Pump-dump excitation

E" dissociated by another. It is also related to a two- vs. two-photon scenario n 6.1) since, as shown in Figure 3.20, pump-dump excitation contains two-... 

PUMP-DUMP EXCITATION WITH MANY LEVELS TANNOR-RICE SCHEME... 

Flexibility can also be elegantly addressed by more sophisticated experimental techniques focusing on photoinduced isomerisation in the early stages of a supersonic expansion. The pioneering work of the Zwier group demonstrated how IR or UVAJV pump-dump excitations (SEP, Fig. 7) in the early expansion can be used to measure accurately conformational distribution together with isomerisation... 

Figure 37. Electronic excitation of the NaK wavepacket from the inner turning point of the ground X state. The X A transition is considered. The initial wave packet is prepared by two quadratically chirped pulses within the pump-dump mechanism. Taken from Ref. [37].

Figure 39. Pump-dump control of NaK molecule by using two quadratically chirped pulses. The initial state taken as the ground vibrational eigenstate of the ground state X is excited by a quadratically chirped pulse to the excited state A. This excited wavepacket is dumped at the outer turning point at t 230 fs by the second quadratically chirped pulse. The laser parameters used are = 2.75(1.972) X 10-2 eVfs- 1.441(1.031) eV, and / = 0.15(0.10)TWcm-2 for the first (second) pulse. The two pulses are centered at t = 14.5 fs and t2 = 235.8 fs, respectively. Both of them have a temporal width i = 20 fs. (See color insert.) Taken from Ref. [37].

Figure 40. Pump-dump control of NaK by using two quadraticaUy chirped pulses. The initial state and the first step of pump are the same as in Fig. 39. The excited wave packet is now dumped at R 6.5cio on the way to the outer turning point. The parameters of the second pulse are a ) = 1.929 X 10 eVfs , = 1.224eV, and I = 0.lOTWcm . The second pulse is centered at...

The ideas presented here use a weak UV pulse. One could also imagine using strong UV pulses, e.g. in one of the schemes presented by Sola et al. in this book, which alter the BO potentials by mixing them. These schemes usually involve three electronic states. This alters the discussion somewhat since even in the weak-field limit a trivial solution may be found in a pump-dump setup the wave packet is first excited to a repulsive state, where the (now fast) dynamics takes place and when the wave packet has reached the desired location it is dumped to the excited bound state. Exploring various three-state setups is a topic for future research. 

A more sophisticated version of the Tannor-Rice scheme exploits both amplitude and phase control by pump-dump pulse separation. In this case the second pulse of the sequence, whose phase is locked to that of the first one, creates amplitude in the excited electronic state that is in superposition with the initial, propagated amplitude. The intramolecular superposition of amplitudes is subject to interference whether the interference is constructive or destructive, giving rise to larger or smaller excited-state population for a given delay between pulses, depends on the optical phase difference between the two pulses and on the detailed nature of the evolution of the initial amplitude. Just as for the Brumer-Shapiro scheme, the situation described is analogous to a two-slit experiment. This more sophisticated Tannor-Rice method has been used by Scherer et al. [18] to control the population of a level of I2. The success of this experiment confirms that it is possible to control population flow with interference that is local in time. 

In general, the results of the calculations establish that it is possible to guide the reaction to preferentially form one or the other product with high yield. Note that, unlike the original Tannor-Rice pump-dump scheme, in which the pulse sequences that favor the different products have different temporal separations, the complex optimal pulses occupy about the same time window. Indeed, the optimal pulse shape that generates one product is very crudely like a two-pulse sequence, which suggests that the mechanism of the enhancement of product formation in this case is that the time delay between the pulses is such that the wavepacket on the excited-state... 

An intuitive method for controlling the motion of a wave packet is to use a pair of pump-probe laser pulses, as shown in Fig. 13. This method is called the pump-dump control scenario, in which the probe is a controlling pulse that is used to create a desired product of a chemical reaction. The controlling pulse is applied to the system just at the time when the wave packet on the excited state potential energy surface has propagated to the position of the desired reaction product on the ground state surface. In this scenario the control parameter is the delay time r. This type of control scheme is sometimes referred to as the Tannor-Rice model. 

Summary. An effective scheme for the laser control of wavepacket dynamics applicable to systems with many degrees of freedom is discussed. It is demonstrated that specially designed quadratically chirped pulses can be used to achieve fast and near-complete excitation of the wavepacket without significantly distorting its shape. The parameters of the laser pulse can be estimated analytically from the Zhu-Nakamura (ZN) theory of nonadiabatic transitions. The scheme is applicable to various processes, such as simple electronic excitations, pump-dumps, and selective bond-breaking, and, taking diatomic and triatomic molecules as examples, it is actually shown to work well. 

The remainder of this paper is organized as follows In Sect. 5.2, we present the basic theory of the present control scheme. The validity of the theoretical method and the choice of optimal pulse parameters are discussed in Sect. 5.3. In Sect. 5.4 we provide several numerical examples i) complete electronic excitation of the wavepacket from a nonequilibrium displaced position, taking LiH and NaK as examples ii) pump-dump and creation of localized target wavepackets on the ground electronic state potential, using NaK as an example, and iii) bond-selective photodissociation in the two-dimensional model of H2O. A localized wavepacket is made to jump to the excited-state potential in a desirable force-selective region so that it can be dissociated into the desirable channel. Future perspectives from the author s point of view are summarized in Sect. 5.5. 

In order to demonstrate the efficiency and robustness of the formulations presented in Sect. 5.2 and 5.3, three practical applications are considered here. In the first part of this section, we consider the complete excitation of a wavepacket from a nonequilibrium displaced position, which is directly related to the idea of bond-selective breaking, as explained in the Introduction . This is demonstrated numerically by taking diatomic molecules LiH and NaK as examples. In the second part, we consider the complete pump-dump control and creation of a localized wavepacket using quadratic chirping within the pump-dump mechanism. The bond-selective photodissociation of the H20 molecule is discussed in the third part of this subsection as an example of a multidimensional system. 

The method of electronic excitation by a quadratically chirped pulse mentioned above can be applied to a wavepacket moving away from the turning point, so this technique can be applied to various processes such as pump-dump, wavepacket localization and selective bond-breaking, as we will discuss in the rest of this section. 

Fig. 5.7. Pump-dump control of NaK molecule using two quadratically chirped pulses. The initial state is taken as the ground vibrational eigenfunction of the ground state X1S+ and this is excited by a quadratically chirped pulse to the excited state A1E+. The excited wavepacket is dumped at the outer turning point t cs 230 fs by the second quadratically chirped pulse. The laser parameters used are...

Consider now the pump-dump scenario where, for generality, we assume a pump pulse whose spectral width is sufficiently large to encompass a large number of levels. As in Section 3.5, a molecule with Hamiltonian HM is subjected to two temporally separated pulses e(t) = sx(t) + ed(t). The probability of forming channel q at energy E is now given by the extension of Eq. (3.77) to many level excitations by ex(l), that is,... 

As a simple example, consider the model [264] shown in Figure 8.16. The system is initially in a mixture of the ground vibrational state of D and L. The pump laser carries the system to a single excited vibrational state of the excited electronic state, and the dump laser returns the system to an excited vibrational state of the ground electronic state. This then is a pump dump scenario, but transitions are solely between bound states. 

To examine a particular case, consider the pump—dump control discussed in Section 3.5 and Chapter 4. Here a sequence of two pulses first excite a molecule to a set of intermediate bound states with wave func and energy and then to dissociate these states. We denote the two (k = 1,2) by... 

Numerical results using this technique were obtained [471] for the pump-dump photodissociation of Na2 to optimize the production of either Na(3s) + Na(3p) or Na(3s) + Na(4s). In this case optimal control often required pulses that were fairly heavily structured in laser phase and frequency. A more detailed study [471] indicated that this structure was necessary for the dissociation pulses, but not necessary for the excitation pulse. Further, as is often the case with OCT, pulses with very different structures were found to achieve similar control objectives in different ways. 

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