Coherent rotational motion

The development of a new form of spectroscopy based on the exploitation of the time evolution of the coherence associated with the rotational motion of an excited molecule. Conventional spectroscopies depend on the measurement of differences between the energy levels of a molecule, which become more and more difficult to measure and to interpret as the size of the molecule increases. In contrast, the intervals between recurrences in the coherent rotational motions of large molecules are directly related to the moments of inertia of the molecules and can be used to determine their structures. 

Experiments on bacteriorhodopsin (BR), which is the basis for a light-driven proton pump in halobacteria, were recently reported [96], The primary photoreaction is believed to be a trans-to-cis isomerization. Absorption of a 620-nm pulse by BR in membranes was followed by measurements of stimulated emission at various probe wavelengths between 695 and 930 nm. The rapid (ti 200 fs) decay of stimulated emission itensity at the bluer wavelengths, slower decay (T2 500 fs) at redder wavelengths, and biexponential decay at intermediate wavelengths were interpreted in terms of partially coherent rotational motion along the Sj potential surface. 

D. Coherent rotational motion. Build a wave-packet of (rigid rotor) rotational states and show that it will revive. 

The value of the jump distance in the )0-relaxation of PIB found from the study of the self-motion of protons (2.7 A) is much larger than that obtained from the NSE study on the pair correlation function (0.5-0.9 A). This apparent paradox can also be reconciled by interpreting the motion in the j8-regime as a combined methyl rotation and some translation. Rotational motions aroimd an axis of internal symmetry, do not contribute to the decay of the pair correlation fimction. Therefore, the interpretation of quasi-elastic coherent scattering appears to lead to shorter length scales than those revealed from a measurement of the self-correlation function [195]. A combined motion as proposed above would be consistent with all the experimental observations so far and also with the MD simulation results [198]. 

Figure 14. (a) Potential-energy surfaces, with a trajectory showing the coherent vibrational motion as the diatom separates from the I atom. Two snapshots of the wavepacket motion (quantum molecular dynamics calculations) are shown for the same reaction at / = 0 and t = 600 fs. (b) Femtosecond dynamics of barrier reactions, IHgl system. Experimental observations of the vibrational (femtosecond) and rotational (picosecond) motions for the barrier (saddle-point transition state) descent, [IHgl] - Hgl(vib, rot) + I, are shown. The vibrational coherence in the reaction trajectories (oscillations) is observed in both polarizations of FTS. The rotational orientation can be seen in the decay of FTS spectra (parallel) and buildup of FTS (perpendicular) as the Hgl rotates during bond breakage (bottom). 

The development of new forms of spectroscopy based on nonlinear optical processes and on the exploitation of the time evolution of the coherence associated with the rotational motion of an excited molecule. 

One way of studying molecular motions involves monitoring the reduction of dipole-dipole couplings probed by DQ spinning sidebands. The site selectivity is particularly high for heteronuclear DQ coherences. In Fig. 8, simulated sideband patterns are plotted for the C-H group, which is a sensitive probe of phenylene rotational motions, often met in practice. At low temperatures, one would expect... 

Referring to transverse relaxation processes that give rise to loss of phase coherence, three motional domains can be defined fast tumbling, where the intrinsic linewidth is Lorentzian in character slow tumbling, where the rotational correlation time is comparable to the inverse of the anisotropy of the magnetic interaction very slow tumbling, where the intrinsic linewidth is once again Lorentzian, but the observed linewidth is simply a powder pattern. 

In the last few years Nelson and co-workers [63-65] have presented a new approach to light scattering spectroscopy, named impulsive stimulated light scattering (ISS), which seems to be able to detect one particle rotational correlation functions. In ISS, one induces coherent vibrational motion by irradiating the sample with two femtosecond laser pulses, and... 

In the preceding sections, the rotational degrees of freedom were not included in the treatment of the coherent control processes. In what follows, a discussion of various aspects of rotational motion is presented. Several authors addressed the influence of rotations in the connection with laser control [192, 202, 203]. 

B. W. Shore, The Theory of Coherent Atomie Excitation, (John Wiley Sons, Nerv York, Chichester, Brishene, Toronto, Singapore, 1991), vol. 1 and vol. 2, 1735 pp. Nasvrov. K..A., Wigiier representation of rotational motion. J. Phvs. A Math. Gen., 32, p. 6663 - 6678 (1999). 

Correlation time for phase coherence of two spins Correlation time for translational jump motion Correlation time for rotational motion... 

Peterlin. In polyethylene, the reduction in second moment with temperature, although substantial, was much less than that expected for coherent rotation, and was qualitatively ascribed to coherent rotational oscillation about the chain axis (see also Ref. 28). This conclusion is consistent with the much steeper fall in second moment for y = 90° than for 7 = 0°. We will find that this explanation was later rejected after more detailed studies. In polyoxymethylene the fall in second moment with temperature was not greatly dependent on the angle between the draw direction and Hq, and no particular mechanism was proposed for the molecular motion. 

Control of molecular orientation and/or alignement in space has been proposed and extensively studied by Seideman, in which she designs to creat a coherent standing wavepacket for rotational motion in terms of a non-resonant laser field [386]. 

The results presented in this chapter show that the use of proper effective models, in combination with calculations based on the exact vibrational Hamiltonian, constitutes a promising approach to study the laser driven vibrational dynamics of polyatomic molecules. In this context, the MCTDH method is an invaluable tool as it allows to compute the laser driven dynamics of polyatomic molecules with a high accuracy. However, our models still contain simplifications that prevent a direct comparison of our results with potential experiments. First, the rotational motion of the molecule was not explicitly described in the present work. The inclusion of the rotation in the description of the dynamics of the molecule is expected to be important in several ways. First, even at low energies, the inclusion of the rotational structure would result in a more complicated system with different selection rules. In addition, the orientation of the molecule with respect to the laser field polarization would make the control less efficient because of the rotational averaging of the laser-molecule interaction and the possible existence of competing processes. On the other hand, the combination of the laser control of the molecular alignment/orientation with the vibrational control proposed in this work could allow for a more complete control of the dynamics of the molecule. A second simplification of our models concerns the initial state chosen for the simulations. We have considered a molecule in a localized coherent superposition of vibrational eigenstates but we have not studied the preparation of this state. We note here that a control scheme for the localiza-... 

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