Coherent control using wave packets

When a molecule is excited by an ultrashort laser pulse with an appropriate center frequency, a localized wave packet can be created in the excited electronic state because of the excitation of a coherent superposition of many vibrational-rotational states. It follows from fundamental laws that the d3mamics of molecular wave packets is governed by a time-dependent Schrodinger equation (eqn 2.29), where H is the relevant Hamiltonian of the given molecule. Because molecular potential-energy surfaces are anharmonic, this molecular wave packet tends to spread both in position (coordinates) and in momentum. However, in addition to expansion or defocusing, the wave packet also suffers delocalization at a certain instant of time. Coherent quantum 

The idea of the experiment on controlling the vibrational dynamics of the I2 molecule is schematically illustrated in Fig. 12.2(a) (Kohler et al. 1995a). The desired final state (or target) in this case is the minimum-uncertainty Gaussian distribution ApAx = h/2 (where Ap is the momentum uncertainty and Ax is the coordinate uncertainty) in the electronically excited state B centered on the position Rq = 0.372 nm, in which the iodine atoms are moving toward each other with a chosen mean velocity. It is necessary to find the laser pulse E t) that will excite the molecule from its ground state to form a vibrational wave packet with the best possible overlap with the final state (the target) at the chosen instant of time (550 fs in this case). 

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The ability to create and observe coherent dynamics in heterostructures offers the intriguing possibility to control the dynamics of the charge carriers. Recent experiments have shown that control in such systems is indeed possible. For example, phase-locked laser pulses can be used to coherently amplify or suppress THz radiation in a coupled quantum well [5]. The direction of a photocurrent can be controlled by exciting a structure with a laser field and its second harmonic, and then varying the phase difference between the two fields [8,9]. Phase-locked pulses tuned to excitonic resonances allow population control and coherent destruction of heavy hole wave packets [10]. Complex filters can be designed to enhance specific characteristics of the THz emission [11,12]. These experiments are impressive demonstrations of the ability to control the microscopic and macroscopic dynamics of solid-state systems. 

In the control scheme [13,17] that we have focused on, the time evolution of the interference terms plays an important role. We have already discussed more explicit forms of Eq. (7.75). One example is the Franck-Condon wave packet considered in Section 7.2.2 another example, which we considered above, is the oscillating Gaussian wave packet created in a harmonic oscillator by an (intense) IR-pulse. Note that the interference term in Eq. (7.76) becomes independent of time when the two states are degenerate, that is, AE = 0. The magnitude of the interference term still depends, however, on the phase S. This observation is used in another important scheme for coherent control [14]. 

Coherent control Control of the motion of a microscopic object by using the coherent properties of an electromagnetic held. Coherent phase control uses a pair of lasers with long pulse durations and a well-defined relative phase to excite the target by two independent paths. Wave packet control uses tailored ultrashort pulses to prepare a wave packet at a desired position at a given time. 

As mentioned above, the temporal coherence of the laser light has revolutionized the investigation of chemical processes in real time because it has made possible the preparation, and subsequent evolution, of wave packets in molecular and atomic systems. This coherent character of laser light is currently used for quantum control of chemical processes. Although this field is still in its infancy, important scientific and technological applications are expected in the near future and will undoubtedly extend beyond chemistry. 

Two main approaches to the control of molecules using wave interference in quantum systems have been proposed and developed in different languages . The first approach (Tannor and Rice 1985 Tannor et al. 1986) uses pairs of ultrashort coherent pulses to manipulate quantum mechanical wave packets in excited electronic states of molecules. These laser pulses are shorter than the coherence lifetime and the inverse rate of the vibrational-energy redistribution in molecules. An ultrashort pulse excites vibrational wave packets, which evolve freely until the desired spacing of the excited molecular bond is reached at some specified instant of time on a subpicosecond timescale. The second approach is based on the wave properties of molecules as quantum systems and uses quantum interference between various photoexcitation pathways (Brumer and Shapiro 1986). Shaped laser pulses can be used to control this interference with a view to achieving the necessary final quantum state of the molecule. The probability of production of the necessary excited quantum state and the required final product depends, for example, on the phase difference between two CW lasers. Both these methods are based on the existence of multiple interfering pathways from the initial... 

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