J. Phys. Chem. 1996, 100, 7789-7796
7789
Femtosecond Study of Multiphoton Ionization Processes in K2: From Pump-Probe to Control# R. de Vivie-Riedle,*,† K. Kobe,‡ J. Manz,† W. Meyer,§ B. Reischl,† S. Rutz,‡ E. Schreiber,*,‡ and L. Wo1 ste‡ Institut fu¨ r Physikalische und Theoretische Chemie, Freie UniVersita¨ t Berlin, Takustrasse 3, D-14195 Berlin, Germany; Institut fu¨ r Experimentalphysik, Freie UniVersita¨ t Berlin, Arnimallee 14, D-14195 Berlin, Germany; and Institut fu¨ r Physikalische und Theoretische Chemie, Fachbereich Chemie, UniVersita¨ t Kaiserslautern, Erwin Schro¨ dingerstrasse, D-67663 Kaiserslautern, Germany ReceiVed: September 18, 1995; In Final Form: March 26, 1996X
Experimental and theoretical pump-probe studies are performed for the K2 molecule. Special molecular spectroscopic properties combined with the dynamics induced by “femtosecond state preparation” facilitate the transition from pump-probe to control spectroscopy. Hereby, the intensity of the laser field serves as a control parameter in the observed multiphoton processes. In the monitored transient ion signal we can distinguish the effect of two processes, i.e., multiphoton ionization (MPI) and resonant impulsive stimulated Raman scattering (RISRS). As a consequence, the temporal evolution of the ion signal reflects the induced dynamics of either the first excited state A1Σu+ or the ground state X1Σg+ of the potassium dimer.
1. Introduction Recently, femtosecond techniques have been advanced in wide spectral regions (from UV to near-IR)1 to directly probe molecular motions in real time. Various examples of bound state dynamics2-11 have been investigated by experimental and theoretical groups over the past few years. On the experimental side, the dynamics of exemplary molecules have been studied successfully by means of pump-probe spectroscopy on a femtosecond time scale.2-7 Here, besides transient fluorescence spectroscopy the technique of transient MPI was applied. The principle of this method is sketched in Figure 1a. A first ultrashort laser pulse prepares a coherent superposition of vibrational eigenstates in an excited electronic state. Hence, a vibrational wave packet is produced propagating on the potential energy surface of this excited state. The wave packet’s motion is probed by a second time-delayed ultrashort laser pulse. This pulse is used to ionize the molecule. The oscillatory changes of the detected ion signal vs delay time reflect the wave packet’s propagation and reveal besides the vibrational period detailed information about the transition pathways between the electronic states involved. On the theoretical side, time-dependent quantum calculations allow to simulate these pump-probe ionization experiments. The calculations yield the ionization pathways as well as the transition mechanisms of the multiphoton processes.4-9 The interplay of theory and experiment then enabled an excellent understanding of the laser pulse induced MPI dynamics of small molecules. In particular, Gerber, Engel, et al.5,6 have studied the femtosecond time-resolved MPI of the Na2 molecule in great detail. Beyond this, it is now of high interest to develop new farreaching concepts that use these special dynamics of coherent superpositions of states prepared by femtosecond laser pulses. The main goal is to influence a molecular system, either to focus on vibrational modes in selected potential energy surfaces or #
Dedicated to J. L. Kinsey. Institut fu¨r Physikalische und Theoretische Chemie, Freie Universita¨t Berlin. ‡ Institut fu ¨ r Experimentalphysik, Freie Universita¨t Berlin. § Universita ¨ t Kaiserslautern. X Abstract published in AdVance ACS Abstracts, April 15, 1996. †
S0022-3654(95)02740-7 CCC: $12.00
Figure 1. Schematic diagram for (direct) two-photon ionization (TPI) and (indirect) multiphoton ionization via RISRS processes.
to guide the system into distinctive reaction channels. The control of reaction channels by femtosecond pulses was first suggested theoretically by Tannor, Kosloff, and Rice12,13 and was later on also observed in experiments by Zewail, Gerber, et al.14,15 In both cases the delay time between pump and probe (control) laser pulse was the control parameter. With some modifications of the powerful pump-probe technique it is possible to drive a molecular wave packet to a desired location on the potential energy surface (PES) from which selective dynamic processes (e.g. chemical reactions14,15) can be initiated. An excellent candidate to investigate the principles of a control experiment should be a simple molecule, which is relatively easy to handle, both theoretically and experimentally. Here we choose the potassium dimer as adequate molecular system. Experimentally, Rutz and Schreiber16 could detect the wave packet propagation in the first excited electronic state (A1Σu+). In addition, Kobe et al.17,18 found the wave packet propagation with a temporal period which can be assigned to the ground state of K2. In this paper, we present consistent experimental and theoretical investigations which demonstrate that the intensity of the initial laser field will be the tool for control of the observed dynamics. In extension to the strategy of Tannor, Kosloff, and Rice, we shall demonstrate that different laser intensities induce different transition pathways (cf. Figures © 1996 American Chemical Society
7790 J. Phys. Chem., Vol. 100, No. 19, 1996
de Vivie-Riedle et al. TABLE 1: Experimental and Theoretical Laser Pulse Parameters for Moderate and High Power moderate power wavelength (nm) pulse width (fs) spectral width (cm-1) peak power (GW cm-2)
Figure 2. Argon ion laser used to pump a femtosecond laser (femtosecond titanium:sapphire laser for moderate pulse power, picosecond titanium:sapphire laser with fiber compressor for high pulse power). 1% of the laser output is used to control the laser parameters by means of a spectrometer (S) and an autocorrelator (A). The laser is splitted with a 50% beam splitter, and one part passes the delay unit. Both laser beams are recombined in the interaction region of the cluster chamber. Potassium vapor is produced in the oven and coexpanded with argon. The so-produced cluster beam is collimated using a molecular beam skimmer. Potassium cluster ions produced by interaction of the laser beams with the cluster beam are focused by the ion optics into the quadrupole mass filter (QMS) and continuously detected by means of a secondary electron multiplier (SEM). The LangmuirTaylor detector (LTD) is used to control the cluster beam intensity I0. The intensity I of ions is recorded as a function of the delay time ∆t.
1, a and b), e.g., competing direct MPI via electronic excited states vs indirect MPI via RISRS into the molecule’s ground state; see refs 19-28. In contrast to emission spectroscopy where a continuous wave laser or a nanosecond laser pulse is used to populate specific vibrational eigenstates of the initial (here electronic ground) state,29 the RISRS processes prepare a coherent vibrational state within the pump pulse duration which evolves on the ground state surface and whose vibrational motions can now be detected in the transient ion signal. The reported control mechanism is in line with other work on similar subjects6,10,19,20,30,31 and our investigations on K2 will particularly lead to new aspects compared to Na2 in this series of homologues. Complementary aspects have already been reported for Cs2.32 In this article we will start with a brief description of our experimental (section 2) and theoretical (section 3) approach to investigate the dynamics of MPI processes in K2. The results are presented in section 4 where we discuss and compare the theoretical and experimental data received for moderate and high laser field excitation. Here, we emphasize the intensity dependence of the temporal evolution of the probed ion signal. Finally, a conclusion is presented in section 5. 2. Experiment The experimental setup to study the vibrational dynamics of K2 is presented in Figure 2. Femtosecond light pulses with a
high power
exp
theor
exp
theor
840 60-70 190 0.5
840 60 245 0.5-2.2
840 50-60 260 5
840 60 245 9
wavelength λcentral ) 840 nm are produced in an ultrashort laser system based on a regeneratively modelocked titanium:sapphire laser. For pump-probe experiments with moderate pulse power the titanium:sapphire laser is operated in the femtosecond mode where the group velocity dispersion (GVD) is resonatorinternally compensated by four built-in prisms. The resulting 60-70 fs pulses (fhwm, assuming sech2 shape) with a bandwidth of 190 cm-1 are emitted with an average power of about 1.2 W and a repetition rate of 80.5 MHz. Therefore, the peak power of the laser pulses reaches about 0.5 GW/cm2 in the focus of a 400 mm lens. To gain even higher power of the laser pulses the titanium:sapphire laser is run in the picosecond mode by use of a Gires-Tournois interferometer to compensate for the GVD. The emitted picosecond pulses have a width of 1.4 ps (fhwm, assuming sech2 shape). A fiber compressor is used to extend the spectral width of these picosecond pulses to an amount sufficiently broad for femtosecond pulses with a pulse width of 50-60 fs duration. A four-pass prism compensator is applied to compensate for the GVD of the transmitted upchirped pulses. The so-generated femtosecond pulses have a spectral width of about 260 cm-1 and a peak power of 5 GW/cm2 when focused with a 400 mm lens into the interaction region of our experiment. The laser data for both setups are summarized in Table 1. To realize a one-color pump-probe experiment, a Michelsonlike arrangement is built up to split the laser beam and to realign it collinearly with the same polarization. A dc-motor-driven translation stage to position a retroreflector is installed in one of the Michelson branches. A femtosecond laser pulse (probe pulse) running through this arm of the Michelson arrangement is optically delayed with respect to a pulse (pump pulse) running through the other Michelson branch. The arrival time difference ∆t of the two femtosecond pulses at the interaction region is given by ∆t ) 2∆x/c, where ∆x is the difference of the lengths between the Michelson branches and c is the speed of light for the used wavelength in air. The detour ∆x and therefore ∆t is controlled by an optical encoder with an accuracy ∆tmin < 0.5 fs. After recombination of the pump and the probe beam the average power in each beam amounts to about 200 and 170 mW for the moderate and the high-power experiment, respectively. To produce a “cold” potassium cluster beam pure potassium is evaporated with a partial pressure of about 100 mbar. Argon is used as an inert carrier gas to coexpand the resulting potassium vapor through a 70 µm nozzle. For a stable potassium cluster beam a temperature of about 850 K is required. The addition of the carrier gas with a pressure of about 5 bar provides cold clusters with vibrational and rotational temperatures Tvib < 50 K and Trot < 10 K, respectively. The stability of the cluster beam was better than 10%. Before entering the interaction and detection chamber, the cluster beam is skimmed by means of a 1 mm orifice skimmer. The laser beams cross the cluster beam in a right angle in the interaction/detection chamber. A quadrupole mass filter selects the ions which are produced by photoabsorption. The mass filter has an absolute resolution of 0.3 amu in the mass region of K2 (≈80 amu); therefore, the
Multiphoton Ionization Processes in K2
J. Phys. Chem., Vol. 100, No. 19, 1996 7791
resolution m/∆m is better than 260. The isotope-selected cluster ions are continuously detected by a secondary electron multiplier. To examine the vibrational dynamics of the various electronically excited states which are involved in the different ionization pathways, the mass spectrometer is tuned to the desired mass peak of the specific K2 isotopomer. Then the ion signal produced by the pump and probe laser beams is recorded as a function of the delay time ∆t between the pulses. 3. Theory Different theoretical methods exist to describe ultrafast multiphoton ionization processes in diatomics and have been discussed in detail in previous work.4-6,8,9 Here we will outline the special features of our approach with respect to the K2 pump-probe experiment for moderate and high laser field intensities. Since we want to describe a low-temperature molecular beam experiment the rotational degrees of freedom can be neglected and we suppose that the initial state of the system is the lowest vibrational state φ0,V)0 of the electronic ground state:
( )( ) ψ0(r, t)0) φ0,V)0(r) ψ1(r, t)0) 0 · · ) · · · · ψn(r, t)0) 0
(1)
The nuclear wave functions ψi are the projections of the total wave functions on the involved electronic surfaces labeled i ) 0, 1, 2, ... for convenience. They depend on the nuclear coordinate r and on the time t. We shall compare our simulations with the experimental results obtained for pump and probe laser pulses with a wavelength of 840 nm. Due to this wavelength and to the selection rules for optical transitions, there are five relevant electronic states which are able to participate in the MPI process. The corresponding potential curves for the X1Σg+, A1Σu+, 41Σg+, 21Πg states of the neutral and the K2+ ion ground state are displayed in Figures 6 and 7 and the states are abbreviated as X, A, 4, 2, and I, respectively. The electronic continuum due to the ejection of the electron with kinetic energy Ek is represented by a quasicontinuum, i.e., by a sufficiently large number N of discrete electronic states.33 Due to the orthogonality of the electronic basis functions the time-dependent Schro¨dinger equation transforms into N sets of five coupled first-order differential equations which are written in matrix representation:
() (
ψX1Σg ψA1Σu ∂ ψ ip 41Σg ∂t ψ21Πg
)
ψI,k(Ek) HXX HAX 0 0 0
HXA HAA H4A H2A
0 0 HA4 HA2 H44 0 H22 0
0
HIk4 HIk2
)( )
ψX1Σg 0 ψA1Σu 0 I H4k · ψ41Σg I H2k ψ21Πg (HIkk+Ek) ψI,k(Ek)
(2)
Equation 2 is solved without any further approximation, and within the model all multiphoton processes are included. The calculation is repeated for different values of the kinetic energy Ek and all contributions to the ion signal are added. The method converges reasonably fast for the simulation of the present K2
Figure 3. Calculated electronic transition dipole moments of the X1Σg+ f A1Σu+, A1Σu+ f 41Σg+, and A1Σu+ f 21Πg transitions.
pump-probe experiments and allows a careful analysis to locate the region of the transition pathway. The interval of the total continuum superimposed on the ion ground state is (0, 0.38 eV). In the case of moderate laser field intensities34,35 it was found that under these conditions the contribution of a single optimal selected photon energy Ek already defines the dominant features of the total transient ionic signal. The selection follows the rules of the classical differential potential analysis.36 The matrix elements of the Hamiltonian (see eq 2) describing the neutral molecular states are given by Hii ) Tr + Vi, where Tr ) P2/2m is the kinetic energy operator and Vi are the potential energy surfaces. The off-diagonal elements describe the interaction with the laser field in the semiclassical dipole approximation and they are given by Hij ) -µij‚E(t) with the electronic transition dipole moments µij. The electromagnetic field E(t) is given by E(t) ) Epump(t) + Eprobe(t + ∆t), where Epump/probe(t) ) E0 cos ωt s(t). E0 is the maximum amplitude of the electromagnetic field, ω the laser frequency, and s(t) a shape function. Gaussian functions are chosen as adequate shape functions for both pump and probe pulse. The matrix elements representing the continuous part of the Hamiltonian are given by HIkk ) 〈φI,k|HI|φI,k〉 and HIki ) 〈φI,k| -µI‚E(t)|φi〉 with electronic basis functions of the continuum φI,k and the electronic wave functions of the neutral state φi. The basic technique used to propagate the wave packet in the spacial domain is the FFT method.37,38 Two of the electronic states, namely the 21Πg and the 41Σg+ state, are very close in energy. To elucidate the transition pathways connected to them the total excitation mechanism is separated in a first step into two independent processes including alternatively the 21Πg or the 41Σg+ state. In a second step all four states plus the ion continuum are included in eq 2. The potential energy surfaces Vi and the dipole transition moments µij between the neutral states are obtained from ab initio data.39 These calculations involve carefully saturated GTO basis sets and include the effective core polarization potential (CPP) as defined and applied to other alkaline dimers in refs 40. About 50 electronic states have been investigated, and where comparison with experiment was possible, agreement to within 30-80 cm-1 for the excitation energies and to better than 1 cm-1 for vibrational frequencies was obtained. A ∼2% accuracy is expected for the dipole transition moments, as observed for corresponding results on Li2 and Na2.40 The employed dipole transition moments are shown in Figure 3. Up to now the transition moments into the ion state were not available from ab initio calculations. For the subsequent application, we assume that they are independent of Ek, that they have the same values for both transitions 21Πg f ion and
7792 J. Phys. Chem., Vol. 100, No. 19, 1996
de Vivie-Riedle et al.
Figure 4. Comparison between the measured pump-probe and calculated ionization signal as a function of delay time between the laser pulses at moderate pulse intensities (cf. Table 1), adapted from ref. 34. The fluctuations in the experimental pump-probe signal are mainly caused by instabilities of the molecular beam during the experiment. The ratio of the shown modulation amplitude compared to the overall averaged ion intensity amounts to 0.6 (exp) and 1.9 (theor). The difference is due to the fact that, in contrast to the theoretical data, the experimental ion signal contains a constant fraction of produced ions, which originates from the interaction of single pump or probe pulse with the molecules.
41Σg+ f ion and that this value is 1/3µA4 (re). This introduces two arbitrary factors which scale the calculated ionic populations and the relative contributions from the 41Σg+ and the 21Πg state. These factors imply slightly different experimental and apparent theoretical intensities without effecting the resulting patterns of the ion signals. The specific parameters for the theoretical moderate and strong laser pulses, adjusted to the experimental ones are also presented in Table 1. In the subsequent presentation of the results for moderate intensities, we use an intensity of 2.2 GW/cm2 for clear graphical presentations of the rather small populations in the 21Πg state. Gratifyingly, the resulting theoretical pattern of the ion signal does not change in the intensity region of 0.5-2.2 GW/cm2. 4. Results and Discussion Experimental and theoretical femtosecond pump-probe studies for the K2 molecule are performed for moderate and high laser intensities. The comparison of typical experimental and theoretical total ion signals for delay times up to 10 ps is presented in Figures 4 and 5 for moderate and high laser intensities, respectively. The first obvious difference is that the transient ion signal for moderate laser intensity shows a distinct oscillation, whereas for high laser field excitation the oscillatory structure is rather poorly resolved. The disturbed oscillatory structure might be due to interferences of different wave packet signals. To elucidate the ionization mechanism for the two selected laser intensities the relevant snapshots of the transition processes are presented in Figures 6 and 7. The actual wave packets are represented by the absolute values of their amplitudes. In both cases the delay time between pump and probe pulse is 300 fs, the time period in which the wave packet of the A1Σu+ state is located close to its outer classical turning point. In each case only the wave packets which participate in the dominant pathway are shown. In the present four state plus ion continuum model, two main transition pathways can be distinguished. Ionization pathway a involves the electronic states X1Σg+, A1Σu+, 21Πg, and the ion ground state continuum whereas ionization pathway b involves the electronic states X1Σg+, A1Σu+, 41Σg+, and the ion ground state continuum. In Figure 8a,b, the corresponding norm of the involved states as well as
Figure 5. Comparison between the measured pump-probe and calculated ionization signal as a function of delay time between the laser pulses at high pulse intensities (cf. Table 1). Panel a shows the ion population when only the 41Σg+ state is included in the calculation, panel b the experimental signal, and panel c the resulting ion population (upper curve) when both states 41Σg+ and 21Πg are included in the calculation together with the interference term 2 Re 〈ψ(Ek)|ψ(Ek′)〉 (lower curve) of both ionization pathways in the ion continuum. The fluctuations in the experimental pump-probe signal are mainly caused by instabilities of the molecular beam during the experiment. The ratio of the shown modulation amplitude compared to the overall averaged ion intensity amounts 0.5 (exp) and 1.1 (theor). The difference is due to the fact that, in contrast to the theoretical data, the experimental ion signal contains a constant fraction of produced ions, which originates from the interaction of single pump or probe pulse with the molecules.
Figure 6. Snapshots of the wave packets in their respective electronic states for a delay time of 300 fs between pump and probe laser for the (direct) (1 + 2)-multiphoton ionization (MPI) process in K2 (moderate laser field). The wave packets are represented by their absolute values. The two-photon step is indicated by the arrows. The 21Πg state is included in the dynamical calculation, the 41Σg+ state is inactive.
the total norm is presented for the same two selected laser intensities. In the case of moderate laser fields, detailed calculations have shown that the only efficient ionization pathway is pathway a.
Multiphoton Ionization Processes in K2
Figure 7. Snapshots of the wave packets in their respective electronic states for a delay time of 300 fs between pump and probe laser are shown for the (indirect) (2 + 3) multiphoton ionization process in K2 (high laser field). The wave packets are represented by their absolute value. The effect of the RISRS process is indicated by the curved arrow. The subsequent three-photon step is indicated by the arrows. The 41Σg+ state is included in the dynamical calculation, the 21Πg state is inactive.
Figure 8. Change of population in the electronic states of K2 involved in the MPI processes presented together with the exciting pump and probe laser pulses for a delay time of 300 fs. Panel a shows the situation for laser pulses of moderate intensities and panel b for high laser intensities. The creation of a ground state wave packet by RISRS processes as well as the Rabi-type process is seen for the more intense laser pulse in panel b.
According to refs 34 and 35, the pump pulse prepares a wave packet in the A1Σu+ state (Figure 6a), centered energetically at the vibrational level V ) 11. The 21Πg state is populated to only a small amount with a wave packet centered at V ) 3. The potential energy gap ∆A2 of 1.494 eV at the outer (r ) 5.4 Å) and of 1.576 eV at the inner turning points (r ) 4.35 Å) of the A1Σu+ state wave packet are of decisive importance in this process. Even taking into account the energy width due to the rather short pump pulse, it is exclusively the potential energy difference at the outer turning point which is in good resonance with the laser frequency (of 840 nm ) 1.475 eV). Therefore,
J. Phys. Chem., Vol. 100, No. 19, 1996 7793 significant transitions into the ion ground state are possible, only while the A1Σu+ state wave packet is at its outer turning point. Now the probe pulse can ionize the molecule using the 21Πg state as a resonant state. This process is indicated in Figures 6, b and c, which show the situation around the maximum of the probe pulse. The transition occurs, as indicated by the arrows, at the outer turning point (pathway a) of the wave packet in the A1Σu+ state. In summary, a “direct” pure (1 + 2) multiphoton (MPI) process into the ion ground state takes place in the case of moderate laser intensities. In this context “pure” means that the first step is a pure one-photon process, i.e., the 21Πg state need not be populated, and the second step, induced by the probe laser, is a pure two-photon excitation from the A1Σu+ state via the 21Πg state into the ion continuum. The snapshots correspond to a calculation for one optimally selected kinetic energy Ek ) 0.263 eV, which is indicated by the shortened arrow in Figure 6b. In the transition process for higher laser fields the contribution of the 41Σg+ state becomes important. To illustrate this process let us first consider the simulation when exclusively the 41Σg+ state, but not the 21Πg state, is included in the calculation (see Figure 7a-c). Here, the pump pulse prepares wave packets both in the A1Σu+ and in the 41Σg+ states (Figure 7a); i.e., a two-photon excitation takes place. Simultaneously, a significant motion of the wave packet on the electronic ground state surface (centered at V ) 1) is induced by efficient RISRS processes from the excited states (mainly from the A1Σu+ state), as indicated schematically in Figure 1b and 7a. Again the wave packet of the A1Σu+ state is at its outer turning point when the probe pulse is turned on (Figure 7b). Simultaneously, the wave packet in the 41Σg+ state has moved even further away from its inner turning point. Figure 7b,c shows the situation of the dynamics around the maximum of the probe pulse. Due to the enhanced (compared to moderate laser fields) amplitude motion on the ground state surface, now a transition pathway at its inner turning point is opened (pathway b). The turning point of the ground state wave packet is shifted to shorter bond lengths from 3.82 to 3.75 Å which now corresponds well to the inner turning point of the wave packet in the 41Σg+ state (3.76 Å). This opens a new pathway b, different from process a, and an efficient direct resonant three-photon transition (as seen above in Figure 7b) at the inner turning point of the wave packet in the X1Σg+ ground state takes place. The process b can be enhanced by two- and one-photon transitions from the A1Σu+ and 41Σg+ states, respectively. A third conceivable enhancement via the inner turning point of the 21Πg state wave packet at 4.35 Å remains inactive, because here the energy gap ∆A2 stays out of optimal resonance, as in the case of moderate laser intensities. The snapshots are taken for one optimally selected kinetic energy Ek ) 0.209 eV of the ionic continuum, which is indicated by the shortened arrow in Figure 7b. The increasing role of the excitation scheme b at higher laser intensities reflects the intensity dependent enhancement of the RISRS process. Basically, higher laser intensities just stimulate more Raman processes and their effect on the ground state wave packet is enforced. Similar investigations are reported by Banin et al.19 for a two-electronic surface system. They pointed out the significance of Nπ (N ) 1, 2, ...) pulse conditions for the RISRS process. The π pulse is defined by 1/2Wtf ) π with the pulse duration tf and W ≈ µ(r)(1/htf)∫0E(t′) dt′.41 According to ref 19, the π pulse condition creates a dynamical “hole” in the position distribution of the ground state at the point of resonance, while increase in laser intensities leads to faster Rabi cycling and the 2π pulse cycles the amplitude back to the ground state inducing there a momentum kick to the hole. Thus for a
7794 J. Phys. Chem., Vol. 100, No. 19, 1996 pulse with the proper integrated fluence of 2π the contribution from the excited states’ dynamics in the transient ion signal can be minimized and the motion of the coherent vibrational state in the ground state can be maximized. We adapt these considerations to explain the intensity-dependent enhancement of the RISRS process in the present high vs moderate power pump-probe experiments for the potassium dimer. Here up to four electronic states plus the ion continuum can be involved. However, to discuss the effect of the RISRS process on the ground state dynamics we can focus our considerations exclusively on the dominant X1Σg+-A1Σu+ interaction. For this subsystem the present high power pulse yields 1/2Wtf ≈ 4.14 ≈ 1.3 π. For this estimate the transition dipole moment µXA(r) ) µXA(re) ) 4.5 ea0 was used. Thus the employed higher laser pulses exceed the π pulse condition. Accordingly, the ground state population after the pump pulse is nearly 50% (see Figure 8b) and the begin of Rabi cycling during the pump pulse can be recognized. A large-amplitude motion on the ground state surface is induced (see Figure 7a). In contrast, for moderate intensities the present laser pulse is estimated to be 0.62 π, i.e., a fraction of a π pulse. Thus a hole is created in the ground state at the domain of resonance (see Figure 6a), but without efficient momentum kick, and only 31% (see Figure 8a) of the total population stays in the ground state. Thus the dynamics on the excited A state are dominant. The ionization pathways a and b are confirmed by comparison of the temporal evolution of the theoretical and experimental ion signals (see Figures 4 and 5). In the case of moderate laser intensities (Figure 4) the experimental and theoretical curves show strong oscillations with a period of 500 fs. They correspond to the oscillation periods of the induced wave packet in the A1Σu+ state.34,35 Measurement and theory are in good agreement in terms of the position of the maxima and envelope intensity modulation. Sharp variations in the ion signal intensity occur in the simulation for delay times larger then 6 ps. In the same time range the noise in the experimental data is increased. As no level of noise exists in the simulation, we think that the sharp beat structure originates from wave packet interferences as reported in ref 32. In case of moderate laser intensities for which the transition paths of preparing pump and ionizing probe laser photon are located at different turning points (see Figure 6), these interferences can only occur when the wave packet in the A1Σu+ state begins to spread. The existence of only one ionization pathway a in the case of moderate laser fields is reflected in the pure oscillations of the experimental and theoretical total ion signal. No interference with other pathways occurs. The findings are strongly supported by the Fourier transform (FT) of the experimental and theoretical ion signal (Figure 9a,b). The Fourier analysis exhibits a dominant band structure with ωA(V,V+1) = 66 cm-1 and ωA(V,V+2) = 133 cm-1 due to coherent excitation of vibrational eigenstates of the A1Σu+ state with ∆V ) 1 and 2, respectively. The very weak single line at about 90 cm-1 is attributed to the electronic ground state. This line does not occur in the theoretical Fourier spectrum, because in the simulation for moderate intensities only the electronic states relevant for transition pathway a are included. High laser intensities change the dynamical situation. Now, in principle, two ionization pathways (a and b) are accessible. The oscillation period of 380 fs in the experimental signal (Figure 5b) and in the theoretical simulation (Figures 5a,c) corresponds to the vibrational motion of the wave packet in the ground state induced by the RISRS process and indicates that ionization pathway b is now dominant. Again a structure of sharp modulations is superimposed on the ion signal. The
de Vivie-Riedle et al. interference between pump and probe laser pulse prepared wave packets is now more pronounced because the ionization pathway b is located at the inner turning point for both pulses. In Figure 5a exclusively the ionization pathway b is considered in the calculation. This simulation already reproduces correctly the positions of the maxima in the pump-probe spectrum. The FT of the experimental ion signal (Figure 9c) shows the most prominent peaks (B) in the frequency range of 87-90 cm-1 of the ground state and therefore also supports the interpretation that the dynamics of the ground state are dominantly reflected in the transient ion signal. The frequency resolution is not optimal because the corresponding real time spectrum is only recorded up to 10 ps. The spectroscopic properties of K2, i.e., the possibility of the two different ionization pathways for the vibrational motion in the A1Σu+ state via a and in the X1Σg+ state via b, localized at outer and inner turning point, respectively, make it possible to detect the RISRS process in the transient ion signal. Another aspect of the high-power pump-probe spectrum is the experimentally observed beat structure of 2.6 ps (Figure 5b). Again the existence of two different ionization pathways is of decisive importance. The vibrational periods of the involved excited potential surfaces (A1Σu+, 41Σg+, and 21Πg) lie in the range of 500-620 fs. Their beat frequency with the ground state oscillations of 380 fs has a period of 1.3 ps. Thus the experimentally observed beat frequency of 2.6 ps can only be caused by the influence of two additional ionization pathways. They may be located for instance at the inner and outer turning points mirroring half the oscillation period of the wave packet in one of the excited states. The two states 41Σg+ and 21Πg in combination just open the possibility to reflect half the oscillation period of the wave packet in the A1Σu+ state, i.e., the first (via the 41Σg+ state at the inner turning point) and second harmonic (via the 21Πg state at the outer turning point) transition from the A1Σu+ state into the ion continuum. Therefore, the experimentally observed beat structure with a period of about 2.6 ps in the temporal evolution of the ion signal cannot be reproduced in the calculated signal when the 41Σg+ state is included exclusively in eq 2 (Figure 5a). More extensive calculations were performed taking into account both pathways simultaneously. The resulting coherent sum of the continuum contributions (upper curve) together with the interference term 2 Re 〈ψI,k(Ek)|ψI,k′(Ek′)〉 (lower curve) of the two dominant contributions (Ek ) 0.263 eV for pathway a and Ek′ ) 0.209 eV for pathway b) are shown in Figure 5c. Comparison with the experimental curve demonstrates that the intensity modulation observed in the experiment is due to the interference terms of the continuum. The neglect of the interference term in the calculation results in an ion signal which reflects dominantly the vibration in the A1Σu+ state, i.e., the 500 fs oscillation period. Besides this it was found that the total ion signal is sensitive to the relative strength of the two ionization pathways with the conclusion that they should be of similar strength. This finding is also supported by the Fourier spectrum of the experimental data (Figure 9c), which shows next to the highest peak (B) at the frequency of the X1Σg+ state strong peaks at the frequencies of the A1Σu+ state (A and C). The theoretical FT (Figure 9d) also shows a strong peak (B) at the frequency of the ground state, however, the strongest peak (A) is at the frequency of the A1Σu+ state. One possible reason for the different intensities in the experimental and theoretical FT is that in the simulation the transition into the ion continuum is chosen to be of equal strength for both pathways. Therefore, not only the transition dipole moments between the neutral states but also the transitions 41Σg+ f ion continuum and alternatively
Multiphoton Ionization Processes in K2
J. Phys. Chem., Vol. 100, No. 19, 1996 7795
Figure 9. Fourier transform for moderate intensity of (a) experimental and (b) theoretical data from a 40 ps scan and for high intensity of (c) experimental and (d) theoretical data from a 10 ps scan. In panels c and d, the dominant frequencies of the ground state are marked with B and the frequencies of the A1Σu+ state with A and C (second harmonic).
21Πg f ion continuum are important when several ionization pathways located at different positions contribute to the ion signal. The assumed parameters for the corresponding transition dipole moments may be the reason for the fact that the beat structure in the theoretical pump-probe spectrum is not as pronounced as the experimental one. However, from the theoretical results we can conclude that in the case of high laser power the contributions from the ionization pathway b cause the oscillation period and the contributions from process a the broadening of the oscillations in the total ion signal, and that the interference of both pathways, including the contributions from first and second harmonic transition, are responsible for the beat structure. 5. Conclusion The characteristics of pump and probe pulses, namely wavelength, intensity, and pulse width, induce special dynamics
by “femtosecond state preparation” in the molecules. They define the potential curves involved, the energetic location of the wave packets on the PES, and consequently also the location of the turning points with respect to the nuclear coordinate. The position of the turning points defines the possible regions for optimal resonant transitions. For a given wavelength the variation of the laser field intensity influences the probability of multiphoton processes, the number of Rabi cycles, and the efficiency of RISRS processes.10,20 In the case of the potassium dimer we could realize and investigate some of these effects. During the transition from moderate to high laser fields the contributions from the energetically close lying 41Σg+ and 21Πg states influence decisively the resulting ionization pathways and consequently the total ion signal. In the case of moderate laser fields only the pathway a via the 21Πg state is accessible. More intense laser fields, however, induce a large-amplitude motion on the ground state surface by an efficient RISRS process. The
7796 J. Phys. Chem., Vol. 100, No. 19, 1996 oscillatory shift of the wave packet around its equilibrium position is now large enough so that its inner turning point is shifted toward shorter bond lengths and reaches a nuclear conformation which now fulfills the resonance conditions with the laser frequency at the inner turning point via the A1Σu+ and 41Σg+ states and opens the pathway b. The 41Σg+ state thus becomes a resonant state in the three-photon excitation scheme. Its Franck-Condon (FC) window at the inner turning point in the X1Σg+ state, however, is not selective. It is also open for transitions from the A1Σu+ and 41Σg+ state, due to the relative position of the potential curves. The dominant contribution to the total ion signal originates from the X1Σg+ state’s vibrational motion, but the frequencies of all the other states involved can be resolved in the Fourier spectrum.17 The role of the 21Πg state changes as well during the transition from moderate to high intensities. In any case, the 21Πg state opens an important transition path. Its FC window is located at the outer turning point of the wave packet in the A1Σu+ state and allows an optimal resonant transition which is the first step of the significant two-photon ionization process. In the case of moderate laser intensities this two-photon ionization signal reflects the motion of the wave packet in the A1Σu state. For high laser intensities, the same FC window opens the way to the second harmonic transition from the A1Σu+ state, which then is reflected in the beat structure as coherent superposition of the first and second harmonic of the A1Σu+ state vibrational motion and the ground state vibrational motion. By shaping a perfect 2π pulse, transition pathway b should be even more pronounced. The possibility to choose between different pathways via different electronic states in the excitation ladder of K2 opens the way from pump-probe to control spectroscopy. The analysis shows that under specific spectroscopic conditions, for fixed photon energy and pulse duration, the intensity (as in other cases6,19,20) of the laser field serves as a control parameter, which may switch on different excitation mechanisms, i.e., MPI or RISRS plus MPI. The special molecular properties are that the forms of the potential surfaces involved and the relative positions of their minima have to differ. The induced femtosecond dynamics can then probe selected molecular modes. Contrary to the lighter homologue Na2, in K2 these modes are reflected already in the oscillation periods of the transient ion signal and not only in the Fourier spectrum.6 This is rendered possible by the existence of the two ionization pathways a and b. If both pathways would be located at the inner turning point neither the vibration of the wave packet in the A1Σu+ state for moderate intensities nor the vibration of the wave packet in the X1Σg+ state could be resolved independently in the pump-probe spectrum. Thus, the effect of the RISRS process can, contrary to the Na2,6 be detected directly in the transient ion signal of K2. Under this aspect the K2 molecule can be regarded as a model system whose properties should also be found in larger systems with more degrees of freedom and reaction channels. We think that this example nicely demonstrates that femtosecond chemistry is providing exciting new discoveries in the field of control of chemical and physical processes. In the optimal case, reaction pathways can be selected either to investigate special modes and/or to achieve product selectivity. Acknowledgment. Generous financial support by the Deutsche Forschungsgemeinschaft DFG through project SFB 337 and a Habilitationsstipendium (for R.dV.-R.), and by Fonds der Chemischen Industrie is gratefully acknowledged. References and Notes (1) Kaiser, W., Ed. Ultrashort Laser Pulses and Applications: Topics in Applied Physics; Springer: Berlin, 1988; Vol. 60. Hasche, T.; Ashworth,
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