Advances in Multi-Photon Processes and Spectroscopy

The following sections are included:

• Preface
• Contents

We present basic theoretical ideas underlying multiphoton ionization and laser control of molecules. Approaches to describe molecular electronic structure, spinorbit coupling, dynamic Stark shifts, dressed states, and multiphoton excitations are shortly reviewed. Control techniques such as phase-dependent dissociation, photon locking, and spatial hole burning are explained and illustrated exemplarily using halogenated methanes (CH₂BrI, CH₂I₂) as model systems. Theoretical approaches are compared with experiments and the complex signals resulting from phenomena like electronic wavepackets are elucidated and understood. Hence, we show how strong-field control concepts developed for simple systems can be transferred to more complex ones and advance our ability to control molecular dynamics.

Intense (10¹²–10¹³ W/cm²) phase-controlled laser fields consisting of a fundamental pulse and its second-harmonic pulse induce directionally asymmetric tunneling ionization and resultant orientation-selective molecular ionization in the gas phase. It is demonstrated that orientation-selective molecular ionization induced by phase-controlled ω + 2ω laser fields reflect the geometric structure of the highest occupied molecular orbital. This method is robust, being free of constraints such as: the laser wavelength; pulse duration, polarity, and weight of molecules, and thus can be applied to a wide range of molecules. Moreover, this method provides a powerful tool for tracking the quantum dynamics of photoelectrons by using phase-dependent oriented molecules as a phase reference in simultaneous ion–electron detection.

Interaction of atoms or molecules with intense laser fields is an emerging subject of atomic, molecular, and optical physics. Investigation in dynamics of these systems will be able to uncover various new phenomena and change ourway of controlling the evolution of matter in microscale. This chapter summarizes a number of the studies in recent years and is intended for authors to explain some basic features of polyatomic molecules in intense laser fields and their dynamic processes induced by femtosecond laser pulses. It is hoped that this chapter is informative and gives the readers some insight into this field of fundamental science.

We describe recent experimental studies of internal conversion via conical intersection in pyrazine. Ultrafast S₂ – S₁ internal conversion is observed in real time using a time-resolved photoelectron imaging (TRPEI) method with a time resolution of 22 fs. This method enables us to obtain a time-energy map of the photoelectron angular anisotropy, which unambiguously reveals the signature of internal conversion. Furthermore, the time-energy map of the photoelectron kinetic energy distribution (PKED) exhibits vibrational quantum beats of totally symmetric modes in S₁ after internal conversion. We also studied similar conical intersections between D₁(π⁻¹) and D₀(n⁻¹) by He(I) photoelectron spectroscopy and pulsed field ionization photoelectron spectroscopy. The existence of ultrafast internal conversion from D₁ to D₀ is confirmed by broadening of He(I) photoelectron spectra of pyrazine and deuterated pyrazine. Comparison of these spectra with one-color resonance-enhanced multiphoton ionization (REMPI) spectra of the 3s Rydberg states clearly indicates that the conical intersection between D₁ and D₀ induces ultrafast internal conversion from the Rydberg state with a D₁ ion core to that with a D₀ ion core.

The following sections are included:

• Introduction
• HEOM versus Path Integral Formalism: Background
  • Generic form and terminology of HEOM
  • Statistical mechanics description of bath influence
  • Feynman–Vernon influence functional formalism
  • General comments
• Memory-Frequency Decomposition of Bath Correlation Functions
  • PSD of Bose function
  • Brownian oscillators decomposition of bath spectral density function
• Optimized HEOM Theory With Accuracy Control
  • Construction of HEOM via path integral formalism
  • Accuracy control on white-noise residue ansatz
  • Efficient HEOM propagator: Numerical filtering and indexing algorithm
• HEOM in Quantum Mechanics for Open Systems
  • The HEOM space and the Schrödinger picture
  • HEOM in the Heisenberg picture
  • Mixed Heisenberg–Schrödinger block-matrix dynamics in nonlinear optical response functions
• Two-Dimensional Spectroscopy: Model Calculations
• Concluding Remarks
• Acknowledgments
• References

We calculate the electron dynamics in a crystalline solid in the presence of strong, ultrashort laser pulses within time-dependent density functional theory. The evolution of the electron orbitals is given by the time-dependent Kohn–Sham equation which includes the electric field of the laser pulse. There are several issues that arise in developing a practical computational method to implement the theory. The first is to separate the macroscopic and microscopic length scales in the dynamics. The second is treatment of the medium polarization. Both these are overcome by a suitable choice of the electromagnetic gauge. The resulting computational framework can be applied to a wide variety of optical phenomena in solids. On a purely microscopic scale, the method may be used to calculate dielectric properties of crystalline solids. For an ultrashort laser pulse of moderate intensity, it may be used to investigate mechanisms of coherent phonon generation. As the field strength increases, it may describe dense electron-hole excitations in solids leading to an optical breakdown. At the most general level, the present formalism can treat the fully coupled dynamics between macroscopic electromagnetic fields and microscopic electron dynamics. Although it is extremely demanding computationally, this will provide the most comprehensive description for the interaction of strong and ultrashort laser pulses with solids.