Coherent pulse

Tannor D J and Rice S A 1988 Coherent pulse sequence control of product formation in chemical reactions Adv. Chem. Rhys. 70 441 -524... 

Tannor D J, Kosloff R and Rice S A 1986 Coherent pulse sequence induced control of selectivity of reactions exact quantum mechanical calculations J. Chem. Rhys. 85 5805-20, equations (1)-(6)... 

When considering a coherent pulse of light, it is necessary to superimpose a collection of plane waves, as in Eqs. (1.27) and (1.28). In doing so it is reasonable to make the simplifying assumption that all the modes of the pulse propagate in the same direction (chosen as the z axis) and that all the pulse modes have the same polarization direction a. We can therefore eliminate the integration over the k directions and write Eq. (1-27) (in an infinite volume) as... 

To characterize partially coherent pulses [189, 190] consider a Gaussian pulse with time profile cjt) and phase <5T(r), that is,... 

A strict derivation of the comb properties is not feasible as it depends on the special dispersion characteristics of the laser cavity and these data are not accessible with the desired degree of accuracy. Instead we only assume that the laser emits a stable coherent pulse train without any detailed consideration of how this is possible. Further we assume that the electric field E(t), measured for example at the output coupler, can be written as the product of a periodic envelope function A ) and a carrier wave C(t) ... 

The idea of using a train of coherent pulses for the observation of the IS to 2S transition in hydrogen was first suggested by BAKLANOV et al. in 1976 [10]. The observation of Doppler-free spectra using a coherent pulse train from a synchronously pumpecl dye laser was demonstrated by ECKSTEIN et.al [11]. 

In 1964, the spin echo experiment was extended to the optical regime by the development of the photon echo experiment (3,4). The photon echo began the application of coherent pulse techniques in the visible and ultraviolet portions of the electromagnetic spectrum. Since its development, the photon echo and related pulse sequences have been applied to a wide variety of problems including dynamics and intermolecular interactions in crystals, glasses, proteins, and liquids (5-8). Like the spin echo, the photon echo and other optical coherent pulse sequences provide information that is not available from absorption or fluorescence spectroscopies. 

In 1993, the first ultrafast vibrational echo experiments on condensed matter systems were performed using a free electron laser as the source of temporally short, tunable infrared pulses (11). Recently, the development of Ti sapphire laser-based optical parametric amplifier (OPA) systems has made it possible to produce the necessary pulses to perform vibrational echoes using a tabletop experimental system (12,13). The development and application of ultrafast, IR vibrational echoes and other IR coherent pulse sequences are providing a new approach to the study of the mechanical states of molecules in complex molecular systems such as liquids, glasses, and proteins (14-20). While the spin echo, the photon echo, and the vibrational echo are, in many respects, the same type of experiment, the term vibrational echo is used to distinguish IR experiments on vibrations from radio frequency experiments on spins or vis/UV experiments on electronic states. In this chapter, recent vibrational echo experiments on liquids, glasses, and proteins will be described. 

Background suppression in VES is in some respects analogous to NMR background suppression techniques (56,57). In both types of spectroscopy, coherent pulses sequences are used to remove unwanted spectral features. 

Figure 1. Gradient-enhanced heteronuclear single quantum coherence pulse sequence with coherence transfer selection and artifact suppression gradients. All pulses are of phase x unless otherwise indicated.

COHERENT PULSE SEQUENCE CONTROL OF PRODUCT FORMATION IN CHEMICAL... 

V. Coherent Pulse Sequence Control of Product Formation in Chemical Reactions... 

The designs of the previously mentioned selectivity schemes ignore the possibility of control of the evolution of excitation energy via exploitation of the coherence properties of the coupled matter-electromagnetic field system. Several schemes that do exploit the coherence of the time evolution of a wavepacket excitation have recently been proposed. This chapter is concerned with one of these schemes, namely, the use of coherent pulse sequences to control product formation in chemical reactions. We shall see that this scheme follows naturally from an understanding of the characteristics of time-delayed coherent anti-Stokes Raman spectroscopy (CARS) and of photon echo spectroscopy. 

Recently, in this laboratory, we have applied time-dependent quantum mechanics-wavepacket dynamics to several bona fide time-domain spectroscopies. Specifically, we have formulated time-dependent theories of coherent-pulse-seque nee-induced control of photochemical reaction, picosecond CARS spectroscopy, and photon echoes. These processes all involve multiple pulse sequences in which the pulses are short or comparable in time scale to the... 

Time-domain spectroscopies entail a major shift in emphasis from traditional spectroscopies, since the experimenter can control, in principle, the duration, shape, and sequence of pulses. One may say that traditional, CW spectroscopy, is passive—the experimenter attempts to study static properties of a particular molecule. Coherent pulse experiments are active in that, given a set of molecular properties (which may in fact be known from various spectroscopies), one tries to arrange for a desired chemical product, or to design a pulse sequence that will probe new molecular properties. The time-dependent quantum mechanics-wavepacket dynamics approach developed here is a natural framework for formulating and interpreting new multiple pulse experiments. Femtosecond experiments yield to a particularly simple interpretation within our approach. 

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