The dynamic evolution of CS2 4d and 6s Rydberg wave packet components has been experimentally visualized via femtosecond time-resolved photoelectron imaging coupled with time-resolved mass spectroscopy. The temporal evolution of the four components of the prepared Rydberg wave packet is directly observed as time-dependent changes of the intensities of different parts in the main photoelectron peak. Furthermore, time-resolved photoelectron angular distributions (PADs) clearly reflect the different component characters of 4d and 6s molecular orbitals. The lifetime of Rydberg wave packets is determined to be about 830fs and their decay is attributed to predissociation. Our results suggest the possibility of directly visualizing and determining the amplitudes and relative phases of different electronic and vibrational wave packet components in polyatomic molecules.
© 2011 OSA
Recent advances in ultrashort laser technology have made it practical to investigate chemical reactions on the time scale of chemistry itself . In particular, the direct visualization or manipulation of chemical reaction pathways has been the subject of many theoretical and experimental studies, such as Rydberg wave packets in atoms , molecular wave packets , coherent control of molecular systems , molecular charge transfer , non-adiadatical dynamics [6,7] and so on. A typical subject, and the one of interest here, is the wave packet created when several quantum states are coherently excited by broadband ultrashort laser pulses.
Wave packet dynamics has attracted considerable attention in recent years . Wave packet revivals had been theoretically predicted [9,10] and were later experimentally verified for a large of very different quantum systems, e.g., atomic Rydberg levels [11,12], molecular vibrational and rotational states [13–16]. Additionally, wave packet interferences had been observed in vibrating molecules of I2 [17,18]. Recently, using excited-state dynamics of NaI as an example, Takatsuza et al.  theoretically demonstrated that wave packet bifurcations and mixings could be observed as time-dependent splittings of peaks in the photoelectron spectra. The time-evolving wave packets contain a wealth of information about the dynamics of interest, however, they are often so short-lived that they elude visualization and post a challenge to scientists for decades.
For the detailed study of the wave packet dynamics, time-resolved photoelectron imaging (TR-PEI) has proven to be a powerful technique . TRPEI measures both the energy (i.e. partial cross section) and angular (i.e. differential cross section) distribution of the photoelectrons simultaneously as well as their correlation as a function of time. In particular, the sensitivity of the photoelectron angular distribution to the electronic symmetry translates into useful information regarding the discrimination and visualization of wave packet dynamics.
In this paper, we report a direct observation of the dynamic evolution of Rydberg wave packet components in carbon disulfide (CS2) and visualize this event as time-dependent changings of the intensities of different parts of the main photoelectron peak in the photoelectron spectra. In addition, the corresponding photoelectron angular distributions also clearly reflect the different component characters of the Rydberg wave packet. Compared with previous studies discussed above that mainly concentrate on how the entire wave packet evolves on the different potential surface, we focus particularly on how the wave packet components evolve.
Carbon disulfide presents the simplest polyatomic system that can permit well planned ultrafast time-resolved superposition state (i.e. wave packet) experiments with well-defined initial and final states. A Rydberg wave packet is created within the 4d and 6s Rydberg manifolds following two-photon 266.7 nm excitation. As shown in Fig. 1(a) and 1(b), due to the large spectral width of the pump pulses, all the spin-orbit states of the 4d and 6s Rydberg states are coherently excited to form the four components of the Rydberg wave packet [21,22]. To measure the temporal evolution behavior of the wave packet components, we project the Rydberg wave packet onto the well-studied cationic ground state by another 800 nm ionizing pulse. The relevant states accessible and spectral assignments are taken directly from literatures [21–27], as will be discussed below.
The femtosecond laser system employed in the present work has been described in detail elsewhere [28,29]. Briefly, the femtosecond laser seed pulse is generated by a self-mode-lock Ti:sapphire oscillator pumped by a CW second harmonic of an Nd:YVO4 laser, and then amplified by an Nd:YLF pumped regenerative amplifier to generate a 1 kHz pulse train centered at 800 nm of 45 fs pulse width with maximum energy of 1 mJ/pulse. The fundamental light at 800 nm is split into two equal intensity beams and one of them forms the probe leg of the experiment. The other beam is split again by an 80%/20% beam splitter to generate the pump pulse. The former (80% part) is frequency doubled by a 0.5 mm thick BBO crystal to produce the second harmonic generation (SHG) pulse centered at 400 nm. The SHG and the latter fundamental(20% part) are then overlapped spatially and temporally into another 0.2 mm thick BBO crystal to generate the third harmonic generation (THG) pulse of 267 nm, namely, the pump pulse. The pump and probe beams are recombined collinearly at a dichroic mirror prior to being softly focused on the molecular beam with a spherical plano-convex lens (f = 250 mm). Polarization directions of the pump and probe lasers are parallel to each other and to the face of the two-dimensional (2D) position sensitive detector. The relative time delay between the pump and probe pulses are accurately monitored by a computer-controlled linear translation stage (PI, M-126.CG1).
The time-resolved photoelectron imaging setup is similar to our ion velocity imaging system, which has been described elsewhere . The key modification is made by adding a multilayer μ-metal shielding to avoid disturbance of the external magnetic fields when collecting the photoelectrons. The liquid sample (CS2, 99.9% purity), seeded in helium buffer gas at a background pressure of 2 atm, is expanded through a pulsed valve to generate a pulsed molecular beam. The beam is skimmed and introduced into the ionization chamber where it is intersected perpendicularly with the linear polarized pump and probe laser beams. The generated photoelectrons are extracted and accelerated by the electrostatic immersion lens and projected onto a 2D position sensitive detector comprising a microchannel plate/phosphor screen and a charge-coupled device camera. Each image is accumulated over 30 000 laser shots. Three-dimensional (3D) distribution reconstructions are performed by the basis-set expansion (BASEX)  forward convolution method.
As shown in Fig. 2(a) , a typical TOF (Time of flight) mass spectrum of CS2, recorded with the 266.7 nm pump and 800 nm probe at zero delay time, yields only one peak at 7.1μs, corresponding to the parent ion CS2 + with the m/e ratio of 76/+. Normally, the time-resolved photoelectron imaging experiments are required to be conducted with background signals low enough to ensure minimum ionization from either beam operating independently. Thus, in our pump-probe experiments, the excitation pulse energy is attenuated to be less than 1 μJ/pulse and the optimal ionization pulse energy is controlled to be near 30 μJ/pulse. Consequently, nearly no background signals are generated from either beam independently. Where noted, as mentioned above, soft focus is adopted in order to avoid space charge effect and strong field effects, such as Stark shift and dissociative ionization. It is evident that neither C+ nor CS+ fragments are observed in the TOF mass spectrum at zero delay time. The scans have been extended to as long as 20 ps and fragment ions such as C+ or CS+ are also not observed at any delay time.The CS and C are not ionized by the pump or probe pulse as a result of the low pulse intensities even though the neutral molecules of CS2 could predissociate at certain delay time. Therefore, it is reliable that the contribution to the total photoelectron signal from the fragment ions such as C+ or CS+ can be completely neglected. In addition, it should be noted that the isotope effect is not observed in our TOF spectrum and the formation of clusters is also minimized by performing the interaction on the rising edge of the molecular beam pulse.
The photoion yields are recorded as a function of the delay time between the pump and probe pulses, and these provide a measure of the lifetime of the excited states. The time-dependent ion signal of CS2 + is represented in Fig. 2(b). The decay profile is fitted to a single exponential decay convoluted with a Gaussian that describes the instrument response function. A lifetime of 830 fs is obtained. The brow-up of the fit in the first 200 fs is presented in Fig. 2(c). And the fit residue is given by the black line in Fig. 2(d). The green line is included to guide the eye. Inversion symmetry requires a two-photon electronic excitation to populate only symmetric, gerade, electronic states. Besides, as shown in Fig. 1(b), the CS2 absorption spectrum is void of any features in the region near 266.7 nm , so the one-photon 266.7 nm excitation process does not occur. Additionally, according to the spectral assignments [21–27], the CS2 is excited into the 4d and 6s Rydberg manifolds by two photons of 266.7 nm. Therefore, a Rydberg wave packet is then formed as a result of our broad excitation bandwidth (approximately 490 cm−1). The temporal evolution of the Rydberg wave packet is then monitored by another 800 nm ionizing pulse. As a result, the transient dynamics reflects temporal evolution of the Rydberg wave packet with a lifetime of 830 fs and the decay of the Rydberg wave packet is likely attributed to predissociation [27,33]. The dynamics of this decay will be discussed later by energy analysis of the corresponding photoelectrons released from the probe laser pulse. In addition, it’s known that the probe pulse (800 nm) is acted as the pump pulse in the negative time delay. However, as shown in Fig. 2(b), no any enhancement of the signal is observed in the negative time delay direction. On the contrary, the signal shows strong enhancements in positive time delay direction when the pump pulse (266.7 nm) serves as the pump source. So, it is evident that molecules are excited by the THG pulse and subsequently ionized by the fundamental pulse in the present experiment.
Figure 3(a) shows typical photoelectron images measured at various delay times with the pump and probe laser wavelengths of 266.7 and 800 nm, respectively. The upper row shows the raw images, whereas the lower row corresponds to slices through the 3D photoelectron scattering distributions observed at quoted time delays. The linear polarizations of the pump and probe lasers are aligned vertical in the plane of the figure. The rings with different radii stand for different photoelectron kinetic energy components. Two well-resolved concentric rings are observed in the images, especially at the delay time of 10 fs, where the inner ring is associated with the lower kinetic energy electrons and the outer ring corresponds to the higher energy electrons.
The corresponding photoelectron kinetic energy distributions (PKEDs) of these images are shown in Fig. 3(b). The PKEDs are characterized by a relative change of main peak intensities in the energy spectra with the delay time changing. This can be more readily visualized from the lower energy photoelectron peaks, which are amplified in the inset of Fig. 3(b). The higher energy photoelectron peaks are obvious just for earlier delay times. The energy gap between the higher and the lower energy photoelectron peaks is 1.54 eV, which is very close to the energy of one-photon 800 nm. To further check whether it results from the multiphoton process, we designed further experiments by increasing the energy of probe pulse in the same pump-probe scheme and also used only the 800 nm pulse with much higher energy to perform multiphoton ionization experiments. All of these extra results provide direct evidence that the higher photoelectron peaks indeed result from absorption of another 800 nm pulse, whilst we also conclude that multiphoton ionization occurs only when both the pump and probe pulses nearly overlap in time. Therefore, we will mainly focus on the lower energy photoelectron peaks in the following discussions.
Compared with Fig. 3(b), Fig. 3(c) shows the 3D map of tens of time-dependent PKEDs for the lower energy photoelectron peaks as a function of photoelectron kinetic energy (PKE) and delay time, which fully demonstrates the dynamic characteristic of PKEDs. As shown in Fig. 1(a), the assignments of the photoelectron spectra are based on the assumption that the [3/2] spin-orbit component (or [1/2] spin-orbit component) of neutral Rydberg levels could be only ionized to the [3/2] component (or [1/2] component) of the ground ion . Thus the 4d and 6s Rydberg states correlate with the vibrationally excited levels of the [3/2] and [1/2] spin-orbit components of CS2 +. Additionally, the FWHM (Full Width at Half Maximum) of our lower energy photoelectron peaks is found to be nearly the same as that of the photoelectron band shown in Fig. 3(b) in Ref. 21, from which one can find that the top peaks arising from ionization to both the [3/2] and [1/2] spin-orbit components are clear, but much of the peak is overlapped and not distinguishable. Thus, it’s believable that the expected Rydberg wave overlapped and not distinguishable. Thus, it’s believable that the expected Rydberg wave packets are created within the 4d and 6s Rydberg manifolds as a result of our broad excitation bandwidth. Therefore, the relative changing of the main peak intensities in Fig. 3(c) represents the evolution of the four components of the Rydberg wave packets. This suggests that the dynamic evolution of Rydberg wave packet components can be visualized by the photoelectron energy spectra, which is very similar to the method reported by Takatsuza et al.  in observing of wave packet bifurcations and mixings as time-dependent splittings of peaks in the photoelectron spectra. However, the superposition of these spin-orbit components includes not only electronic excitation but also vibrational excitation; therefore, details of the dynamics may become obscured by averaging over these states . This may be why the quantum beat is not observed in Fig. 2(b). The resultant wave function can be simply represented in the following form:Fig. 2(b), which can be further understood from the relative phase differences between the components of the wave packets. Importantly, the time-domain analysis provides a useful approach for determining relative phase differences between different components.
In the energy domain, PADs have been shown to provide an extremely sensitive probe of the time evolution of the electronic composition of the wave packets. Time-resolved PADs are extracted from the time-resolved reconstructed images. Figure 4(a) shows the time dependence of the PADs in the angle range between 0 and 180 degree. More quantitatively, in the cylindrically symmetric system, in which the pump and probe laser polarization vectors are parallel to each other, the laboratory frame PADs following three-photon ionization can be expanded as Eq. (2) :Fig. 4(b)–4(g) show six typical polar plots of the PADs at different delay times and the corresponding anisotropy coefficients β2, β4 and β6 resulting from fitting the PADs to Eq. (2) are listed in Table 1 .
The changes in the PADs directly reflect changes in orbital character. Hence, as plotted in Fig. 4(b)–4(g), the initial shape of the PADs is more or less the same with each other and then changes dramatically with the time delaying, especially at the neighboring directions of θ = 30° and 150°. These changes are also clear in the values of β2, β4 and β6 in Table 1 and Fig. 4(a).These changes seen indicate that the initial component of the Rydberg wave packets is mainly in 4d orbital character and then gradually evolves into the mixing of 4d and 6s orbital characters, whereas the component representing a main characteristic of 6s orbital is remarkably enhanced since the delay time of 380 fs. Generally, the time evolution of the PADs is predominantly determined by changes in the electronic symmetry of the excited state. However, as a result of the identical electronic symmetries (Πg) for both the 4d and 6s Rydberg states and the correlated ion state, the symmetries of the outgoing photoelectron distributions can’t be completely distinguished from symmetry analysis of the PADs .
In the case of one-photon ionization of a one-electron atom, for an s orbital electron, the outgoing photoelectron is a pure p wave, yielding the anisotropy parameter β = 2; for other initial electron orbital angular momentum states, the anisotropy parameter is reduced due to interference between the two outgoing partial waves . There is a similar situation for molecules, especially for atomiclike Rydberg states. This qualitatively suggests that photoelectrons emitted from the 6s Rydberg levels lead to much lager anisotropy parameters than ones emitted from the 4d Rydberg levels. Although the possibility that each component of the Rydberg wave packets can be exactly discerned is almost excluded, the best fit values of the anisotropy parameters listed in Table 1 at initial delay times is much less than ones since the delay times of about 380 fs, which is thoroughly consistent with the arguments above.
As an added support for our arguments, the energies and quantum defects of Rydberg states can be obtained by 38]. For molecules composed of second-row atoms, typical δ values are 0.9–1.2 for s orbital, while the δ values of p orbital are about 0.3–0.5, and δ values of d orbital are about 0 . For the sake of simplicity and convenience, only the PKEs resulting from the [1/2] spin-orbit component at the delay times of 10 fs and 380 fs are taken into account. Using Eq. (3), the quantum defect values for the delay times of 10 fs and 380 fs are calculated to be 0.216 and 2.112, with principal quantum numbers of 4 and 6, respectively. As argued above, the quantum defect values of 0.216 and 2.112 may mainly result from the 4d and 6s Rydberg states, respectively, which is in considerable agreement with the experimental values of 0.002 and 2.048 for 4d and 6s Rydberg states reported by Leone et al.  and Cossart-Magos et al. , respectively.
We have experimentally visualized the dynamic evolution of CS2 4d and 6s Rydberg wave packet components via femtosecond time-resolved photoelectron imaging coupled with time-resolved mass spectroscopy. The Rydberg wave packets are created within the 4d and 6s Rydberg manifolds following two photons of the 266.7 nm pump pulse, and their temporal evolution is monitored by another 800 nm ionizing pulse. The lifetime of these Rydberg wave packets is determined to be about 830fs and their decay is attributed to predissociation. The dynamic evolution of the four wave packet components is directly observed as time-dependent changes of the intensities of different parts in the main photoelectron peak. Furthermore, the corresponding photoelectron angular distributions clearly reflect the different component characters of 4d and 6s molecular orbitals. Our results suggest the possibility of directly visualizing and determining the amplitudes and relative phases of different electronic and vibrational wave packet components in polyatomic molecules. Such direct investigations, if possible, would be interesting in themselves, but also quite significant to relevant studies of electron transfer, wave packet engineering, reaction control, electronic wave packet chirp in high-order harmonic generation (HHG). Also, from the perspective of quantum measurement, time-evolving electronic wave packets provide a bridge between quantum mechanics and the classical concept of the trajectory of an electron and shed light on the evolution of quantum entanglement between electronic and nuclear motion.
This work was supported by the Knowledge Innovation Program of the Chinese Academy of Sciences (KJCX1-YW-N30) and National Natural Science Foundation of China (No. 20973194 and No. 10704083).
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