Control coherent

This technique is called coherent control, because the time-dependent phase of the wavefunction of the coherently excited state is controlled in order to optimize the result of the molecular decay [898,899], 

Normally, only the frequency and the intensity of a light field are considered in the interaction of radiation with matter. With the availability of short-pulse radiation with well-defined phase properties it has become possible to interact coherently with matter, opening up new possibilities of controlling chemical reactions and light-matter interactions. We will here consider two aspects of this quickly evolving field coherent chemistry and interference effects profoundly changing the absorptive properties of matter. 

Coherent Chemistry. Short-pulse laser radiation normally leads to broad and rather unspecific excitation of vibrational modes (See also Sect. 10.4). By tailoring the pulses, which typically would have a pulse length of 100 fe, by sending them into a pulse shaper, certain modes can be enhanced and others be suppressed. In particular, discrimination between chiral molecules (right- or left-handed) otherwise performing in an identical way could be considered, A pulse shaper is a stretcher-like arrangement (Sect. 8.7.2) with 

---

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). 

Warren W S, Rabitz H and Dahleh M 1993 Coherent control of quantum dynamics the dream is alive Science 259 1581... 

A valuable resource, reviewing both theoretical and experimental progress on coherent control to date. 

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

Nelson K A 1994 Coherent control optics, molecules, and materials Ultrafast Phenomena /X ed P F Barbara, W H Knox, G A Mourou and A H Zewail (Berlin Springer) pp 47... 

Related results of promotion (catalysis) and inliibition of stereonuitation by vibrational excitation have also been obtained for the much larger molecule, aniline-NHD (CgH NHD), which shows short-time chirality and stereonuitation [104. 105]. This kind of study opens the way to a new look at kinetics, which shows coherent and mode-selective dynamics, even in the absence of coherent external fields. The possibility of enforcing coherent dynamics by fields ( coherent control ) is discussed in chapter A3.13. 

Other possible choices are to use two pairs of frequencies which together have the same energies. The key point is that quantum interference between the two pathways can be used to control the branching ratio. This coherent-control approach is very general and can be used in virtually any branch of molecular dynamics, including scattering and photo-dissociation. 

Figure B3.4.18. A schematic use of coherent control in AB A -i- B, A -i- B dissociation use of a single high-frequency photon (co) or tluee low-intensity (a)/3) photons would lead to emerging wavefimctions in both arrangements. However, by properly combining the amplitudes and phases of the single- and tluee-photon paths, the wavefimction would emerge in a single channel.

In Section II, the basic equations of OCT are developed using the methods of variational calculus. Methods for solving the resulting equations are discussed in Section III. Section IV is devoted to a discussion of the Electric Nuclear Bom-Oppenhermer (ENBO) approximation [41, 42]. This approximation provides a practical way of including polarization effects in coherent control calculations of molecular dynamics. In general, such effects are important as high electric fields often occur in the laser pulses used experimentally or predicted theoretically for such processes. The limits of validity of the ENBO approximation are also discussed in this section. 

Many of the initial theoretical models used to vahdate the concept of coherent control and optimal control have been based on the interaction of the electric field of the laser light with a molecular dipole moment [43, 60, 105]. This represents just the first, or lowest, term in the expression for the interaction of an electric field with a molecule. Many of the successful optimal control experiments have used electric fields that are capable of ionizing the molecules and involve the use of electric field strengths that lead to major distortions of the molecular electronic structure. With this in mind, there has been discussion in the... 

This chapter has provided a brief overview of the application of optimal control theory to the control of molecular processes. It has addressed only the theoretical aspects and approaches to the topic and has not covered the many successful experimental applications [33, 37, 164-183], arising especially from the closed-loop approach of Rabitz [32]. The basic formulae have been presented and carefully derived in Section II and Appendix A, respectively. The theory required for application to photodissociation and unimolecular dissociation processes is also discussed in Section II, while the new equations needed in this connection are derived in Appendix B. An exciting related area of coherent control which has not been treated in this review is that of the control of bimolecular chemical reactions, in which both initial and final states are continuum scattering states [7, 14, 27-29, 184-188]. 

Coherent Control with Femtosecond Laser Pulses, Eur. Phys. J. Sci. D, 14(2), (2001). 

P. Brumer and M. Shapiro, Coherent Control of Molecular Dynamics, John Wiley Sons, Inc., New York, 2003. 

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 < ),... 

The present chapter has no ambition to cover all these topics. We focus solely on the information content of the two-pathway coherent control approach, where the energy-domain, single quantum states approach to the control problem simplifies the phase information and allows analysis at the most fundamental level. We regret having to limit the scope of this chapter and thus exclude much of the relevant literature. We hope, however, that this contribution will entice the reader to explore related literature of relevance. 

Polyatomic molecules provide a still richer environment for studying phase control, where coupling between different dissociation channels can occur. Indeed, one of the original motivations for studying coherent control was to develop a means for bond-selective chemistry [25]. The first example of bond-selective two-pathway interference is the dissociation of dimethyl-sulfide to yield either H or CH3 fragments [74]. The peak in Fig. 11 is indicative of a resonance embedded in an elastic continuum (case 4). 

The previous sections focused on the case of isolated atoms or molecules, where coherence is fully maintained on relevant time scales, corresponding to molecular beam experiments. Here we proceed to extend the discussion to dense environments, where both population decay and pure dephasing [77] arise from interaction of a subsystem with a dissipative environment. Our interest is in the information content of the channel phase. It is relevant to note, however, that whereas the controllability of isolated molecules is both remarkable [24, 25, 27] and well understood [26], much less is known about the controllability of systems where dissipation is significant [78]. Although this question is not the thrust of the present chapter, this section bears implications to the problem of coherent control in the presence of dissipation, inasmuch as the channel phase serves as a sensitive measure of the extent of decoherence. 

Although coherent control is now a mature field, much remains to be accomplished in the study of the channel phase. There is no doubt that coherence plays an important role in large polyatomic molecules as well as in dissipative systems. To date, however, most of the published research on the channel phase has focused on isolated atoms and diatomic molecules, with very few studies addressing the problems of polyatomic and solvated molecules. The work to date on polyatomic molecules has been entirely experimental, whereas the research on solvated molecules has been entirely theoretical. It is important to extend the experimental methods from the gas to the condensed phase and hence explore the theoretical predictions of Section VC. Likewise interesting would be theoretical and numerical investigations of isolated large polyatomics. A challenge to future research would be to make quantitative comparison of experimental and numerical results for the channel phase. This would require that we address a sufficiently simple system, where both the experiment and the numerical calculation could be carried out accurately. 

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. 

A. D. Bandrauk, Y. Fujimura, and R. J. Gordon (eds.), Laser Control and Manipulation of Molecules, American Chemical Society Oxford University Press, New York 2002 W. Potz and A. Schroeder (eds.), Coherent Control in Atoms, Molecules, and Semiconductors, Kluwer Academic Publishers, Dordrecht, 1999. 

We follow the convention adopted by the literature on coherent control via the one- versus three-photon excitation method, where the frequency of the three-photon field is denoted coi and that of the one-photon field is denoted C03. 

M. Sukharev and T. Seideman, Coherent control approaches to light guidance in the nanoscale, J. Chem. Phys. 124, 144707 (2006). 

Nakamura, Y., Pashkin, Y.A. and Tsai, J.S. (1999) Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature, 398, 786-788. 

Single (or multiple) electrons or holes can be bound locally to a small semiconductor nanostructure or to a single impurity in a solid. The resulting discrete energy levels can be used to define a spin qubit. Coherent control and read-out... 

---