Coherent Spectroscopy

This chapter provides an introduction to different spectroscopic techniques that are based either on the coherent excitation of atoms and molecules or on the coherent superposition of light scattered by molecules and small particles. The coherent excitation establishes definite phase relations between the amplitudes of the atomic or molecular wave functions this, in turn, determines the total amplitudes of the emitted, scattered, or absorbed radiation. 

Either two or more molecular levels of a molecule are excited coherently by a spectrally broad, short laser pulse (level-crossing and quantum-beat spectroscopy) or a whole ensemble of many atoms or molecules is coherently excited simultaneously into identical levels (photon-echo spectroscopy). This coherent excitation alters the spatial distribution or the time dependence of the total, emitted, or absorbed radiation amplitude, when compared with incoherent excitation. Whereas methods of incoherent spectroscopy measure only the total intensity, which is proportional to the population density and therefore to the square ir of the wave function iff, the coherent techniques, on the other hand, yield additional information on the amplitudes and phases of ir. 

Within the density-matrix formalism (Vol. 1, Sect. 2.9) the coherent techniques measure the off-diagonal elements pab of the density matrix, called the coherences, while incoherent spectroscopy only yields information about the diagonal elements, representing the time-dependent population densities. The off-diagonal elements describe the atomic dipoles induced by the radiation field, which oscillate at the field frequency u and which represent radiation sources with the field amplitude Ak(r, t). Under coherent excitation the dipoles oscillate with definite phase relations, and the phase-sensitive superposition of the radiation amplitudes Ak results in measurable interference phenomena (quantum beats, photon echoes, free induction decay, etc.). 

After switching off the excitation sources, the phase relations between the different oscillating atomic dipoles are altered by different relaxation processes, which perturb the atomic dipoles. We may classify these processes into two categories  

The techniques of coherent spectroscopy that are discussed below allow the elimination of the inhomogeneous contribution and therefore represent methods of Doppler-free spectroscopy, although the coherent excitation may use spectrally broad radiation. This is an advantage compared with the nonlinear Doppler-free techniques discussed in Chap. 2, where narrow-band single-mode lasers are required. 

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Figure Al.6.16. Diagram showing the directionality of the signal in coherent spectroscopy. Associated with the carrier frequency of each interaction with the light is a wavevector, k. The output signal in coherent spectroscopies is detemiined from the direction of each of the input signals via momentum conservation (after [48a]).

Champion P M, Rosea F, Chang W, Kumar A, Christian J and Demidov A 1998 Femtosecond coherence spectroscopy of heme proteins XVith int. Conf on Raman Spectroscopy ed A M Heyns (New York Wley) pp 73-6... 

Zhu L, Li P, Huang M, Sage J T and Champion P M 1994 Real time observation of low frequency heme protein vibrations using femtosecond coherence spectroscopy Phys. Rev. Lett. 72 301-4... 

References 29-33 introduce the notion of coherence spectroscopy in the context of two-pathway excitation coherent control. Within the energy domain, two-pathway approach to coherent control [25, 34—36], a material system is simultaneously subjected to two laser fields of equal energy and controllable relative phase, to produce a degenerate continuum state in which the relative phase of the laser fields is imprinted. The probability of the continuum state to evolve into a given product, labeled S, is readily shown (vide infra) to vary sinusoidally with the relative phase of the two laser fields < ),... 

Equation (65) illustrates that in the limit of ultrashort pulses the two-pathway method loses its value as a coherence spectroscopy 8s is fixed at it/2 irrespective of the system parameters. From the physical perspective, when the excitation is much shorter than the system time scales, the channel phase carries no imprint of the system dynamics since the interaction time does not suffice to observe dynamical processes. 

We began our analysis in Section II and ended it in Section VC2 by making the connection of the time- and energy-domain approaches to both coherence spectroscopy and coherent control. It is appropriate to remark in closing that new experimental approaches that combine time- and energy-domain techniques are currently being developed to provide new insights into the channel phase problem. We expect that these will open further avenues for future research. 

S. Ramakrishna and T. Seideman, Coherence spectroscopy in dissipative media a Liouville space approach, J. Chem. Phys. 122, 084502 (2005). 

Breit-Wigner phase, two-pathway excitation, coherence spectroscopy energy domain, 180-182 low-lying resonance, continuum excitation, 169-170... 

Coarse-grained approaches, multiparticle collision dynamics, 90-92 Coarse velocity, linear thermodynamics, regression theorem, 18-20 Coherence spectroscopy, two-pathway excitation ... 

Continuum excitation, coherence spectroscopy isolated resonance ... 

Damping effects, transition state trajectory deterministic driving, 209-213 stochastically moving manifolds, 215-222 De Broglie wavelength, two-pathway excitation, coherence spectroscopy 165-166 Decoherence, two-pathway excitation, coherence spectroscopy ... 

Dipole matrix elements, one- vs. three-photon excitation, coherence spectroscopy, 163—166... 

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