Advances in Multi-Photon Processes and Spectroscopy

The following sections are included:

• PREFACE
• CONTENTS

Significant progress has been made in achieving experimental laser control of molecules due to advances in ultrafast laser technology utilizing femtosecond pulse shaping capabilities. In addition, the advent of few-cycle femtosecond as well as attosecond pulses has made possible observation and manipulation of electronic and nuclear motions. In this chapter, we review theoretical foundations for exploring quantum optimal control of molecular dynamics driven by laser fields. The goal is to present the theoretical machinery for simultaneous control of electronic transitions and nuclear motion in a molecule. The presentation encompasses quantum optimal control theory (OCT), quantum control landscape (QCL) analysis, a two-point boundary-value quantum control paradigm (TBQCP), and the TBQCP-based algorithms to search for optimal control fields. Optimal control schemes in the context of the TBQCP are formulated using the Born–Oppenheimer (BO) concept for the separation of electronic and nuclear degrees of freedom, generalized to include the electric field amplitude as an additional degree of freedom. The TBQCP formulations are tailored in the weak and strong field limits and in the very short-time (sub-femto/attosecond) limit, with the goal of providing a unified treatment of optimal control over molecular dynamics. Numerical examples are presented to demonstrate the utility of the TBQCP optimal control search algorithms.

The topic of this survey article has seen a renaissance during the past couple of years. Here we present and extend the results for various phenomena which we have published from 2012–2014, with gratitude to our coauthors. The new phenomena include (a) the first reduced nuclear flux densities in vibrating diatomic molecules or ions which have been deduced from experimental pump–probe spectra; these “experimental” nuclear flux densities reveal several quantum effects including (b) the “quantum accordion”, i.e., during the turn from bond stretch to bond compression, the diatomic system never stands still — instead, various parts of it with different bond lengths flow into opposite directions. (c) Wavepacket interferometry has been extended from nuclear densities to flux densities, again revealing new phenomena: For example, (d) a vibrating nuclear wave function with compact initial shape may split into two partial waves which run into opposite directions, thus causing interfering flux densities. (e) Tunneling in symmetric 1-dimensional double-well systems yields maximum values of the associated nuclear flux density just below the potential barrier; this is in marked contrast with negligible values of the nuclear density just below the barrier. (f) Nuclear flux densities of pseudorotating nuclei may induce huge magnetic fields. A common methodologic theme of all topics is the continuity equation which connects the time derivative of the nuclear density to the divergence of the flux density, subject to the proper boundary conditions. (g) Nearly identical nuclear densities with different boundary conditions may be related to entirely different flux densities, e.g., during tunneling in cyclic versus non-cyclic systems. The original continuity equation, density and flux density of all nuclei, or of all nuclear degrees of freedom, may be reduced to the corresponding quantities for just a single nucleus, or just a single degree of freedom.

One of the ultimate goals in understanding a chemical reaction is to know how each nucleus in a reactant moves during product formation. It remains a daunting challenge to gain a thorough knowledge of the reaction coordinates particularly for polyatomic molecules, because of the many degrees of freedom of their nuclear motions. To deepen our understanding of the multi-dimensional nuclear dynamics in chemical reactions, we carried out ultrafast spectroscopy with ~10-fs pulses and observed nuclear wavepacket motions in the excited state in the time domain. In this chapter, we review our studies on the femtosecond structural dynamics of polyatomic molecules in the excited state and discuss the nature, mechanism, and dynamics of ultrafast reactions, which have been revealed through the time-domain observation of molecular vibrations.

Water interfaces are ubiquitous in the world. They play a crucial role in many physical, chemical, and biological systems. However, because very few experimental techniques are available for probing water/interfaces, the understanding at the molecular level of their physical and chemical properties is still poor. Sum frequency vibrational spectroscopy (SFVS) is so far the only technique that is capable of providing vibrational spectra of water surface/interface. It is applicable to study the structure of bare surface and buried interface with sub-monolayer sensitivity. The newly developed phase-sensitive SFVS technique provides spectrum directly from experiment, with being the second order susceptibility. The spectrum obtained for the water interfaces allows much improved understanding of the water interfacial structure, in analogy to Imε,with ε being the dielectric constant, for the absorption or emission spectrum. This chapter covers recent advances in study of a few representative water interfaces, including water/air, water/hydrophobic material interfaces, with emphasis on phase-sensitive SFVS.

Magneto-chiral dichroism (MChD) is an interesting phenomenon in which the absorbance of a chiral molecule depends on the magnetic field direction. MChD has been given considerable attention not only in magneto-optical devices but also in new asymmetric synthetic methods and the origin of the homochirality of life, since the MChD of two enantiomers is opposite in nature. On the other hand, the MChD of organic compounds, which can be well correlated with living beings, has not been reported; thus, the relationship between MChD and the homochirality of life has been considered to be poor. Recently, the presence of MChD in organic compounds was demonstrated for the first time. In this chapter, the MChD of organic compounds is described not only by comparing with previous observations for metal compounds, but also in terms of the theoretical explanations. Because the MChD originates from the π-electronic properties of aggregates of conventional organic aromatic compounds (benzene derivatives, polycyclic aromatic hydrocarbons, chlorophylls, and so on), such as the orbital angular momentum and the exciton chirality, the MChD of the π – π* transitions not only has significant advantages such as tunable wavelengths and high chemical reactivity that are useful for asymmetric synthetic methods and magneto-optical devices, but also opens up new possibilities for clarifying the asymmetry in biological systems.

The following sections are included:

• Appendix
• Index