Chapter 20. Semiclassical Dynamics and Two-Photon Spectroscopy: Raman Scattering

Eric Heller

Abraham Nitzan

Abstract This chapter focuses on spectroscopic applications of time dependent quantum mechanics focusing on molecular spectroscopy in condensed phases. (1) Molecular spectroscopy in the dressed state picture. (2) Resonance Raman scattering. (3) Resonance energy transfer. (4) Collective excitation and emission. (5) Thermal relaxation and dephasing (the Bloch equations, relaxation of a prepared state, dephasing (decoherence), the absorption lineshape, homogeneous and inhomogeneous broadening, motional narrowing, thermal effects in resonance Raman scattering). (6) A case study: Resonance Raman scattering and fluorescence from Azulene in a Naphthalene matrix. (7) Probing inhomogeneous bands (hole-burning spectroscopy, photon echoes, single-molecule spectroscopy. (8) Optical response functions.

Shaul Mukamel

1. Introduction 2. Quantum Dynamics in Hilbert Space 3. The Density Operator and Quantum Dynamics in Liouville Space 4. Quantum Electrodynamics, Optical Polarization, and Nonlinear Spectroscopy 5. Nonlinear Response Functions and Optical Susceptibilities 6. The Optical Response Functions of a Multilevel System with Relaxation 7. Semiclassical Simulation of the Optical Response Functions 8. The Cumulant Expansion and the Multimode Brownian Oscillator Model 9. Fluorescence, Spontaneous-Raman and Coherent-Raman Spectroscopy 10. Selective Elimination of Inhomogeneous Broadening Photon Echoes 11. Resonant Gratings, Pump-Probe, and Hole Burning Spectroscopy 12. Wavepacket Dynamics in Liouville Space The Wigner Representation 13. Wavepacket Analysis of Nonimpulsive Measurements 14. Off-Resonance Raman Scattering 15. Polarization Spectroscopy Birefringence and Dichroism 16. Nonlinear Response of Molecular Assemblies The Local-Field Approximation 17. Many Body and Cooperative Effects in the Nonlinear Response

W. H. Louisell, Pierre Meystre

Stimulated two-photon induced Raman scattering (hyper-Raman scattering) in an amplifier consisting of four-level atoms is analyzed semiclassically, via the coupled density matrix and Maxwell equations. We consider conditions typically encountered in the optical regime and in vapors. We show that even in the linear regime, it is characterized by a significant depletion of the atomic ground-state population, thus invalidating perturbative analyses based, for instance, on the nonlinear susceptibility tensor. Two major regimes of operation are found, one in which the population is completely consumed by the interaction ("linear regime"), and one in which the pump laser is depleted ("nonlinear regime"). Both regimes are, however, characterized by small photon conversion efficiencies. The tuning range is also briefly discussed.