacuum state and the atom is prepared in the atomic ‘coherent state’ (a superposition of atomic states).     

Degrees of mutual coherence of a 3D polarization state

Abstract

The absolute values of the three degrees of mutual coherence between the analytic signals representing the components of the electric field of a given three-dimensional (3D) polarization state are relative quantities that depend on the laboratory reference frame considered. The extremal values for the said absolute values are determined and analyzed. The reduction to the well-known conventional 2D case is retrieved in a natural way.     

Electron spectrum of atoms ionized by an ultrashort laser pulse of relativistic intensity

Energy transfer to electrons in atoms ionized by an ultrashort laser pulse of relativistic intensity (I > 10¹⁹ W/cm²) is considered. The ionization process is taken into account using the mechanism of direct suppression of the Coulomb barrier in a laser field. The acceleration of electrons in the laser wave field is described in terms of the classical relativistic equation of motion. Electron energies in the final state are determined as dependent on the average intensity of a laser pulse with a given shape. A distribution of the final energies of electrons upon multiple ionization of a complex atom is found.     

Two-colour strong-field ionization and dissociation of H2 using 780 and 390 nm femtosecond pulses

Abstract

We report the observation of a substantial enhancement in H₂ ⁺ and H⁺ ion production when the two-colour (780 and 390 nm) pulses are superposed. A strong dependence of ion yield on the relative directions of the polarization of the two fields is observed. The experimental results are discussed and compared with existing theoretical calculations.     

Multiphoton Jaynes-Cummings Model without the Rotating-wave Approximation

Abstract

The general time evolution of operators in the multiphoton Jaynes-Cummings model without the rotating-wave approximation is obtained. The contributions of the counter-rotating terms to atomic dynamics and field squeezing are examined in multiphoton processes.     

Higher-generation Schrödinger cat states in cavity QED

Abstract

Higher-generation Schrödinger cat states of the quantized electromagnetic field can be produced in a high-Q cavity, starting from a coherent state, through the passage of prepared Rydberg atoms interacting dispersively across it. These states are natural generalizations of the even and odd coherent states, the N ^th-generations corresponding to specific superpositions of 2 ^N states on a circle in phase space with well defined parity, and present very peculiar properties. Their photon statistics interchange between super- and sub-Poissonian behaviours and the nature of the photon bunching oscillates as the field intensity in the cavity is varied. For higher-generation even states, the minimum value of the Mandel factor almost reaches ?1.0 and the state represents the Fock state |2 ^N ). Squeezing properties and the Wigner function of these higher-generation Schrödinger cat states are also considered.     

Collapse-revival Phenomenon in the Jaynes-Cummings Model Interacting with the Multiphoton Holstein-Primakoff SU(2) Coherent State

Abstract

We have analysed the behaviour of the atomic population inversion of the two-level atom interacting with a single-mode field initially prepared in the multiphoton Holstein-Primakoff SU(2) coherent state. It is shown that the behaviour of the atomic inversion depends on the parameters characterizing the initial state of the field. In particular, the atomic inversion can exhibit periodical oscillations as well as the collapse-revival phenomenon.     

Cavity field spectrum for multiphoton Jaynes-Cummings model

Abstract

The field spectra in an ideal cavity for the multiphoton Jaynes-Cummings model are studied. The analytical expression for the spectrum is obtained from the finite double-Fourier transform of the two-time field correlation function. The spectral differences between the initial coherent and initial thermal states are discussed, and the comparisons between the field spectra and atomic emission spectra for k = 2, 3 and 4 are presented. It is shown that the kth power of the photon annihilation operator and atomic lowering operator are subjected to identical forms of a second-order differential equation, in which the coefficients consist of the constants of motion. The field spectrum in the cavity and the emission spectrum of the atom for the initial vacuum state are compared.     

The orientational phase transition at a vortex in3He-B

The orientational phase transition in the vicinity of a single vortex in³He-B is studied. It is the phase transition from a uniformn-texture withn parallel to the magnetic field and the vortex line to ann-texture that is nonuniform near the vortex. The problem of the instability of the the uniformn-texture is equivalent to the quantum mechanical two-dimensional problem of a bound state in a field with an attractive potential 1/r ². The orientational phase transition at a vortex array is also considered. In the limit of large vortex density the orientational phase transition transforms to the phase transition studied by Gongadze et al. The theoretical results are compared with the observed phase transition at a vortex in³He-B.