Incoherence

Consider, Figure Al.6.32 in which a system is initially populated with an incoherent distribution of populations with Boltzmaim probabilities, = 1. The simple-minded definition of cooling is to... 

In the case of polarized, but otherwise incoherent statistical radiation, one finds a rate constant for radiative energy transfer between initial molecular quantum states i and final states f... 

Finally, if one has a condition with incoherent radiation of a small band width Av exciting a broad absorption band with a(v + A ) one finds ... 

Altematively, in the case of incoherent (e.g. statistical) initial conditions, the density matrix operator P(t) I 1>(0) (v(01 at time t can be obtained as the solution of the Liouville-von Neumann equation ... 

Modem photochemistry (IR, UV or VIS) is induced by coherent or incoherent radiative excitation processes [4, 5, 6 and 7]. The first step within a photochemical process is of course a preparation step within our conceptual framework, in which time-dependent states are generated that possibly show IVR. In an ideal scenario, energy from a laser would be deposited in a spatially localized, large amplitude vibrational motion of the reacting molecular system, which would then possibly lead to the cleavage of selected chemical bonds. This is basically the central idea behind the concepts for a mode selective chemistry , introduced in the late 1970s [127], and has continuously received much attention [10, 117. 122. 128. 129. 130. 131. 132. 133. 134... 

Unlike the typical laser source, the zero-point blackbody field is spectrally white , providing all colours, CO2, that seek out all co - CO2 = coj resonances available in a given sample. Thus all possible Raman lines can be seen with a single incident source at tOp Such multiplex capability is now found in the Class II spectroscopies where broadband excitation is obtained either by using modeless lasers, or a femtosecond pulse, which on first principles must be spectrally broad [32]. Another distinction between a coherent laser source and the blackbody radiation is that the zero-point field is spatially isotropic. By perfonuing the simple wavevector algebra for SR, we find that the scattered radiation is isotropic as well. This concept of spatial incoherence will be used to explain a certain stimulated Raman scattering event in a subsequent section. 

Schaertel S A, Albrecht A C, Lau A and Kummrow A 1994 Interferometric coherent Raman spectroscopy with incoherent light some applications Appi. Rhys. B 59 377-87... 

Morita N and Yajima T 1984 Ultrafast-time-resolved coherent transient spectroscopy with incoherent light Rhys. Rev. A 30 2525-36... 

Asaka S, Nakatsuka H, Fujiwara M and Matsuoka M 1984 Accumulated photon echoes with incoherent light in Nd -doped silicate glass Rhys. Rev. A 29 2286-9... 

Beech R and Hartmann S R 1984 Incoherent photon echoes Rhys. Rev. Lett. 53 663-6... 

Kummrow A and Lau A 1996 Dynamics in condensed molecular systems studied by incoherent light Appi. Rhys. B 63 209-23... 

Dugan M A, Melinger J S and Albrecht A C 1988 Terahertz oscillations from molecular liquids in CSRS/CARS spectroscopy with incoherent light Chem. Rhys. Lett. 147 411-19... 

Ulness D J and Albrecht A C 1996 Four-wave mixing in a Bloch two-level system with incoherent laser light having a Lorentzian spectral density analytic solution and a diagrammatic approach Rhys. Rev. A 53 1081-95... 

Rather different circumstances are encountered when considering THz remote sensing of extraterrestrial sources. The major source of THz opacity in the Earth s atmosphere is water vapour, and from either high, dry mountain sites or from space there are windows in which the background becomes very small. Incoherent instruments which detect the faint emission from astronomical sources can therefore be considerably more sensitive than their laboratory... 

The Goeppert-Mayer two- (or multi-) photon absorption, mechanism (ii), may look similar, but it involves intennediate levels far from resonance with one-photon absorption. A third, quasi-resonant stepwise mechanism (iii), proceeds via smgle- photon excitation steps involvmg near-resonant intennediate levels. Finally, in mechanism (iv), there is the stepwise multiphoton absorption of incoherent radiation from themial light sources or broad-band statistical multimode lasers. In principle, all of these processes and their combinations play a role in the multiphoton excitation of atoms and molecules, but one can broadly... 

Figure B2.5.13. Schematic representation of the four different mechanisms of multiphoton excitation (i) direct, (ii) Goeppert-Mayer (iii) quasi-resonant stepwise and (iv) incoherent stepwise. Full lines (right) represent the coupling path between the energy levels and broken arrows the photon energies with angular frequency to (Aco is the frequency width of the excitation light in the case of incoherent excitation), see also [111].

Now let us consider tire implications of tliese results for energy transfer. First we recognize tliat tliere is no directed energy transfer of tire fonn considered in the incoherent case. Molecules in tire dimer cannot be recognized as well defined separate entities tliat can capture and translate excitation from one to anotlier. The captured excitation belongs to tire dimer, in otlier words, it is shared by botli molecules. The only counteriDart to energy migration... 

Pullerits T, Chachisvilis M, Fedchenia I and Sundstrom V 1994 Coherent versus incoherent energy transfer in the lightharvesting complexes of photosynthetic bacteria Lietuvos Fizikos Zurnalas 34 329-38... 

Major breakthroughs in early ultrafast VER measurements were made in 1972 by Laubereau et al [22], who used picosecond lasers in an SRS pump-incoherent anti-Stokes Raman probe configuration, to study VER of C-H... 

In the classical picture developed above, the wavepacket is modeled by pseudo-particles moving along uncorrelated Newtonian trajectories, taking the electrons with them in the form of the potential along the Uajectory. In this spirit, a classical wavepacket can be defined as an incoherent (i.e., noninteracting) superposition of confignrations, X/(, t)tlt,(r, t)... 

In the derivation used here, it is clear that two approximations have been made—the configurations are incoherent, and the nuclear functions remain localized. Without these approximations, the wave function fonn Eq. (C.l) could be an exact solution of the Schrddinger equation, as it is in 2D MCTDH form (in fact is in what is termed a natural orbital form as only diagonal configurations are included [20]). 

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