Atoms in Strong Light Fields

The monograph is devoted to phenomena of nonlinear optics appearing on a macro­ scopic level in the interaction of intense light with an isolated atom. It is a first attempt to summarize the elementary phenomena of nonlinear optics and present the various methods used in experiment and theory. In essence, this book can be considered an expanded version of the new aspect of quantum mechanics and atomic physics that in time will be incorporated into te- books on this subject. By the middle of this century the interaction of light with atoms had become one of the most investigated branches of physics. However, in the mid-sixties the development of high-power lasers changed this situation completely. It is a well-known fact that lasers are essentially new sources of light with high intensity, sharp directivity, and practically ideal monochromaticity. Entirely new phenomena came up in the studies of the interaction of light with atoms. In an intense light field, multiphoton transitions become important. The field disturbs the atomic levels, shifting, broadening, and mixing them. In an extremely strong field the atom ceases to be a bound system. These and similar phenomena on the atomic (microscopic) level determine the variations in the averaged, macroscopic properties of the medium, variations that cause nonlinear-optics phenomena, which radically change the fundamental classical laws of the interaction of light with matter.

1.1 The Strong Light Field.- 1.1.1 The Classical Nature of the Field.- 1.1.2 The Parameters of a Light Field.- 1.2 The Atom.- 1.2.1 One-Electron and Multi-Electron Approximations.- 1.2.2 The Structure of Atomic Spectra.- 1.2.3 Selection Rules.- 1.3 Interaction of an Atom and a Light Field.- 1.3.1 The Dipole Approximation.- 1.3.2 The Hamiltonian of the Dipole Interaction.- 1.3.3 An Atom in a Circularly Polarized Electromagnetic Field.- 1.3.4 The F loquet Theorem.- 1.3.5 Monochromatic Perturbation as a Stationary Problem.- 1.3.6 Exact Solutions.- 2. Time-Dependent Perturbation Theory.- 2.1 First-Order Perturbation Theory.- 2.1.1 The System of Equations.- 2.1.2 The Probability of One-Photon Transitions.- 2.1.3 Monochromatic Perturbations.- 2.1.4 Sudden Perturbations.- 2.1.5 Large Perturbation Times.- 2.1.6 The Role of the Shape of the Envelope of the Electromagnetic Field.- 2.1.7 Criteria of Applicability.- 2.2 Second-Order Perturbation Theory.- 2.2.1 Probability of a Two-Photon Transition.- 2.2.2 Transitions Induced by Two Perturbations.- 2.2.3 Large Perturbation Times.- 2.2.4 Sudden Perturbations.- 2.2.5 Criteria of Applicability.- 2.3 The Diagrammatic Technique for Monochromatic Perturbations...- 2.3.1 First-Order Perturbation Theory.- 2.3.2 Second-Order Perturbation Theory.- 2.3.3 The Rules for Constructing Diagrams.- 2.3.4 Partial Summation of Diagrams.- 2.4 Perturbation Theory of Arbitrary Order.- 2.4.1 The Amplitudes of Different Processes.- 2.4.2 Large Perturbation Times.- 2.4.3 Criteria for Applying Perturbation Theory of Arbitrary Order.- 2.4.4 Convergence of Expansion Series in Perturbation Theory.- 2.5 Monochromatic Perturbation and Degenerate States.- 2.5.1 A Single Degenerate Level.- 2.5.2 Mixing Degenerate Levels in a Field Due to the Presence of Other Level s.- 2.5.3 Near-Degenerate Levels.- 2.5.4 Time-Dependent Diagrams.- 2.5.5 Two-Photon Mixing of Degenerate States in Low-Frequency Fields.- 2.5.6 One-Photon Mixing of Degenerate States in Low-Frequency Fields.- 2.5.7 Competition Between One- and Two-Photon Mixing.- 2.5.8 Approximate Degeneracy.- 2.5.9 Criteria of Applicability.- 2.6 The Green’s Function in Time-Dependent Perturbation Theory.- 2.6.1 The Green’s Function.- 2.6.2 Application of the Green’s Function.- 2.6.3 Realistic Atomic Potentials.- 3. The Resonance Approximation.- 3.1 A Two-Level System in a Resonance Field.- 3.1.1 Wave Functions.- 3.1.2 Criteria of Applicability.- 3.1.3 Adiabatic Introduction of Perturbations.- 3.1.4 Sudden Perturbations.- 3.1.5 Adiabatic or Sudden Perturbation?.- 3.1.6 Quasi-Energies in the Resonance Case.- 3.2 Multi-Photon Resonance.- 3.2.1 Two-Photon Resonance.- 3.2.2 Criteria of Applicability.- 3.2.3 Multi-Photon Resonance.- 3.3 Degeneracy in a Resonance Field.- 3.3.1 Equations.- 3.3.2 Basis Solutions.- 3.3.3 Adiabatic Introduction of a Perturbation.- 3.3.4 Approximate Degeneracy.- 3.3.5 Degeneracy and the Influence of Light on an Atom.- 3.4 A Two-Level System in a Circularly Polarized Electromagnetic Field.- 3.4.1 Statement of the Problem.- 3.4.2 Solution and Discussion.- 3.5 A Two-Level System in a Resonance Field: Time-Dependent Parameters.- 3.5.1 The System of Equations.- 3.5.2 An Exactly Solvable Problem.- 3.5.3 The General Solution.- 3.6 A Three-Level System in Two Fields.- 3.6.1 Mixing in a Three-Level System.- 3.6.2 Zero Detuning.- 3.6.3 Population Inversion in a Three-Level System.- 4. The Adiabatic Approximation.- 4.1 General Theory.- 4.1.1 The Landau-Dykhne Adiabatic Approximation.- 4.1.2 The Born-Fock Adiabatic Approximation.- 4.2 Bound-Bound Resonance Transitions.- 4.2.1 Transition Probability per Unit Time.- 4.2.2 Criterion of Applicability.- 4.2.3 The Limiting Transition in Perturbation Theory.- 4.2.4 Resonance Mixing in a Two-Level System.- 4.2.5 Transitions in Multi-Level Systems.- 4.3 A Two-Level System in a Strong Field of Arbitrary Frequency.- 4.3.1 Adiabatic Wave Functions.- 4.3.2 Average Populations.- 4.3.3 Results, Limiting Cases, and a Comparison with Numerical Calculations.- 4.4 Transitions Between Degenerate States.- 4.4.1 Reducing the Problem Concerning Degenerate States to One Involving a System that Has a Constant Dipole Moment.- 4.4.2 Degeneracy and Transition Probability.- 4.5 Bound-Free Transitions.- 4.5.1 Comparison of the Perturbation in Discrete and Continuous States.- 4.5.2 Probability of a Transition in a Low-Frequency Field.- 4.5.3 Limiting Cases.- 5. Laser Radiation.- 5.1 Intensity of Radiation.- 5.1.1 Spatial-Temporal Distribution of the Intensity of Laser Radiation.- 5.1.2 Dependence of the Intensity on the Type, the Design,.- and the Mode of Operation of a Laser.- 5.1.3 Increasing the Intensity of Laser Radiation.- 5.1.4 Varying the Intensity of Laser Radiation.- 5.1.5 Measuring the Intensity of Radiation.- 5.2 Frequency of the Radiation.- 5.2.1 Changes in the Tunability and Spectral Narrowing.- 5.2.2 The Single-Mode Laser.- 5.2.3 The Measurement of Laser Frequency.- 5.3 The Polarization of the Radiation.- 5.4 The Monochromaticity of Laser Radiation.- 6. Experimental Aspects.- 6.1 Atomic Target.- 6.2 Competing Processes.- 6.2.1 Collisions Between Identical Atoms.- 6.2.2 Collisions with Electrons.- 6.3 The Self-Induced Distortion of Intense Light in Atomic Targets.- 6.4 Experimental Methods for Studying the Phenomena Produced by Strong Electromagnetic Fields Interacting with Atoms.- 6.4.1 Detecting Ions.- 6.4.2 Absorption of Light.- 6.4.3 One-Photon Absorption.- 6.4.4 Two-Photon Absorption.- 6.4.5 Multi-Photon Ionization Spectroscopy.- 6.4.6 Detecting the Light Produced in the Target.- 6.5 The Measurement of the Main Parameters that Characterize the Interaction Between Intense Electromagnetic Radiation and an Atom.- 6.5.1 Degree of Nonlinearity.- 6.5.2 Multi-Photon Cross Sections.- 7. Nonresonant Phenomena.- 7.1 Nonlinear Atomic Susceptibilities.- 7.1.1 The Scattering of Light and the Linear Susceptibility.- 7.1.2 The Nonlinear Scattering of Light and Nonlinear Susceptibility.- 7.1.3 Linear and Nonlinear Susceptibilities and the Perturbation of Atomic Spectra.- 7.2 Perturbation of Isolated Atomic States.- 7.2.1 Dynamic Polarizability of an Isolated Nondegenerate Atomic State.- 7.2.2 Dynamic Hyper-Polarizability.- 7.2.3 Criteria for Applying Perturbation Theory.- 7.2.4 The Dynamic Polarizability as a Function of the Perturbing Field.- 7.2.5 Experimental Data.- 7.3 Perturbation of Degenerate States.- 7.3.1 Two Adjacent Levels.- 7.3.2 The General Case.- 7.3.3 A Perturbation in an Elliptically Polarized Field.- 7.3.4 Perturbation of the Hydrogen Atom Spectrum.- 7.4 Nonlinear Scattering of Light.- 7.4.1 The Interrelation of Nonlinear Scattering Processes.- Due to an External Field.- 7.4.2 Spontaneous Two-Photon Scattering.- 7.4.3 Stimulated Two-Photon Emission.- 7.4.4 Hyper-Raman Scattering.- 7.4.5 Generation of the Third Harmonic.- 7.4.6 Other Processes Determined by x(3).- 7.5 Nonresonant, Nonlinear Ionization.- 7.5.1 The Mechanisms of Nonlinear Ionization.- 7.5.2 Numerical Estimates.- 7.6 Ionization in a Short-Range Potential.- 7.6.1 Tunneling Ionization.- 7.6.2 Ionization by a Circularly Polarized Field.- 7.6.3 Ionization by an Elliptically Polarized Field.- 7.6.4 The Intermediate Case (?2~1).- 7.6.5 Nonlinear Detachment of an Electron from a Negatively Charged Ion.- 7.7 The Ionization of Atoms.- 7.7.1 The Power-Law Dependence of the Ionization Probability on the Field Strength.- 7.7.2 Dependence of the Multi-Photon Cross Section on the Frequency and the Degree of Ellipticity of the Light.- 7.7.3 Criteria for Applying Perturbation Theory.- 7.7.4 Calculation of Multi-Photon Cross Section and Their Comparison with Experimental Data.- 7.7.5 The Angular Distribution of the Emitted Photoelectrons.- 7.7.6 Tunneling Ionization of Atoms (? « 1).- 7.7.7 The Intermediate Case (?2~l).- 8. Resonance Phenomena.- 8.1 Spontaneous Emission of Light by an Atom in a Resonance Field.- 8.1.1 The Natural Line Width.- 8.1.2 The Lorentzian Line Shape.- 8.1.3 Spontaneous Emission of Photons in a Weak Resonance Field.- 8.1.4 Spontaneous Emission of Photons in a Strong Resonance Field.- 8.1.5 Introduction of an External Field into the Resonance Excitation.- 8.2 Resonance Fluorescence.- 8.2.1 A Weak External Field.- 8.2.2 Criterion for Applying Perturbation Theory.- 8.2.3 The Density-Matrix Method.- 8.2.4 Elastic (Rayleigh) Scattering in Strong Fields.- 8.2.5 Inelastic Scattering.- 8.2.6 Comparison with Experiment.- 8.2.7 The Bloch-Siegert Shift.- 8.2.8 The Test Field.- 8.2.9 Multi-Photon Resonance.- 8.3 Multi-Photon Excitation and Emission.- 8.3.1 Selection Rules for Multi-Photon Transitions.- 8.3.2 The Probability of Multi-Photon Bound-Bound Transitions.- 8.3.3 Quadrupole Transitions.- 8.3.4 Multi-Photon Mixing of Resonance States.- 8.3.5 Competing Processes in the Multi-Photon Excitation of Atoms.- 8.3.6 Stimulated Multi-Photon Emission.- 8.4 Spontaneous Raman Scattering.- 8.4.1 A Weak Perturbation.- 8.4.2 Raman Scattering Frequencies for a Strong Perturbation.- 8.4.3 The Probability of Raman Scattering Under the Influence of a Strong Perturbation.- 8.4.4 Multi-Photon Raman Scattering.- 8.5 A Three-Level System in Two Resonance Fields.- 8.5.1 The System of Equations.- 8.5.2 Perturbation Theory.- 8.5.3 A Strong External Field.- 8.5.4 Two Strong External Fields.- 8.6 Resonance Ionization of Atoms.- 8.6.1 Resonance Ionization in a Weak Field.- 8.6.2 Mechanisms of Resonance Ionization in a Strong Field.- 8.6.3 Multi-Photon Ionization in a Strong Field.- 8.6.4 Resonance Ionization in the Adiabatic Inversion Field.- 8.6.5 The Polarization of Electrons and Nuclei in the Event of Resonance Ionization.- 8.6.6 Angular Distribution of the Electrons in the Resonance Ionizaton Process.- 9. Conclusion.- 9.1 The Role of the Non-monochromaticity of Laser Radiation.- 9.1.1 Direct Multi-Photon Ionization.- 9.1.2 Tunneling Ionization in a Variable Field.- 9.1.3 Multi-Photon Excitation of Atoms.- 9.1.4 Perturbation of Atomic Levels.- 9.2 Many-Electron Approximation.- 9.2.1 The Dynamic Polarization of the Atomic Core.- 9.2.2 Two-Electron Multi-Photon Ionization.- 9.3 Ultrahigh Fields.- 9.4 Highly Excited Atomic States in a Strong Electromagnetic Field.- 9.4.1 Radiative Transitions Between Highly Excited Atomic States.- 9.4.2 The Dynamic Polarizabili ty of Highly Excited Atomic States.- 9.4.3 Multi-Photon Ionization of Highly Excited States.- 9.4.4 Tunneling Ionization from Highly Excited States.- 9.4.5 Stochastic Instability of the Classical Electron in a Variable Field and the Diffusion Ionization of Highly Excited Atoms.- Notation Index.- References.