Wavepacket coherence control

These examples, although few and preliminary, nonetheless indicate the direction in which time-resolved spectroscopy of reactive species is headed. More detailed examinations of unstable structures between chemical reactants and products will certainly follow. A major goal in this area will be direct observation of coherent wavepacket propagation through local potential maxima (i.e., transition states). Experimental control over wavepacket momentum through potential maxima will be especially important in evaluating solvent effects, barrier recrossing probabilities, and so on. Methods that permit observation and control of transition state production may be anticipated. 

An additional result that emerges from our study concerns the extent to which wavepacket control is possible using coherent pulse sequences. In a two-level system one can exchange the phases of the two levels with a 7t pulse and, in effect, achieve time reversal of the state of the system. In a multilevel system the extent of control is much more restricted. The center of the wavepacket evolves according to the Franck-Condon principle and Hamilton s equations of motion, which in turn are dictated by nature s potential energy surfaces. What can be controlled by the experimenter is the instant at which the wavepacket changes surfaces. This concept forms the basis for a scheme for controlling the selectivity of a reaction,24,25 which we discuss in the next section. 

This section begins with a brief description of the basic light-molecule interaction. As already indicated, coherent light pulses excite coherent superpositions of molecular eigenstates, known as wavepackets , and we will give a description of their motion, their coherence properties, and their interplay with the light. Then we will turn to linear and nonlinear spectroscopy, and, finally, to a brief account of coherent control of molecular motion. 

The pioneering use of wavepackets for describing absorption, photodissociation and resonance Raman spectra is due to Heller [12, 13,14,15 and 16]- The application to pulsed excitation, coherent control and nonlinear spectroscopy was initiated by Taimor and Rice ([17] and references therein). 

A comprehensive discussion of wavepackets, classical-quantum correspondence, optical spectroscopy, coherent control and reactive scattering from a unified, time dependent perspective. 

G. Coherence Control of Wavepackets Reactive and Nonreactive Systems... 

Coherent control by varying the time delay between a pump laser pulse that prepares an evolving wavepacket in the system and a probe laser pulse that excites the desired product state has also been demonstrated with two-photon ionization. 

Selective excitation of wavepackets with ultrashort broadband laser pulses is of fundamental importance for a variety of processes, such as the coherent control of photochemical reactions [36-39] or isotope separation [40--42]. It can also be used to actively control the molecular dynamics in a dissipative environment if the excitation process is much faster than relaxation. For practical applications it is desirable to establish an efficient method that allows one to increase the target product yield by using short laser pulses of moderate intensity before relaxation occurs [38]. 

Since the classical treatment has its restrictions and the applicability of the quantum OCT is limited to low-dimensional systems due to its formidable computational cost, it would be very desirable to incorporate the semiclassical method of wavepacket propagation like the Herman-Kluk method [20,21] into the OCT. Recently, semiclassical bichromatic coherent control has been demonstrated for a large molecule [22] by directly calculating the percent reactant as a function of laser parameters. This approach, however, is not an optimal control. 

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. 

Currently, a major theme in atomic, molecular, and optical physics is coherent control of quantum states. This theme is manifested in a number of topics such as atom interferometry, Bose-Einstein condensation and the atom laser, cavity QED, quantum confutation, quantum-state engineering, wavepacket dynamics, and coherent control of chemical reactions. 

The coherence is reflected in the third term of the density function which is therefore called interference term. In our context we use the term passive control, if particular wavepackets are prepared in the Franck-Condon (FC) region by specific pump laser pulses which are then turned off. In this case, the weight of the partial waves does no longer change after the excitation, the further change is only due to the time-dependent phases, while the wavepackets evolve under the influence of the potential surfaces. The term active control is used, if the laser field remains turned on during the... 

---