Quadratically chirped pulse

Figure 34. Contour map of the nonadiabatic transition probability Pn induced by quadratically chirped pulse as a function of the two basic parameters a and p. Taken from Ref. [37]-...

Figure 36. Time variation of the wave packet population on the ground X and excited B states of LiH. The system is excited by a single quadratically chirped pulse with parameters 0(a, = 5.84 X 10 eV fs , = 2.319 eV, and / = 1.00 TWcm . The pulse is centered at t = 0...

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 41. Selective bond breaking of H2O by means of the quadratically chirped pulses with the initial wave packets described in the text. The dynamics of the wavepacket moving on the excited potential energy surface is illustrated by the density, (a) The initail wave packet is the ground vibrational eigen state at the equilibrium position, (b) The initial wave packet has the same shape as that of (a), but shifted to the right, (c) The initail wave packet is at the equilibrium position but with a directed momentum toward x direction. Taken from Ref. [37]. (See color insert.)...

Figure 58. Changes of the wavepacket populations on the respective states (upper panels) under the 3.5TWcm quadratically chirped pulses (lower panels) during the sequential pump-dump scheme via the (a) I A —> I B pumping at CHD and [(b) and (c)] 2 A I B —> I A pump...

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. 

At the resonance w(t) = A(x), the adiabatic potentials i.e. the eigenvalues of (5.9) show avoided crossing and the population splits into the two adiabatic Floquet states. In the case of quadratically chirped pulses, the instantaneous frequency meets the resonance condition twice and near-complete excitation can be achieved due to the constructive interference. The nonadi-abatic transition matrix Ujj for the two-level problem of (5.9) is given by the ZN theory [33] as... 

For excitation by quadratically chirped pulses, the transition timescale 2Ttr is slightly longer than the time interval 2tx between the two crossings,... 

According to (5.35), the most fortunate circumstance for the present scheme is a system with heavy mass and parallel potential energy surfaces (A(x) const.). The steepness of the potential difference A(x) is the most crucial parameter it not only affects the validity of this level approximation (5.8) but it also changes the efficiency of excitation according to (5.32). It is obvious that a narrow wavepacket can be relatively easily excited by a quadratically chirped pulse (cf. 5.32). However, a narrow one can easily break the level approximation (5.35) because of the broad distribution in momentum space. The optimal width of a wavepacket can be roughly estimated as... 

The time dependence of the wavepacket population on the X and B states are plotted in Fig. 5.3 for the case of a quadratically chirped pulse centered at tp = Ofs with a full temporal duration r = 20 fs. More than 86% of the initial state is excited to the B state within a few femtoseconds (see Fig. 5.3). After the excitation, Fe on the B state potential spreads rapidly due to the very light mass of LiH and the flatness of the potential. Finally, however,... 

Fig. 5.4. Initial and final wavepackets of LiH excited by the same quadratically chirped pulse as that in Fig. 5.3. Initial wavepacket refers to the wavepacket propagated up to the pulse center according to the ground surface Hamiltonian Hg excited wavepacket (approximate) refers to the result obtained using the level approximation as Pi2 x) g(x, 0) 2 and excited wavepacket (exact) refers to the numerical solution of (5.1). The latter two are backward-propagated to the pulse center at time t = tp according to the excited state Hamiltonian He...

Fig. 5.6. Time variations of the wavepacket populations in the X1 X 1 and /111 states of NaK. The system is excited by a quadratically chirped pulse with parameters = 3.13 x 102eV/fs2, plo = 1.76eV and / = 0.20TW/cm2. The pulse is...

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...

Fig. 5.8. Pump-dump control of NaK using two quadratically chirped pulses. The initial state and the first pump step are the same as in Fig. 5.7. The excited wavepacket is now dumped at R 6.5 ao on the way to the outer ( urn irig point. The first pulse is the same as that in Fig. 5.7, but the second one is different a = 1.929 x 10 2oV/fs2, = 1.224eV and I = 0.10TW/cm2. The second pulse...

Table 5.2. Quadratically chirped pulses for the bond-selective photodissociation of H2O...

First, we present the dynamics of the initial wavepacket a. Initially the system stands at the equilibrium position of the electronic ground X. The temporal evolution of the wavepacket Pe generated in the electronic excited state is shown in the left-hand column of Fig. 5.9. Apparently, tp originates in the Frank-Condon (FC) region, which is located at the steep inner wall of the electronically excited A state. The repulsive force of the potential l 0 the drives e(t) downhill toward the saddle point and then up the potential ridge, where Pe(t) bifurcates into two asymptotic valleys, with Ye = 0.495 in channel f. The excitation achieved using this simple quadratically chirped pulse is not naturally bond-selective because of the symmetry of the system. The role played by our quadratically chirped pulse is similar to that of the ordinary photodissociation process, except that it can cause near-complete excitation (see Table 5.1 for the efficiency). This is not very exciting, however, because we would like to break the bond selectively. 

Fig. 5.9. Selective bond-breaking of H2O by means of the quadratically chirped pulses with initial wavepackets a, b and c, as described in Table 5.1. The left-hand, middle and right-hand columns correspond to the cases for the initial wavepackets a, b and c, respectively. The laser-driven dynamics of the wavepackets moving on the excited potential energy surface Ve are illustrated by the density. The time is taken from the center of the pulse (i.e., tp = 0)...

As demonstrated above, bond-selective dissociation can be achieved with high efficiency by using an initial displaced-position and/or a directed-momentum wavepacket. The latter wavepacket can be prepared via the sequence of quadratically chirped pulses or by using semiclassical optimal control theory [34,35],... 

In order to control elementary process (i), an effective scheme based on the concept of quadratic chirping has been proposed [12-17]. It has been demonstrated that this idea can be applied to process (i) and that fast and near-complete selective excitation of a wavepacket can be achieved without significant distortion of its shape through the utilization of specially designed quadratically chirped pulses [18,19]. This method is discussed in the first part... 

Finally, by combining the laser control of electronic transitions of wavepackets using quadratically chirped pulses [18,19] with semiclassical op-... 

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