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Spectroscopy

Abraham Nitzan

Published Jun 14, 2024• 0 citations
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Abstract

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.

DOI
10.1093/9780191947971.003.0018

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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.
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
Abstract A practical approach to understanding light scattering processes in the condensed phase is presented. First a theoretical discussion of the various parameters in resonance light scattering is given and there is a special emphasis on our simplified approach to this question. As with other approaches the two level density matrix in association with a quantum regression theorem leads to two types of emission from an ensemble of molecules at finite temperature (T2 ≠ 2T1). We have called one of these fluorescence and the other sharper emission Raman scattering because it results directly from the presence of a coherent polarization in the medium. A brief discussion of time dependent scattering is also given. An experiment that reproduces the main features of the theory is described for resonance scattering from azulene in naphthalene at 30 K. For all values of the laser frequency (near resonance) both a sharp (Raman) and diffuse (fluorescent) component occurs in the emission spectrum. These spectra when interpreted by the simplified theory yield a value of T2 = 0.7 ps from fluorescence linewidth, and T2 = 0.8 ps from the incoherent to coherent scattering ratio, for the 0–0 two level system of azulene in naphthalene. A discussion of practical aspects of the influence of inhomogeneous line broadening is also presented.
A theory of optical echo spectroscopies of large polyatomic molecules in condensed phases is developed. Using phase space correlation functions, we examine the interrelationships among the following optical measurements: ordinary photon echo, stimulated photon echo, accumulated photon echo, incoherent accumulated photon echo, and pump–probe absorption. Conditions for the elimination of inhomogeneous broadening in these experiments are specified. A multimode Brownian oscillator model is used to account for high frequency molecular vibrations, as well as solvent modes, and electronic dephasing processes. The effects of quantum beats, spectral diffusion, and homogeneous dephasing on the echo signals are studied and compared in detail with pump–probe and hole burning spectroscopy.
Optical spectroscopy provides a useful tool for probing the structure and dynamics of solids. Over the years, optical methods have evolved from absorption spectroscopy to more complex methods such as spectral hole burning, photon echoes, and luminescence line narrowing. The absorption spectrum provides information about inhomogeneous broadening, while the latter approaches provide information about the systematics of the homogeneous line shape information that is often obscured by inhomogeneous broadening. When external perturbations such as strain or electric fields are applied, details of the local site can be obtained. Recently, the ultimate limit of optical spectroscopy has been attained, in which the spectral properties of individual single impurity molecules in a solid can be measured, with all ensemble averaging removed. This novel regime has provided additional, previously unobtainable, information on a highly local scale, such as the direct observation of the spectral shifting of a single molecule produced by configurational transitions of the host. It is to be expected that further surprises await us in this new frontier of single-molecule spectroscopy in solids.
The theory of resonance Raman effect, resonantly enhanced two-photon absorption, and resonance fluorescence---valid also for strong fields---is treated in a unified and simplified way. Dressed states, Bloch equations, and perturbation theory are used to calculate line positions, and integrated intensities both for steady state and transient excitation. The case of adiabatic following is solved explicitly; it occurs when an off-resonance incident pulse is turned on and off slowly. It leads to the identification of Raman scattering, two-photon absorption, and Rayleigh scattering with an adiabatic process while fluorescence and consecutive two-photon absorption with nonadiabaticity. Time-dependent spectra are defined in a rigorous way. Our formulas agree in the various limits with those that appear in the literature.
Time dependent description of resonance Raman scattering is performed for a general system, by a density matrix reformulation of damping theory originally used for resonance fluorescence of atom. Radiative damping in the intermediate states can be described in terms of "damping operator" in realistic situations. In large ergodic systems, the scattering reduces to luminescence if the relaxation time within the excited states is much shorter than the radiative lifetime. In a typical case, time resolved emission spectra consist of various stages (i) scattering complex where absorption and emission are inseparable, (ii) dynamical and then (iii) kinetic relaxations giving rise to the hot luminescence, which finally converges to (iv) the ordinary luminescence from relaxed excited states. Hot luminescence does not appear within a motionally narrowed line. The interpretation of spectra depends also on the method of observation.