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Journal of Physics B Atomic and Molecular Physics

Particle scattering by two level atoms in a strong radiation field

L Hahn, Ingolf Volker Hertel

Published Nov 1, 1972• 19 citations
Publisher

Abstract

A set of coupled equations for the particle scattering by a two level atom in a strong near resonant radiation field is derived from the time dependent Schrodinger equation. This set of equations is discussed in a first and second order approximation. The result can be visualized in terms of a scheme in which the two well separated (nondegenerate) atomic states split, each into two energy levels. The splitting depends on the strength of the field and on the difference between the resonance frequency and the frequency of the incident light and is typically a few meV. In this scheme all possible elastic, quasielastic, inelastic and superelastic transitions between the four levels can be induced by collision processes. In addition, multiphoton processes may occur if the scattered particle remains long enough in the interaction region. Estimates of the two photon gain process for electron and heavy particle scattering by sodium atoms in a dye laser field are given. It is suggested that the superelastic processes may play an important role in laser induced gas breakdown, even if the laser frequency does not coincide with any atomic transition. Spontaneous emission of atoms in laser fields is also treated. The results are similar to the particle scattering processes.

DOI
10.1088/0022-3700/5/11/005

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A set of coupled equations for the particle scattering by a two level atom in a strong near resonant radiation field is derived from the time dependent Schrodinger equation. This set of equations is discussed in a first and second order approximation. The result can be visualized in terms of a scheme in which the two well separated (nondegenerate) atomic states split, each into two energy levels. The splitting depends on the strength of the field and on the difference between the resonance frequency and the frequency of the incident light and is typically a few meV. In this scheme all possible elastic, quasielastic, inelastic and superelastic transitions between the four levels can be induced by collision processes. In addition, multiphoton processes may occur if the scattered particle remains long enough in the interaction region. Estimates of the two photon gain process for electron and heavy particle scattering by sodium atoms in a dye laser field are given. It is suggested that the superelastic processes may play an important role in laser induced gas breakdown, even if the laser frequency does not coincide with any atomic transition. Spontaneous emission of atoms in laser fields is also treated. The results are similar to the particle scattering processes.
Quantum stochastic differential equations have been used to describe the dynamics of an atom interacting with the electromagnetic field via absorption/emission processes. Here, by using the full quantum stochastic Schrödinger equation proposed by Hudson and Parthasarathy, we show that such models can be generalized to include other processes into the interaction. In the case of a two-level atom we construct a model on the basis of some physical requirements, the main being a balance equation on the fluxes of the ingoing and outgoing photons; in this model the atom-field interaction turns out to be due either to absorption/emission processes either to direct scattering processes, which simulate the interaction due to virtual transitions to the levels which have been eliminated from the description. To see the effects of the new terms, we consider both direct and heterodyne detection of the fluorescence light emitted by an atom stimulated by a monochromatic coherent laser and we deduce from these two detection schemes the expressions of the total, elastic and inelastic electromagnetic cross sections and the spectral distribution of the fluorescence light. The total cross section, as a function of the frequency of the stimulating laser, can present not only a Lorentzian shape, but the full variety of Fano profiles; intensity dependent widths and shifts are obtained. The fluorescence spectrum can present complicated shapes, according to the values of the various parameters; when the direct scattering is not important the usual symmetric triplet structure of the Mollow spectrum appears (for high intensity of the stimulating laser), while a strong contribution of the direct scattering process can distort such a triplet structure or can even make it to disappear.
Dressed states of an atom in a classical laser field of frequency close to an atomic transition frequency are obtained, which are a considerable improvement over the usual two-level rotating-wave approximation. These wave functions are used in a calculation of the cross section for elastic electron-atom scattering in a laser field. Numerical calculations for electron-hydrogen scattering demonstrate that scattering involving absorption or emission of photons can be strongly influenced by coupling to the nonresonant states, regardless of the field strength. Inclusion of the counter-rotating terms in the calculation is shown to be essential for extending the applicability of the theory to scattering in nonresonant fields, where a first-order perturbation-theoretic treatment of the atom-field interaction would be expected to be quite justified.
This investigation describes the interaction of a three level atom with two laser fields. One of the transitions from the ground state is in resonance with twice the frequency of the first laser and the other transition from the ground state is in resonance with the second laser. The Green's function formalism is used to derive expressions from which the induced two photon and one photon excitation spectra are computed. Also, approximate expressions are derived for the excitation spectra in the appropriate frequency regions. These results agree well with the numerical computations based upon the precise expressions. The interference between the two transitions produce some splittings; these splittings depend upon the Rabi frequency of the one photon transition. The intensities of the weak peaks depend upon the ratio of the Rabi frequency of the two photon transition to the frequency of the first laser. Some features of the excitation spectra are interpreted in terms of previous knowledge about the behavior of two level atoms in strong laser fields.
The first analysis is made of stimulated Raman scattering and two-photon absorption (emission) processes resulting in a change in the states of two colliding particles. These processes are caused the by interaction between dipole moments induced as a result of polarization of the particles by the radiation. Equations are derived to describe multiphoton transitions during a collision between two particles in a radiation field. Using the approximation of rectilinear trajectories, expressions are derived and analyzed for the cross section of collisional two-photon transitions in weak and strong fields. It is shown that in fields of ≈103 cgs esu, the cross section of these transitions may reach 10–4 cm2
The interaction of a resonant radiation field with two-level atoms (in the long-wavelength limit) is described by a Hamiltonian trilinear in the boson operators. It is shown that the dynamics of the system can be determined nearly exactly if either at least one of the three modes is strongly populated for all times or any two modes are separately strong in two complementary time domains. Explicit results are given in two important specific cases: (i) pumping of a ground-state atomic system by a coherent radiation field and (ii) coherent spontaneous emission. The results are compared with previously known approximate results. Our results are also applicable to certain parametric processes such as parametric amplification, frequency conversion, Raman and Brillouin scattering, etc., where an identical trilinear Hamiltonian is used to describe these processes.
We consider the possible physical processes that may arise in a three-level atom when only two of its levels interact with a strong electromagnetic field and when the atomic transition frequency is nearly equal to once and twice the frequency of the laser field, respectively. There have been found pronounced cooperative effects in the spectrum of the two-level system, which is in resonance with the laser field, arising from the presence of the third level. The excitation spectra describing the transitions from the first excited state into the second excited state and from that to the ground state consist, apart from the two central peaks, of two pairs of sidebands which are induced by the laser field of the neighbouring system. Detailed expressions of the spectral functions for the physical processes of one- and two-photon resonance fluorescence have been derived and discussed in the limit of high photon densities. The excitation spectrum of the low frequency modes has been considered and discussed in detail. It is found that quantum beats in spontaneous emission may appear in the spectra of the one- and two-photon resonance fluorescence arising from the interference between the two atomic transition frequencies and the frequency of the laser field. The importance of the low frequency modes that occur in the processes in question has been pointed out.