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Determination of wave packet dynamics by femtosecond time-resolved pump-dump-probe and four-wave mixing techniques
Journal of Molecular Structure 480–481 (1999) 33–43
Determination of wave packet dynamics by femtosecond time-resolved pump-dump-probe and four-wave mixing techniques T. Chen, V. Engel, M. Heid, W. Kiefer*, G. Knopp, A. Materny, S. Meyer, R. Pausch, M. Schmitt, H. Schwoerer, T. Siebert Institut fu¨r Physikalische Chemie der Universita¨t Wu¨rzburg, Am Hubland, D-97074 Wu¨rzburg, Germany Received 25 August 1998; accepted 30 September 1998
Abstract Femtosecond time-resolved four-wave mixing (FWM) spectroscopy is performed in order to investigate molecular dynamics in iodine molecules in the gas phase. Depending on both the timing of the laser pulses and on the applied FWM technique different dynamics are observed in the FWM transient signals. By using the time-evolution diagrams the varying contribution of ground and excited state dynamics can be explained conclusively. Further, a femtosecond three-color pump-dump-probe scheme in combination with a time-of-flight mass selective detection unit has been applied to study vibrational wave packet dynamics in the electronic ground state of cold K2 molecules. A spectral analysis of the time domain signal reveals two different wave packet contributions: hot wave packets from a stimulated Raman process and cold ones from stimulated emission pumping. 䉷 1999 Elsevier Science B.V. All rights reserved. Keywords: Femtochemistry; Nonlinear spectroscopy; Four-wave mixing; Femtosecond spectroscopy; Ground state wave packet dynamics
1. Introduction Owing to the development of lasers capable to produce ultrashort pulses a new research field opened. Pulses of a few tens of femtoseconds are shorter than relaxation processes, which accompany the act of photochemistry and are even shorter than the elementary intramolecular motions of the molecules involved [1–3]. These pulses allow for a coherent broadband excitation with preparation and detection of rovibrational superposition states. The time evolution of these rovibrational wave packets in the ground as well as electronically excited state give information on the molecular dynamics. * Corresponding author.
The high intensity achieved by femtosecond lasers favours the application of nonlinear methods like four-wave mixing (FWM) spectroscopies for the study of ultrafast intramolecular dynamical processes. Compared with time-resolved resonance Raman scattering, time-resolved femtosecond coherent antiStokes (CARS) or Stokes Raman scattering (CSRS) open new possibilities for the study of processes of ultrafast molecular dynamics [4–10]. Theories for these time-resolved nonlinear spectroscopical methods were developed by several researchers [5,11–16]. However, these methods have not been exploited on the subpicosecond time scale for gas-phase studies until recently. Hayden and Chandler [10] reported the application of femtosecond time-resolved coherent
0022-2860/99/$ - see front matter 䉷 1999 Elsevier Science B.V. All rights reserved. PII: S0022-286 0(98)00651-6
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Raman techniques to excite and monitor the evolution of vibrational coherence in gas-phase samples of benzene as well as of 1,3,5-hexatriene. Using “incoherent” light from a broadband dye laser to achieve femtosecond time resolution in time-delayed degenerate and nondegenerate FWM Yang et al. [17] investigated I2 in the vapor phase. Their signals revealed oscillations corresponding to excited state wave packet dynamics, but no ground state contribution could be detected. Recently, nonlinear FWM techniques were incorporated in different temporal pulse schemes to extract the dynamics of atomic, unimolecular, and bimolecular systems in the gas phase by Zewail and co-workers [18]. For the FWM a threedimensional forward geometry (folded BOXCARS arrangement) [19–21] was chosen. Degenerate FWM (DFWM) as well as a two-color grating experiment [22] were used to replace the probe pulse in a pump– probe scheme. Also the FWM process itself was used to gain information on the decay dynamics of atomic Na. They also suggested temporal pulse schemes, which would probe the ground state dynamics. Alkali metal dimers, which can be produced purely in their vibronic ground state X by a supersonic jet expansion, are of great interest, because some fundamental aspects of femtosecond wave packet spectroscopy could be demonstrated and highlighted with exceptional clarity: wave packet dynamics in several, and also in coupled electronically excited states of Na2 were extensively studied including detailed investigations of the multiphoton ionization pathways in the probe step [23,24] Spin orbit coupled electronic states of K2 were investigated by their influence on the wave packet’s propagation with isotopomer resolution [25]. Interference of wave packets in Cs2 could be generated and detected [26]. Fractional revivals of wave packets because of the beating of portions of the wave packet with different periodicities were also reported in Br2, Na2 and NaK and nicely illustrated with the help of spectrograms [27–29]. In a preceding pump–probe experiment on potassium dimers we could show that the electronic transition dipole moment which is responsible for the ionization probe step varies with the position of the wave packet on its potential surface [30]. However, the method so far has been mainly applied to investigate the vibrational motion of neutral molecules in one of their electronically excited states.
Besides the FWM experiments described above, to our knowledge only a few femtosecond real time experiments in the electronic ground state have been reported: In an ordinary pump probe experiment in the case of very high pump intensity a small contribution of a ground state wave packet can be generated by stimulated emission pumping within a single pump pulse in addition to the dominating generation of a wave packet in an electronically excited state by one photon excitation [31]. A second approach is the socalled NENEPO (NE: negative, NE: neutral, PO: positive) technique: by detaching the extra electron of a singly charged anion with a femtosecond pump pulse a ground state wave packet of the neutral species can be generated and subsequently interrogated by ionizing to the cation. With the NENEPO method the nuclear motion of silver trimers after neutralization has been monitored [32]. In the nanosecond time regime a complete population transfer from a selected rovibrational level in the ground state X via an electronic resonance into a different rovibronic level of X can be accomplished. This stimulated Raman scattering via adiabatic passage, STIRAP was successfully applied also to sodium and potassium dimers [33,34]. In our contribution we report on an experimental concept which enables us to study selectively the femtosecond vibrational wave packet motion in the electronic ground state of potassium dimers. The preparation of the vibrational hot wave packets is realized by a resonant two color stimulated Raman process. The probing scheme uses a time delayed, selectively resonance enhanced multiphoton ionization process. As a useful method for data analysis the spectrogram technique [35] is applied to the transient signals. Thereby it is possible to depict the temporal evolution of the spectral components of the signal.
2. Experimental The experimental apparatus for the femtosecond four-wave mixing (FWM) experiments on iodine in the gas-phase has been described in detail elsewhere [36–39]. Briefly, a Ti:sapphire laser system in combination with two four-pass OPAs were used to create the three femtosecond pulses. The pulses had energies of a few mJ and pulse duration of typically 80 fs. The
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Fig. 1. Femtosecond FWM transients of gaseous iodine (A) fs-DFWM transient (l pu1 l pu2 l put l DFWM620 nmn). (B) fs-CARS transient (lpu lput 620 nm, l S 645 nm, l aS 596 nm). (C) fs-CSRS transient (l pu l pu 615 nm, l aS 591 nm, l S 641 nm).
beam geometry employed in these experiments was a folded BOXCARS configuration. This configuration was employed in order to separate the fs-FWM signal from the incoming beams. In this geometry the phasematching condition is fulfilled. The pulses were
delayed relative to each other by means of Michelson interferometer arrangements. Two of the three laser pulses used in the experiment were kept temporally overlapped and fixed while the delay time of the third laser pulse was varied. The four-wave mixing (FWM)
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transients were recorded as a function of the delay time between the two simultaneous excitation pulses and the third pulse. The signal was spectrally filtered with the help of a monochromator and detected by a fast photomultiplier tube. The sample cell was heated to about 80⬚C, which yields a vapour pressure of iodine of approximately 2 kPa. In the experimental setup to investigate the ground state dynamics via a stimulated Raman process the potassium dimers are produced in a supersonic jet expansion in a two chamber vacuum apparatus. The expansion is back pressured with 1–4 atm of argon gas in order to achieve efficient cooling of the internal degrees of freedom of the dimers. We use a 100 mm nozzle at the potassium oven heated to 700 K and a 1 mm skimmer between the two vacuum chambers. Two laser pulses (pupump and pudump) populate an excited vibrational wave packet in the electronic ground state by a resonance enhanced stimulated Raman process. The wavelengths of pupump and pudump are independently tunable by two optical parametric amplifiers. The wavelength of the delayed probe pulse puprobe is chosen for a selective resonance enhancement of the ionization path from X to the ionic state. The ions are mass selected by means of a reflectron time of flight spectrometer and detected by a microchannel plate. The intensity of the 39,39K2 signal is recorded as a function of the delay time between the creation of the ground state wave packet and the ionization process.
3. Results and discussion 3.1. Femtosecond time-resolved four-wave mixing spectroscopy in gaseous iodine In the following we describe the basic idea of the fstime-resolved four-wave mixing (FWM) experiments. In our experiments three laser fields interact with the ensemble of I2 molecules in the folded BOXCARS arrangement as mentioned above. In all experiments two laser pulses are coincident in time, while the third pulse arrives with a variable time delay Dt. Depending on the relative timing of the three laser pulses, different dynamics in the molecules are probed by one or two photon interactions resulting in the coherent FWM signal. The FWM techniques applied
to the investigation of molecular dynamics in gaseous I2 were the coherent Raman techniques CARS (coherent anti-Stokes Raman scattering) and CSRS (coherent Stokes Raman scattering) and the degenerate four-wave mixing spectroscopy (DFWM). The DFWM transient discussed in the following was recorded using three laser fields having the same central wavelength l 0, which is resonant with discrete rot–vib eigenstates in the excited B state of iodine. While two laser pulses (pu1 and pu2) are coincident in time the third pulse (put ) arrives with a variable time delay. Fig. 1(A) shows a typical DFWM transient of iodine as a function of the delay time Dt between the variable laser pulse, put , and the fixed, simultaneous laser pulses pu1 and pu2. The transient exhibits well defined 300 fs beats, corresponding to a vibrational energy spacing of about 111 cm ⫺1. This agrees well with the experimental vibrational energy spacing in the excited B state of gaseous iodine accessed by the 620 nm lasers. For positive delay times (Dt ⬎ 0) additional beats having about twice this wavenumber appear. These oscillations show a period of 155 fs, which corresponds to an energy spacing of 215 cm ⫺1 and reflects the dynamics of a wave packet within the electronic ground state of iodine. The Fast Fourier Transform (FFT) spectrum (not shown in this article) also confirms the above mentioned interpretation. In the fs-CARS experiment two laser pulses (pu and put ) have the same wavelength, l pu l put . The third laser pulse (S) is tuned to a lower wavelength l S in such a way that the difference between pu and S laser wavelength is resonant with a vibrational Raman transition in the iodine molecule. While one of the pump pulses (pu) and the Stokes pulse S are coincident in time, the second pump pulse put arrives with a variable delay time. Fig. 1(B) shows the experimentally observed CARS intensity as a function of delay time Dt between the pump pulse put and the two time coincident pulses pu and S for I2 vapour. The transient was obtained for a pump wavelength l pu l put 620 nm and a Stokes wavelength l S 645 nm detecting the coherent anti-Stokes signal at l aS 596 nm. For negative delay times (Dt ⬍ 0) of put , the transient is characterized by beats with a period of approximately 300 fs, which corresponds to an energy difference of 111 cm ⫺1. This value agrees with the energy spacing found between the vibrational
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eigenstates of iodine in the excited B state, which are reached by the l put 620 nm laser pulse from the ground state. For positive delay times (Dt ⬍ 0) the signal shows oscillations at about twice the frequency of the oscillations at negative delay times (Dt ⬍ 0). These short time oscillations for Dt ⬍ 0 show a period of 160 fs, corresponding to the wave packet motion prepared by coherent two photon pumping (pu and S) around the third vibrational level in the ground X state of iodine, because the wavelength difference between pu and S laser was tuned to the second overtone (Dv 00 3) of the I2 ground state vibration. The average period of the oscillations corresponds to a vibrational wavenumber spacing of about 208 cm ⫺1. This agrees with the vibrational energy spacing in the ground X state of iodine around v 00 3 as observed from continuum resonance Raman experiments [40]. The fs-CSRS transient displayed in Fig. 1(C) shows a completely different time behaviour than the DFWM (see Fig. 1(A)) or the CARS (see Fig. 1(B)) transient. In the fs-CSRS experiment also three laser fields interact with the ensemble of I2 molecules. Two laser pulses have the same wavelengths, l pu l put , and further on will be referred to, consistently with the CARS experiment, as pump lasers. The third laser (anti-Stokes) is tuned, in contrast to the CARS experiment, to a lower wavelength, l aS, such that the difference between pump and anti-Stokes laser wavelength is resonant with a vibrational transition in the ground state. Fig. 1(C) shows a fs-CSRS transient for gaseous iodine as a function of the delay time Dt between the pulse put and the two time coincident pulses pu and aS. For a pump wavelength l pu l put 615 nm and an anti-Stokes wavelength l aS 591 nm the coherent Stokes signal is detected at l S 641 nm. As it is the case for the CARS transient also here the wavelengths of the pump lasers pu and put determine where the interaction with the excited state potential takes place. The difference of the wavelengths between pump (pu) and anti-Stokes (aS) laser (l aS-l pu), which was chosen to be resonant with the second overtone Dv 00 3 within the ground state of the iodine molecules, gives the position accessed in the ground state potential. The transient shows neither a signal nor a beating structure for negative delay times (Dt ⬍ 0). For positive delay times (Dt ⬍ 0) the transient exhibits well defined 320 fs beats, corresponding to a vibrational energy spacing of about 104 cm ⫺1. This agrees well
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with the experimental vibrational energy spacing in the excited B state of gaseous iodine accessed by the 615 nm pump lasers. Also beats having about twice this wavenumber appear. These can be assigned to the electronic ground state. The FFT spectrum of the CSRS transient (not shown in this article) also exhibits two distinct components at 111 and 208 cm ⫺1. The peak at 111 cm ⫺1 can be assigned to the vibrational coherence in the B state of iodine, while the peak at 208 cm ⫺1 corresponds to the second overtone (Dv 00 3) of iodine in the electronic ground state. That is exactly what could be expected from the experimental conditions as mentioned above. Theory helps to understand the dependence of the observed dynamics on the timing of the laser pulses as well as the variation of the laser wavelengths resulting in the different FWM techniques. The nonlinear polarization responsible for the FWM signal can be theoretically described using density matrix formalism. An elegant method for calculating the elements of the involved density matrix is using Feynman diagrams (an application of this method on the calculation of nonlinear polarizations is described e.g. in Ref. [41]). These diagrams include a time ordering of the possible interactions as well as information about the interaction themselves. The nonlinear susceptibility or polarization is derived by summing up all possible Feynman diagrams. If spectroscopical results in the frequency domain are described by this technique, a selection of important diagrams can be performed on the basis of resonance conditions. This means that the choice of laser frequencies (different FWM techniques) together with the molecular transition determine which diagrams are of importance and which are not. For the femtosecond time resolved experiments on systems, which show coherence much longer than the pulse durations (as is the case for iodine vapour used in the above described experiments) the timing of the laser pulses additionally selects Feynman diagrams which have the right time ordering. Instead of showing Feynman diagrams, we show time-evolution energy ladder diagrams according to Albrecht et al. [42,43], which are equivalent to the Feynman diagrams, (for the formalism associated with these time-evolution diagrams see Refs. [42,43]). These time-evolution diagrams have the advantage, that resonance effects become more obvious. For simplicity, we neglect in our discussion
Fig. 2. Relevant time-evolution diagrams describing the fs-time-resolved FWM processes DFWM, CARS and CSRS for Dt ⬍ 0 (diagrams (A) and (B)) and Dt ⬎ 0 (diagrams (C)(E)). The solid and dashed arrows represent a ket and a bra side transition, respectively. See Refs.[42,43] for details.
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T. Chen et al. / Journal of Molecular Structure 480–481 (1999) 33–43
diagrams starting with transitions from thermally occupied higher vibrational ground state levels. Fig. 2 shows the time-evolution diagrams that illustrate the contributions for the three FWM processes (DFWM,CARS, CSRS) for negative (diagrams (A) and (B)) and positive (diagrams (C)–(E)) delay times. With the help of these diagrams, one can determine in what electronic state (ground state or B state) the wave packet is generated by the laser pulse(s) that interact(s) with the system first. From this, one can easily conclude whether the dynamics of the electronic ground or the B state are monitored by the time dependent FWM signal. In the case of the fs time-resolved DFWM process put prepares for negative delay times (Dt ⬍ 0) a wave packet in the B state. Therefore, the time dependent DFWM signal reflects the dynamics of the excited B state. This is characterized by diagrams (A) and (B). For positive delay times (Dt ⬍ 0) a superposition of the ground and B state dynamics can be observed in the resulting DFWM transient signal. This corresponds to diagrams (C)–(E), which demonstrate the preparation and subsequent DFWM signal of vibrational coherence in the ground state as well as the excited B state. Diagrams (C) and (E) illustrate the motion of a wave packet in the electronic ground state. This wave packet is prepared by the laser pulses pu1 and pu2, which interact simultaneously with the iodine molecules. However, diagram (D) illustrates the dynamics of a wave packet in the excited B state, which is prepared by an excitation similar to a “two-photon” absorption by pu1 and pu2. The quantitative contribution of each diagram to the total DFWM signal can only be determined by means of quantum mechanical calculations. These calculations are in progress and will be published soon. The situation is more complicated for the coherent Raman techniques CARS and CSRS because of the non-degeneracy of the laser and signal wavelengths. The diagrams (A) and (B) corresponding to the CARS process for negative delay times (Dt ⬍ 0) are reflecting the dynamics of a wave packet prepared by put in the B state of iodine. The main contribution to the transient CARS signal for Dt ⬍ 0 is given by diagram (A) because diagram (B) shows in contrast to diagram (A) no Raman resonance. If positive delay times (Dt ⬍ 0) are chosen both pu and S excite the molecules, which afterwards is probed by put .
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Diagram (C) and (E) are reflecting the ground state dynamics in the CARS signal, while diagram (D) illustrates the motion of a wave packet in the B state. However mainly diagram (C) will contribute to the CARS signal for positive delay times because of the missing Raman resonance in the diagrams (D) and (E). Therefore, the fs-CARS signal for Dt ⬍ 0 is mainly determined by diagram (A) and for Dt ⬍ 0 diagram (C) is playing the main role. This is in excellent agreement with the experimental CARS transient (Fig. 1(B)) where for negative delay times (Dt ⬍ 0) the wave packet dynamics in the B state (diagram (A)) and for positive delay time the ground state dynamics (diagram (C)) of iodine can be resolved. Quantum mechanical calculations by Meyer et al. [44] confirmed that for negative delay times mainly diagram (A) and for positive delay times mainly diagram (C) contribute to the transient CARS signal. The time dependent CSRS signal should for negative delay times (Dt ⬍ 0) reflect the dynamics of the excited B state. This is characterized by diagrams (A) and (B), where diagram (B) plays the main role because of the missing Raman resonance in diagram (A). For positive delay times the diagrams (C) and (E) illustrate the motion of a wave packet in the electronic ground state, which was prepared by the simultaneous interaction with pu and aS. Again diagram (C) will play a minor role, because of the fact, that it shows no Raman resonance. However diagram (D) illustrates the dynamics of a wave packet in the excited B state, which is prepared by an excitation similar to a two photon absorption by pu and aS. From this the fsCSRS transient should reflect the dynamics of the B state for Dt ⬍ 0 (diagram (B)) and for Dt ⬍ 0 a superposition of the ground (diagram (E)) and B state (diagram (D)) dynamics should be observed in the resulting CSRS transient signal. The assumption for positive delay times (Dt ⬍ 0) is consistent with the experimental results (see Fig. 1(C)). However for negative delay times (Dt ⬍ 0) no signal at all could be observed in the experimental transient. So the influence of diagram (B) in comparison to the diagrams (D) and (E) seems to be negligible. Only precise quantum mechanical calculations can determine the quantitative contributions of each diagram. Such calculations are under work and will be published in due time.
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Fig. 3. Potential energy curves of the potassium dimer. The wave packet in the X Sg⫹ state is generated by a stimulated Raman process with pump and dump wavelength of 648 nm and 677 nm, respectively. The evolution of the wave packet is interrogated by a time delayed three photon ionization process which is in resonance with the (5) Sg⫹ state.
3.2. Ground state vibrational wave packet spectroscopy of potassium dimers The ground state vibrational wave packets of K2 are created by a resonance enhanced stimulated Raman process from the X Sg⫹ state via the B Pu state back to X (Fig. 3). The potassium dimers in the supersonic jet are assumed to be in their electronic and vibrational ground state before entering the interaction regime. The mean wavelength of the pump pulse was set to 631 nm corresponding to the v 0 B 6 ← v 00 X 0 transition. Corresponding to the spectral width of the pulses of about 200 cm ⫺1 and the vibrational constant of v e(B) 75 cm ⫺1 the B state wave packet consists of about 3–5 coherently excited vibrational states. The dump pulse is time delayed with respect to
Fig. 4. Panel A shows the ion signal as a function of the time delay between pump and the probe pulse. Panel B is the Fourier power spectra of the positive part of the transient ion signal. A very strong peak of the cold stimulated emission pumping ground state wave packet (SEP) and the hot stimulated Raman process ground state wave packet (SRS) can be seen. A small peak because of a wave packet in the B-state is also in the spectrum.
the pump pulse to optimize the population of the hot ground state wave packet. The wavelength of the dump pulse is chosen to be 661 nm. With the vibrational constant of the ground state v e(X) 92 cm ⫺1 and the spectral width of about 300 cm ⫺1 as the convolution of the bandwidths of pump and dump laser pulse the ground state wave packet should consist again of about 3–5 vibrational states with a mean quantum number around 7–8. Both, the wave packet in B and X now start oscillating on their potential energy surface, but because of the different energy spacing between the vibrational levels with different periodicities. The evolution of the wave packet is interrogated by a time delayed three photon ionization process. The contribution of the ground state wave packet to
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Fig. 5. A spectrogram of a 43 ps transient showing the temporal evolution of the hot (at 90 cm ⫺1) and cold (at 93 cm ⫺1) ground state wave packet. A revival of the cold ground state packet can be seen after about 30 ps.
the ion signal can be promoted by carefully choosing the wavelength of the probe laser pulse. One possibility in the given configuration is a probe wavelength of around 800 nm which just happens to be the fundamental wavelength of our amplifier: The ground state wave packet can be ionized by a three photon process, exactly reaching the (5) Sg⫹ state at 25276 cm ⫺1 after absorption of two photons. This resonance increases the efficiency of the path and in particular introduces a coordinate selectivity, as for energetic reasons the excitation of the (5) state is only possible at the
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outer turning point of the wave packet’s motion in X. However, the two photon ionization from the B state surpasses the (5) and (6) states and ends up very high in the ion potential X⫹ (⬃8000 cm ⫺1). At t 0 the ion signal raises and starts oscillating for several ps with a period of 365 fs (Fig. 4(A)). This is the period of the internuclear vibration in the electronic ground state X. The ion signal is a pure image of the ground state vibrational motion. A spectral analysis (Fig. 4(B)) enlightens the origins of the different contributions to the transient signal after t 0. All data points were subjected to a Fourier power spectrum without further manipulation except for a subtraction of the slowly decreasing background. The main features of the Fourier spectrum are the two peaks at 91.5 cm ⫺1 and 87.5 cm ⫺1. The peak at 91.5 cm ⫺1 expresses the dynamics of the ground state wave packet of the vibronic levels 0, 1 and 2, which is generated by a stimulated emission pumping process within the pump pulse itself. The wavenumber differences are D~v0;1 92 cm⫺1 and D~v1;2 91:2 cm⫺1 [45], which match very well with the maximum of the line. The second slightly smaller contribution at 87.5 cm ⫺1 is caused by a stimulated Raman process by the pump and the dump pulse from B(v 00 6) into X(v 00 7,8). According to the anharmonicity of the X state potential the corresponding wavenumber splitting are D~v6;7 87:7 cm⫺1 and D~v7;8 87:0 cm⫺1 [45]. The two small peaks around 70 cm ⫺1 are contributions from the B state wave packet created by a one photon absorption from the pump pulse. The dump pulse also contributes to the stimulated emission pumping but less efficient as its maximum does not reach the B potential and therefore the two photon process expires less enhancement by the electronic resonance. The relative peakheight from the B state wave packet and the X state wave packet again show the strong selection of the ground state dynamics through the special choice of the ionization path. To represent the temporal evolution of the spectra the spectrogram technique [35] is applied to a 43 ps long transient of the same pump dump and probe wavelength (see Fig. 5). With regard to that a window of 8 ps length was laid over the transient signal. Then the part of the transient within the window is Fourier transformed representing one line in the spectrogram. Then the window is shifted for 200 fs across the
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transient signal and the now new contents of the window is again Fourier transformed representing the next line in the spectrogram and so on. The length of a window determines the spectral resolution of the spectrogram. The part of the signal around 90 cm ⫺1 is caused from the hot ground state wave packet generated by stimulated Raman process. It vanishes after 13 ps and no revival of the signal can be seen. The trace around 93 cm ⫺1 originates from the cold wave packet of the stimulated emission pumping. The intensity of the trace decreases within 17 ps but raises again after 30 ps. This behavior of the wave packet is called revival. Resulting from the anharmonicity of the potential surface the wave packet dephases after some 40 roundtrips and is then smeared out in the potential well and therefore delivers no longer a strong contribution to the ion signal. But after some other 40 roundtrips the wave packet rephases again and can be observed in the spectrogram. The calculated revival time for the cold ground state wave packet is 45 ps and therefore matches very nicely with the observed data.
4. Conclusions In this paper we have discussed results from fs-time resolved FWM experiments on iodine vapour. The FWM techniques applied were on one hand the coherent Raman techniques CARS (coherent antiStokes Raman scattering) and CSRS (coherent Stokes Raman scattering) and on the other hand the degenerate four-wave mixing spectroscopy (DFWM). From the transients presented, we were able to obtain information about the wave packet dynamics in the excited B state as well as the electronic ground state. In our experiments, two laser pulses were kept temporally overlapped, while the third laser pulse was varied in time relative to the simultaneous pulses. Depending on both the timing of the variable laser pulse relative to the temporally fixed laser pulses (Dt ⬍ 0: variable laser pulse comes before and Dt ⬎ 0: after the two time coincident laser pulses) and on the applied FWM technique different dynamics in the I2 molecules could be observed. For Dt ⬍ 0 the DFWM transient reveals the dynamics of the excited B state of iodine while for Dt ⬎ 0 a superposition of the ground and excited state
dynamics is probed. The CARS transient signal obtained for negative delay times reveals the wave packet dynamics within the excited state. For positive delay times beats can be seen which have a frequency corresponding to the energy difference of vibrational levels in the electronic ground state. The fs-CSRS transient shows no dynamics for negative delay times. However, for Dt ⬎ 0 the time-dependent coherent Stokes signal is characterized by a superposition of the excited and ground state dynamics. These observations could be explained by means of a selection of Feynman diagrams used to express the density matrix presentation of the nonlinear polarization of the FWM process. The time ordering as well as the resonances involved in the considered nonlinear process drastically reduce the number of diagrams describing the FWM. Instead of the usual presentation we used time-evolution diagrams in order to illustrate possible resonance effects more clearly. With the help of such time-evolution diagrams, it is possible to explain the dynamics observed for the different delay times and the different FWM techniques. Femtosecond vibrational wave packet spectroscopy was also applied to the electronic ground state of potassium dimers cooled in a supersonic jet. Vibrational hot states were coherently populated by a stimulated Raman process with two ultrashort laser pulses of different wavelength. The temporal evolution of the wave packet was monitored by a time delayed three photon process, which was selective to the actual position of the wave packet on the ground state potential energy surface. Two components of the ground state wave packet could be identified resulting from a two color and a one color stimulated Raman process. Using a spectrogram technique dephasing and rephasing of the cold ground state wave packet could be observed.
Acknowledgements This work was funded by the Deutsche Forschungsgemeinschaft (Projekt KI 202/11-1/11-2, Schwerpunktprogramm “Femtosekunden-Spektroskopie elementarer Anregungen in Atomen, Moleku¨len und Clustern”, Projekte KI 202/14-2, EN 241/5-2 and Schwer-punktprogramm “Zeitabhangige Pha¨nomene und Methoden in Quantensystemen der Physik und
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Chemie”, Projekte MA 1564/3-2, EN 241/4-2) and the Fonds der Chemischen Industrie. References [1] G. Mourou, P.F. Barbara, A.H. Zewail, W.H. Knox (Eds.), Ultrafast Phenomena IX, Springer, New York, 1994. [2] A.H. Zewail, Femtochemistry: Ultrafast Dynamics of the Chemical Bond, vols. 1 and 2, World Scientific, Singapore, 1994. [3] J. Manz, L. Wo¨ste (Eds.), Femtosecond Chemistry, vols. 1 and 2, VCH, Weinheim, 1995. [4] W. Zinth, R. Leonhardt, W. Holzapfel, W. Kaiser, IEEE J. Quantum Electron. QE-24 (1988) 455. [5] H. Okamoto, K. Yoshihara, J. Opt. Soc. Am. B 7 (1990) 1702. [6] M. Fickenscher, A. Laubereau, J. Raman Spectrosc. 21 (1990) 857. [7] T. Joo, M.A. Dugan, A.C. Albrecht, Chem. Phys. Lett. 177 (1991) 4. [8] H. Okamoto, K. Yoshihara, Chem. Phys. Lett. 177 (1991) 568. [9] H. Okamoto, K. Yoshihara, Chem. Phys. Lett. 202 (1993) 161. [10] C.C. Hayden, D.W. Chandler, J. Chem. Phys. 103 (1995) 10465. [11] E.J. Heller, Accounts Chem. Res. 14 (1981) 368. [12] E.J. Heller, R.L. Sundberg, J. Phys. Chem. 86 (1982) 1882. [13] S. Mukamel, R.F. Loring, J. Opt. Soc. Am. B 3 (1986) 595. [14] V.F. Kamalov, Y.P. Svirko, Chem. Phys. Lett. 194 (1992) 1. [15] L. Seidner, G. Stock, W. Domcke, J. Chem. Phys. 103 (1995) 3998. [16] W. Domcke, G. Stock, Adv. Chem. Phys. 100 (1997) 1. [17] T.-S. Yang, R. Zhang, A.B. Myers, J. Chem. Phys. 100 (1994) 8573. [18] M. Motzkus, S. Pedersen, A.H. Zewail, J. Phys. Chem. 100 (1996) 5620. [19] J.A. Shirley, R.J. Hall, A.C. Eckbreth, Opt. Lett. 5 (1980) 380. [20] Y. Prior, Appl. Opt. 19 (1980) 1741. [21] S. Maeda, T. Kamisuki, Y. Adachi, in: R.J.H. Clark, R.E. Hester (Eds.), Advances in Non-Linear Spectroscopy, Wiley, Chichester, 1988, p. 253. [22] M.A. Buntine, D.W. Chandler, C.C. Hayden, J. Chem. Phys. 97 (1992) 707. [23] T. Baumert, B. Buhler, M. Grosser, V. Weiss, G. Gerber, J. Phys. Chem. 95 (1991) 8103.
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Determination of wave packet dynamics by femtosecond time-resolved pump-dump-probe and four-wave mixing techniques T. Chen, V. Engel, M. Heid, W. Kiefer*, G. Knopp, A. Materny, S. Meyer, R. Pausch, M. Schmitt, H. Schwoerer, T. Siebert Institut fu¨r Physikalische Chemie der Universita¨t Wu¨rzburg, Am Hubland, D-97074 Wu¨rzburg, Germany Received 25 August 1998; accepted 30 September 1998
Abstract Femtosecond time-resolved four-wave mixing (FWM) spectroscopy is performed in order to investigate molecular dynamics in iodine molecules in the gas phase. Depending on both the timing of the laser pulses and on the applied FWM technique different dynamics are observed in the FWM transient signals. By using the time-evolution diagrams the varying contribution of ground and excited state dynamics can be explained conclusively. Further, a femtosecond three-color pump-dump-probe scheme in combination with a time-of-flight mass selective detection unit has been applied to study vibrational wave packet dynamics in the electronic ground state of cold K2 molecules. A spectral analysis of the time domain signal reveals two different wave packet contributions: hot wave packets from a stimulated Raman process and cold ones from stimulated emission pumping. 䉷 1999 Elsevier Science B.V. All rights reserved. Keywords: Femtochemistry; Nonlinear spectroscopy; Four-wave mixing; Femtosecond spectroscopy; Ground state wave packet dynamics
1. Introduction Owing to the development of lasers capable to produce ultrashort pulses a new research field opened. Pulses of a few tens of femtoseconds are shorter than relaxation processes, which accompany the act of photochemistry and are even shorter than the elementary intramolecular motions of the molecules involved [1–3]. These pulses allow for a coherent broadband excitation with preparation and detection of rovibrational superposition states. The time evolution of these rovibrational wave packets in the ground as well as electronically excited state give information on the molecular dynamics. * Corresponding author.
The high intensity achieved by femtosecond lasers favours the application of nonlinear methods like four-wave mixing (FWM) spectroscopies for the study of ultrafast intramolecular dynamical processes. Compared with time-resolved resonance Raman scattering, time-resolved femtosecond coherent antiStokes (CARS) or Stokes Raman scattering (CSRS) open new possibilities for the study of processes of ultrafast molecular dynamics [4–10]. Theories for these time-resolved nonlinear spectroscopical methods were developed by several researchers [5,11–16]. However, these methods have not been exploited on the subpicosecond time scale for gas-phase studies until recently. Hayden and Chandler [10] reported the application of femtosecond time-resolved coherent
0022-2860/99/$ - see front matter 䉷 1999 Elsevier Science B.V. All rights reserved. PII: S0022-286 0(98)00651-6
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Raman techniques to excite and monitor the evolution of vibrational coherence in gas-phase samples of benzene as well as of 1,3,5-hexatriene. Using “incoherent” light from a broadband dye laser to achieve femtosecond time resolution in time-delayed degenerate and nondegenerate FWM Yang et al. [17] investigated I2 in the vapor phase. Their signals revealed oscillations corresponding to excited state wave packet dynamics, but no ground state contribution could be detected. Recently, nonlinear FWM techniques were incorporated in different temporal pulse schemes to extract the dynamics of atomic, unimolecular, and bimolecular systems in the gas phase by Zewail and co-workers [18]. For the FWM a threedimensional forward geometry (folded BOXCARS arrangement) [19–21] was chosen. Degenerate FWM (DFWM) as well as a two-color grating experiment [22] were used to replace the probe pulse in a pump– probe scheme. Also the FWM process itself was used to gain information on the decay dynamics of atomic Na. They also suggested temporal pulse schemes, which would probe the ground state dynamics. Alkali metal dimers, which can be produced purely in their vibronic ground state X by a supersonic jet expansion, are of great interest, because some fundamental aspects of femtosecond wave packet spectroscopy could be demonstrated and highlighted with exceptional clarity: wave packet dynamics in several, and also in coupled electronically excited states of Na2 were extensively studied including detailed investigations of the multiphoton ionization pathways in the probe step [23,24] Spin orbit coupled electronic states of K2 were investigated by their influence on the wave packet’s propagation with isotopomer resolution [25]. Interference of wave packets in Cs2 could be generated and detected [26]. Fractional revivals of wave packets because of the beating of portions of the wave packet with different periodicities were also reported in Br2, Na2 and NaK and nicely illustrated with the help of spectrograms [27–29]. In a preceding pump–probe experiment on potassium dimers we could show that the electronic transition dipole moment which is responsible for the ionization probe step varies with the position of the wave packet on its potential surface [30]. However, the method so far has been mainly applied to investigate the vibrational motion of neutral molecules in one of their electronically excited states.
Besides the FWM experiments described above, to our knowledge only a few femtosecond real time experiments in the electronic ground state have been reported: In an ordinary pump probe experiment in the case of very high pump intensity a small contribution of a ground state wave packet can be generated by stimulated emission pumping within a single pump pulse in addition to the dominating generation of a wave packet in an electronically excited state by one photon excitation [31]. A second approach is the socalled NENEPO (NE: negative, NE: neutral, PO: positive) technique: by detaching the extra electron of a singly charged anion with a femtosecond pump pulse a ground state wave packet of the neutral species can be generated and subsequently interrogated by ionizing to the cation. With the NENEPO method the nuclear motion of silver trimers after neutralization has been monitored [32]. In the nanosecond time regime a complete population transfer from a selected rovibrational level in the ground state X via an electronic resonance into a different rovibronic level of X can be accomplished. This stimulated Raman scattering via adiabatic passage, STIRAP was successfully applied also to sodium and potassium dimers [33,34]. In our contribution we report on an experimental concept which enables us to study selectively the femtosecond vibrational wave packet motion in the electronic ground state of potassium dimers. The preparation of the vibrational hot wave packets is realized by a resonant two color stimulated Raman process. The probing scheme uses a time delayed, selectively resonance enhanced multiphoton ionization process. As a useful method for data analysis the spectrogram technique [35] is applied to the transient signals. Thereby it is possible to depict the temporal evolution of the spectral components of the signal.
2. Experimental The experimental apparatus for the femtosecond four-wave mixing (FWM) experiments on iodine in the gas-phase has been described in detail elsewhere [36–39]. Briefly, a Ti:sapphire laser system in combination with two four-pass OPAs were used to create the three femtosecond pulses. The pulses had energies of a few mJ and pulse duration of typically 80 fs. The
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Fig. 1. Femtosecond FWM transients of gaseous iodine (A) fs-DFWM transient (l pu1 l pu2 l put l DFWM620 nmn). (B) fs-CARS transient (lpu lput 620 nm, l S 645 nm, l aS 596 nm). (C) fs-CSRS transient (l pu l pu 615 nm, l aS 591 nm, l S 641 nm).
beam geometry employed in these experiments was a folded BOXCARS configuration. This configuration was employed in order to separate the fs-FWM signal from the incoming beams. In this geometry the phasematching condition is fulfilled. The pulses were
delayed relative to each other by means of Michelson interferometer arrangements. Two of the three laser pulses used in the experiment were kept temporally overlapped and fixed while the delay time of the third laser pulse was varied. The four-wave mixing (FWM)
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transients were recorded as a function of the delay time between the two simultaneous excitation pulses and the third pulse. The signal was spectrally filtered with the help of a monochromator and detected by a fast photomultiplier tube. The sample cell was heated to about 80⬚C, which yields a vapour pressure of iodine of approximately 2 kPa. In the experimental setup to investigate the ground state dynamics via a stimulated Raman process the potassium dimers are produced in a supersonic jet expansion in a two chamber vacuum apparatus. The expansion is back pressured with 1–4 atm of argon gas in order to achieve efficient cooling of the internal degrees of freedom of the dimers. We use a 100 mm nozzle at the potassium oven heated to 700 K and a 1 mm skimmer between the two vacuum chambers. Two laser pulses (pupump and pudump) populate an excited vibrational wave packet in the electronic ground state by a resonance enhanced stimulated Raman process. The wavelengths of pupump and pudump are independently tunable by two optical parametric amplifiers. The wavelength of the delayed probe pulse puprobe is chosen for a selective resonance enhancement of the ionization path from X to the ionic state. The ions are mass selected by means of a reflectron time of flight spectrometer and detected by a microchannel plate. The intensity of the 39,39K2 signal is recorded as a function of the delay time between the creation of the ground state wave packet and the ionization process.
3. Results and discussion 3.1. Femtosecond time-resolved four-wave mixing spectroscopy in gaseous iodine In the following we describe the basic idea of the fstime-resolved four-wave mixing (FWM) experiments. In our experiments three laser fields interact with the ensemble of I2 molecules in the folded BOXCARS arrangement as mentioned above. In all experiments two laser pulses are coincident in time, while the third pulse arrives with a variable time delay Dt. Depending on the relative timing of the three laser pulses, different dynamics in the molecules are probed by one or two photon interactions resulting in the coherent FWM signal. The FWM techniques applied
to the investigation of molecular dynamics in gaseous I2 were the coherent Raman techniques CARS (coherent anti-Stokes Raman scattering) and CSRS (coherent Stokes Raman scattering) and the degenerate four-wave mixing spectroscopy (DFWM). The DFWM transient discussed in the following was recorded using three laser fields having the same central wavelength l 0, which is resonant with discrete rot–vib eigenstates in the excited B state of iodine. While two laser pulses (pu1 and pu2) are coincident in time the third pulse (put ) arrives with a variable time delay. Fig. 1(A) shows a typical DFWM transient of iodine as a function of the delay time Dt between the variable laser pulse, put , and the fixed, simultaneous laser pulses pu1 and pu2. The transient exhibits well defined 300 fs beats, corresponding to a vibrational energy spacing of about 111 cm ⫺1. This agrees well with the experimental vibrational energy spacing in the excited B state of gaseous iodine accessed by the 620 nm lasers. For positive delay times (Dt ⬎ 0) additional beats having about twice this wavenumber appear. These oscillations show a period of 155 fs, which corresponds to an energy spacing of 215 cm ⫺1 and reflects the dynamics of a wave packet within the electronic ground state of iodine. The Fast Fourier Transform (FFT) spectrum (not shown in this article) also confirms the above mentioned interpretation. In the fs-CARS experiment two laser pulses (pu and put ) have the same wavelength, l pu l put . The third laser pulse (S) is tuned to a lower wavelength l S in such a way that the difference between pu and S laser wavelength is resonant with a vibrational Raman transition in the iodine molecule. While one of the pump pulses (pu) and the Stokes pulse S are coincident in time, the second pump pulse put arrives with a variable delay time. Fig. 1(B) shows the experimentally observed CARS intensity as a function of delay time Dt between the pump pulse put and the two time coincident pulses pu and S for I2 vapour. The transient was obtained for a pump wavelength l pu l put 620 nm and a Stokes wavelength l S 645 nm detecting the coherent anti-Stokes signal at l aS 596 nm. For negative delay times (Dt ⬍ 0) of put , the transient is characterized by beats with a period of approximately 300 fs, which corresponds to an energy difference of 111 cm ⫺1. This value agrees with the energy spacing found between the vibrational
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eigenstates of iodine in the excited B state, which are reached by the l put 620 nm laser pulse from the ground state. For positive delay times (Dt ⬍ 0) the signal shows oscillations at about twice the frequency of the oscillations at negative delay times (Dt ⬍ 0). These short time oscillations for Dt ⬍ 0 show a period of 160 fs, corresponding to the wave packet motion prepared by coherent two photon pumping (pu and S) around the third vibrational level in the ground X state of iodine, because the wavelength difference between pu and S laser was tuned to the second overtone (Dv 00 3) of the I2 ground state vibration. The average period of the oscillations corresponds to a vibrational wavenumber spacing of about 208 cm ⫺1. This agrees with the vibrational energy spacing in the ground X state of iodine around v 00 3 as observed from continuum resonance Raman experiments [40]. The fs-CSRS transient displayed in Fig. 1(C) shows a completely different time behaviour than the DFWM (see Fig. 1(A)) or the CARS (see Fig. 1(B)) transient. In the fs-CSRS experiment also three laser fields interact with the ensemble of I2 molecules. Two laser pulses have the same wavelengths, l pu l put , and further on will be referred to, consistently with the CARS experiment, as pump lasers. The third laser (anti-Stokes) is tuned, in contrast to the CARS experiment, to a lower wavelength, l aS, such that the difference between pump and anti-Stokes laser wavelength is resonant with a vibrational transition in the ground state. Fig. 1(C) shows a fs-CSRS transient for gaseous iodine as a function of the delay time Dt between the pulse put and the two time coincident pulses pu and aS. For a pump wavelength l pu l put 615 nm and an anti-Stokes wavelength l aS 591 nm the coherent Stokes signal is detected at l S 641 nm. As it is the case for the CARS transient also here the wavelengths of the pump lasers pu and put determine where the interaction with the excited state potential takes place. The difference of the wavelengths between pump (pu) and anti-Stokes (aS) laser (l aS-l pu), which was chosen to be resonant with the second overtone Dv 00 3 within the ground state of the iodine molecules, gives the position accessed in the ground state potential. The transient shows neither a signal nor a beating structure for negative delay times (Dt ⬍ 0). For positive delay times (Dt ⬍ 0) the transient exhibits well defined 320 fs beats, corresponding to a vibrational energy spacing of about 104 cm ⫺1. This agrees well
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with the experimental vibrational energy spacing in the excited B state of gaseous iodine accessed by the 615 nm pump lasers. Also beats having about twice this wavenumber appear. These can be assigned to the electronic ground state. The FFT spectrum of the CSRS transient (not shown in this article) also exhibits two distinct components at 111 and 208 cm ⫺1. The peak at 111 cm ⫺1 can be assigned to the vibrational coherence in the B state of iodine, while the peak at 208 cm ⫺1 corresponds to the second overtone (Dv 00 3) of iodine in the electronic ground state. That is exactly what could be expected from the experimental conditions as mentioned above. Theory helps to understand the dependence of the observed dynamics on the timing of the laser pulses as well as the variation of the laser wavelengths resulting in the different FWM techniques. The nonlinear polarization responsible for the FWM signal can be theoretically described using density matrix formalism. An elegant method for calculating the elements of the involved density matrix is using Feynman diagrams (an application of this method on the calculation of nonlinear polarizations is described e.g. in Ref. [41]). These diagrams include a time ordering of the possible interactions as well as information about the interaction themselves. The nonlinear susceptibility or polarization is derived by summing up all possible Feynman diagrams. If spectroscopical results in the frequency domain are described by this technique, a selection of important diagrams can be performed on the basis of resonance conditions. This means that the choice of laser frequencies (different FWM techniques) together with the molecular transition determine which diagrams are of importance and which are not. For the femtosecond time resolved experiments on systems, which show coherence much longer than the pulse durations (as is the case for iodine vapour used in the above described experiments) the timing of the laser pulses additionally selects Feynman diagrams which have the right time ordering. Instead of showing Feynman diagrams, we show time-evolution energy ladder diagrams according to Albrecht et al. [42,43], which are equivalent to the Feynman diagrams, (for the formalism associated with these time-evolution diagrams see Refs. [42,43]). These time-evolution diagrams have the advantage, that resonance effects become more obvious. For simplicity, we neglect in our discussion
Fig. 2. Relevant time-evolution diagrams describing the fs-time-resolved FWM processes DFWM, CARS and CSRS for Dt ⬍ 0 (diagrams (A) and (B)) and Dt ⬎ 0 (diagrams (C)(E)). The solid and dashed arrows represent a ket and a bra side transition, respectively. See Refs.[42,43] for details.
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diagrams starting with transitions from thermally occupied higher vibrational ground state levels. Fig. 2 shows the time-evolution diagrams that illustrate the contributions for the three FWM processes (DFWM,CARS, CSRS) for negative (diagrams (A) and (B)) and positive (diagrams (C)–(E)) delay times. With the help of these diagrams, one can determine in what electronic state (ground state or B state) the wave packet is generated by the laser pulse(s) that interact(s) with the system first. From this, one can easily conclude whether the dynamics of the electronic ground or the B state are monitored by the time dependent FWM signal. In the case of the fs time-resolved DFWM process put prepares for negative delay times (Dt ⬍ 0) a wave packet in the B state. Therefore, the time dependent DFWM signal reflects the dynamics of the excited B state. This is characterized by diagrams (A) and (B). For positive delay times (Dt ⬍ 0) a superposition of the ground and B state dynamics can be observed in the resulting DFWM transient signal. This corresponds to diagrams (C)–(E), which demonstrate the preparation and subsequent DFWM signal of vibrational coherence in the ground state as well as the excited B state. Diagrams (C) and (E) illustrate the motion of a wave packet in the electronic ground state. This wave packet is prepared by the laser pulses pu1 and pu2, which interact simultaneously with the iodine molecules. However, diagram (D) illustrates the dynamics of a wave packet in the excited B state, which is prepared by an excitation similar to a “two-photon” absorption by pu1 and pu2. The quantitative contribution of each diagram to the total DFWM signal can only be determined by means of quantum mechanical calculations. These calculations are in progress and will be published soon. The situation is more complicated for the coherent Raman techniques CARS and CSRS because of the non-degeneracy of the laser and signal wavelengths. The diagrams (A) and (B) corresponding to the CARS process for negative delay times (Dt ⬍ 0) are reflecting the dynamics of a wave packet prepared by put in the B state of iodine. The main contribution to the transient CARS signal for Dt ⬍ 0 is given by diagram (A) because diagram (B) shows in contrast to diagram (A) no Raman resonance. If positive delay times (Dt ⬍ 0) are chosen both pu and S excite the molecules, which afterwards is probed by put .
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Diagram (C) and (E) are reflecting the ground state dynamics in the CARS signal, while diagram (D) illustrates the motion of a wave packet in the B state. However mainly diagram (C) will contribute to the CARS signal for positive delay times because of the missing Raman resonance in the diagrams (D) and (E). Therefore, the fs-CARS signal for Dt ⬍ 0 is mainly determined by diagram (A) and for Dt ⬍ 0 diagram (C) is playing the main role. This is in excellent agreement with the experimental CARS transient (Fig. 1(B)) where for negative delay times (Dt ⬍ 0) the wave packet dynamics in the B state (diagram (A)) and for positive delay time the ground state dynamics (diagram (C)) of iodine can be resolved. Quantum mechanical calculations by Meyer et al. [44] confirmed that for negative delay times mainly diagram (A) and for positive delay times mainly diagram (C) contribute to the transient CARS signal. The time dependent CSRS signal should for negative delay times (Dt ⬍ 0) reflect the dynamics of the excited B state. This is characterized by diagrams (A) and (B), where diagram (B) plays the main role because of the missing Raman resonance in diagram (A). For positive delay times the diagrams (C) and (E) illustrate the motion of a wave packet in the electronic ground state, which was prepared by the simultaneous interaction with pu and aS. Again diagram (C) will play a minor role, because of the fact, that it shows no Raman resonance. However diagram (D) illustrates the dynamics of a wave packet in the excited B state, which is prepared by an excitation similar to a two photon absorption by pu and aS. From this the fsCSRS transient should reflect the dynamics of the B state for Dt ⬍ 0 (diagram (B)) and for Dt ⬍ 0 a superposition of the ground (diagram (E)) and B state (diagram (D)) dynamics should be observed in the resulting CSRS transient signal. The assumption for positive delay times (Dt ⬍ 0) is consistent with the experimental results (see Fig. 1(C)). However for negative delay times (Dt ⬍ 0) no signal at all could be observed in the experimental transient. So the influence of diagram (B) in comparison to the diagrams (D) and (E) seems to be negligible. Only precise quantum mechanical calculations can determine the quantitative contributions of each diagram. Such calculations are under work and will be published in due time.
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Fig. 3. Potential energy curves of the potassium dimer. The wave packet in the X Sg⫹ state is generated by a stimulated Raman process with pump and dump wavelength of 648 nm and 677 nm, respectively. The evolution of the wave packet is interrogated by a time delayed three photon ionization process which is in resonance with the (5) Sg⫹ state.
3.2. Ground state vibrational wave packet spectroscopy of potassium dimers The ground state vibrational wave packets of K2 are created by a resonance enhanced stimulated Raman process from the X Sg⫹ state via the B Pu state back to X (Fig. 3). The potassium dimers in the supersonic jet are assumed to be in their electronic and vibrational ground state before entering the interaction regime. The mean wavelength of the pump pulse was set to 631 nm corresponding to the v 0 B 6 ← v 00 X 0 transition. Corresponding to the spectral width of the pulses of about 200 cm ⫺1 and the vibrational constant of v e(B) 75 cm ⫺1 the B state wave packet consists of about 3–5 coherently excited vibrational states. The dump pulse is time delayed with respect to
Fig. 4. Panel A shows the ion signal as a function of the time delay between pump and the probe pulse. Panel B is the Fourier power spectra of the positive part of the transient ion signal. A very strong peak of the cold stimulated emission pumping ground state wave packet (SEP) and the hot stimulated Raman process ground state wave packet (SRS) can be seen. A small peak because of a wave packet in the B-state is also in the spectrum.
the pump pulse to optimize the population of the hot ground state wave packet. The wavelength of the dump pulse is chosen to be 661 nm. With the vibrational constant of the ground state v e(X) 92 cm ⫺1 and the spectral width of about 300 cm ⫺1 as the convolution of the bandwidths of pump and dump laser pulse the ground state wave packet should consist again of about 3–5 vibrational states with a mean quantum number around 7–8. Both, the wave packet in B and X now start oscillating on their potential energy surface, but because of the different energy spacing between the vibrational levels with different periodicities. The evolution of the wave packet is interrogated by a time delayed three photon ionization process. The contribution of the ground state wave packet to
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Fig. 5. A spectrogram of a 43 ps transient showing the temporal evolution of the hot (at 90 cm ⫺1) and cold (at 93 cm ⫺1) ground state wave packet. A revival of the cold ground state packet can be seen after about 30 ps.
the ion signal can be promoted by carefully choosing the wavelength of the probe laser pulse. One possibility in the given configuration is a probe wavelength of around 800 nm which just happens to be the fundamental wavelength of our amplifier: The ground state wave packet can be ionized by a three photon process, exactly reaching the (5) Sg⫹ state at 25276 cm ⫺1 after absorption of two photons. This resonance increases the efficiency of the path and in particular introduces a coordinate selectivity, as for energetic reasons the excitation of the (5) state is only possible at the
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outer turning point of the wave packet’s motion in X. However, the two photon ionization from the B state surpasses the (5) and (6) states and ends up very high in the ion potential X⫹ (⬃8000 cm ⫺1). At t 0 the ion signal raises and starts oscillating for several ps with a period of 365 fs (Fig. 4(A)). This is the period of the internuclear vibration in the electronic ground state X. The ion signal is a pure image of the ground state vibrational motion. A spectral analysis (Fig. 4(B)) enlightens the origins of the different contributions to the transient signal after t 0. All data points were subjected to a Fourier power spectrum without further manipulation except for a subtraction of the slowly decreasing background. The main features of the Fourier spectrum are the two peaks at 91.5 cm ⫺1 and 87.5 cm ⫺1. The peak at 91.5 cm ⫺1 expresses the dynamics of the ground state wave packet of the vibronic levels 0, 1 and 2, which is generated by a stimulated emission pumping process within the pump pulse itself. The wavenumber differences are D~v0;1 92 cm⫺1 and D~v1;2 91:2 cm⫺1 [45], which match very well with the maximum of the line. The second slightly smaller contribution at 87.5 cm ⫺1 is caused by a stimulated Raman process by the pump and the dump pulse from B(v 00 6) into X(v 00 7,8). According to the anharmonicity of the X state potential the corresponding wavenumber splitting are D~v6;7 87:7 cm⫺1 and D~v7;8 87:0 cm⫺1 [45]. The two small peaks around 70 cm ⫺1 are contributions from the B state wave packet created by a one photon absorption from the pump pulse. The dump pulse also contributes to the stimulated emission pumping but less efficient as its maximum does not reach the B potential and therefore the two photon process expires less enhancement by the electronic resonance. The relative peakheight from the B state wave packet and the X state wave packet again show the strong selection of the ground state dynamics through the special choice of the ionization path. To represent the temporal evolution of the spectra the spectrogram technique [35] is applied to a 43 ps long transient of the same pump dump and probe wavelength (see Fig. 5). With regard to that a window of 8 ps length was laid over the transient signal. Then the part of the transient within the window is Fourier transformed representing one line in the spectrogram. Then the window is shifted for 200 fs across the
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T. Chen et al. / Journal of Molecular Structure 480–481 (1999) 33–43
transient signal and the now new contents of the window is again Fourier transformed representing the next line in the spectrogram and so on. The length of a window determines the spectral resolution of the spectrogram. The part of the signal around 90 cm ⫺1 is caused from the hot ground state wave packet generated by stimulated Raman process. It vanishes after 13 ps and no revival of the signal can be seen. The trace around 93 cm ⫺1 originates from the cold wave packet of the stimulated emission pumping. The intensity of the trace decreases within 17 ps but raises again after 30 ps. This behavior of the wave packet is called revival. Resulting from the anharmonicity of the potential surface the wave packet dephases after some 40 roundtrips and is then smeared out in the potential well and therefore delivers no longer a strong contribution to the ion signal. But after some other 40 roundtrips the wave packet rephases again and can be observed in the spectrogram. The calculated revival time for the cold ground state wave packet is 45 ps and therefore matches very nicely with the observed data.
4. Conclusions In this paper we have discussed results from fs-time resolved FWM experiments on iodine vapour. The FWM techniques applied were on one hand the coherent Raman techniques CARS (coherent antiStokes Raman scattering) and CSRS (coherent Stokes Raman scattering) and on the other hand the degenerate four-wave mixing spectroscopy (DFWM). From the transients presented, we were able to obtain information about the wave packet dynamics in the excited B state as well as the electronic ground state. In our experiments, two laser pulses were kept temporally overlapped, while the third laser pulse was varied in time relative to the simultaneous pulses. Depending on both the timing of the variable laser pulse relative to the temporally fixed laser pulses (Dt ⬍ 0: variable laser pulse comes before and Dt ⬎ 0: after the two time coincident laser pulses) and on the applied FWM technique different dynamics in the I2 molecules could be observed. For Dt ⬍ 0 the DFWM transient reveals the dynamics of the excited B state of iodine while for Dt ⬎ 0 a superposition of the ground and excited state
dynamics is probed. The CARS transient signal obtained for negative delay times reveals the wave packet dynamics within the excited state. For positive delay times beats can be seen which have a frequency corresponding to the energy difference of vibrational levels in the electronic ground state. The fs-CSRS transient shows no dynamics for negative delay times. However, for Dt ⬎ 0 the time-dependent coherent Stokes signal is characterized by a superposition of the excited and ground state dynamics. These observations could be explained by means of a selection of Feynman diagrams used to express the density matrix presentation of the nonlinear polarization of the FWM process. The time ordering as well as the resonances involved in the considered nonlinear process drastically reduce the number of diagrams describing the FWM. Instead of the usual presentation we used time-evolution diagrams in order to illustrate possible resonance effects more clearly. With the help of such time-evolution diagrams, it is possible to explain the dynamics observed for the different delay times and the different FWM techniques. Femtosecond vibrational wave packet spectroscopy was also applied to the electronic ground state of potassium dimers cooled in a supersonic jet. Vibrational hot states were coherently populated by a stimulated Raman process with two ultrashort laser pulses of different wavelength. The temporal evolution of the wave packet was monitored by a time delayed three photon process, which was selective to the actual position of the wave packet on the ground state potential energy surface. Two components of the ground state wave packet could be identified resulting from a two color and a one color stimulated Raman process. Using a spectrogram technique dephasing and rephasing of the cold ground state wave packet could be observed.
Acknowledgements This work was funded by the Deutsche Forschungsgemeinschaft (Projekt KI 202/11-1/11-2, Schwerpunktprogramm “Femtosekunden-Spektroskopie elementarer Anregungen in Atomen, Moleku¨len und Clustern”, Projekte KI 202/14-2, EN 241/5-2 and Schwer-punktprogramm “Zeitabhangige Pha¨nomene und Methoden in Quantensystemen der Physik und
T. Chen et al. / Journal of Molecular Structure 480–481 (1999) 33–43
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