Rydberg state-mediated photoionisation of dissociating NaK wave packets in the B1Π state

26 May 2000

Chemical Physics Letters 322 Ž2000. 439–446 www.elsevier.nlrlocatercplett

Rydberg state-mediated photoionisation of dissociating NaK wave packets in the B1 P state Renee ´ Andersson a, Jan Davidsson c , Tony Hansson a

a,b,)

Department of Physics, Section for Atomic and Molecular Physics, Royal Institute of Technology, KTH, SE-10044 Stockholm, Sweden b Department of Chemistry, Royal Institute of Technology, KTH, SE-10044 Stockholm, Sweden c Department of Physical Chemistry, Uppsala UniÕersity, Box 532, SE-75121 Uppsala, Sweden Received 29 February 2000; in final form 10 April 2000

Abstract The photoionisation dynamics of NaK molecules in the B1 P state is studied in both frequency and time domain by femtosecond laser spectroscopy. Comparison to model calculations shows that the photoionisation proceeds via intermediateto-high-n Rydberg states. These Rydberg states act as Franck–Condon windows in the time-dependent experiment, and the molecular ions produced by autoionisation of the Rydberg states are shown to reflect the wave packet evolution in the B state. Consequently, Rydberg state-mediated photoionisation is proposed as a viable method for probing molecular wave packet dynamics. q 2000 Elsevier Science B.V. All rights reserved.

1. Introduction In femtosecond pump–probe spectroscopy on gas-phase molecules and van der Waals clusters, photoionisation is the most versatile and therefore most commonly applied probe method. Foremost of its benefits are easily obtainable mass selection of the products and high sensitivity. To be applicable, however, it has to fulfil the universal requirement on any detection method in time resolved pump–probe spectroscopy–sensitivity to molecular configuration. This prerequisite usually poses no problems for reso-

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Corresponding author. The Royal Institute of Technology, Physics Department, KTH, SE-100 44 Stockholm, Sweden. Fax: q46-8-200-430; e-mail: [email protected]

nant multiphoton ionisation of low-lying electronic states via valence states, as the valence states then act as Franck–Condon windows at well-defined internuclear separations w1,2x. When higher-lying valence states are probed, however, the probe photon frequently has sufficient energy to ionise the molecule in a direct transition to the ionisation continuum. In this case, provided the total energy exceeds the local vertical ionisation potential at all internuclear separations and that the electronic transition dipole moment varies insignificantly over the same range, the ionisation probability is relatively insensitive to internuclear separation w3x, and thus no, or very weak, time dependence of the signal is obtained. This loss of configuration sensitivity is due to the bound-continuum character of the photoionisation process, which allows the photoelectron at any internuclear separation to carry away

0009-2614r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 0 0 . 0 0 4 5 0 - 4

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just the amount of energy needed to match the transition to the most probable final ionic state. Conversely, the position sensitivity can be retrieved by selecting the photoelectrons by energy w4,5x, usually at the expense of losing capability of ion mass selection. The latter problem was avoided in recent work by Stert et al. w6x by applying electron energy resolved photoelectron–photoion coincidence detection. The same result can also be obtained by kinetic energy time-of-flight spectroscopy on the ionic fragments ŽKETOF., as is nicely illustrated by Assion et al. in Ref. w7x. Here, we explain by example yet another method for achieving configuration sensitivity in ionisation. It relies on using molecular Rydberg states as Franck–Condon windows and, as we will shortly show, can operate at energies well above the adiabatic ionisation limit. Essential influence of Rydberg states on ionisation dynamics as measured in femtosecond pump–probe spectroscopy has been suggested by Baumert et al. w1x, Davidsson et al. w2x and Schwoerer et al. w8x, but has so far not been systematically analysed. In making use of Rydberg states, our method is similar to zero kinetic energy electron ŽZEKE. spectroscopy w9x. In ZEKE, however, the Rydberg states involved have very high principal quantum numbers, n, as they are detected through electrons released by field ionisation in a weak electrostatic field. The long lifetimes and large collision cross-sections for the high-n Rydberg states leads to collisional effects on the detected signal w9x. By using Rydberg states of lower n as Franck–Condon windows, we circumvent this problem. To illustrate the method of Rydberg state-mediated ionisation we analyse the ionisation of dissociating wave packets in the NaK BŽ1.1 P state by femtosecond spectroscopy both in time and frequency domain. Comparison of the signals to calculations proves the photoionisation to be dominated by pathways involving Rydberg states.

2. Experiment The experimental arrangement consists schematically of three parts – a femtosecond laser system in a standard one-colour pump–probe set-up, a molecular beam source, and a straight time-of-flight ŽTOF.

mass spectrometer. The set-up has been used in previous studies of the NaK molecule and is described in detail elsewhere w2x. Thus, the set-up will here be mentioned only briefly with emphasis on the modifications made for the present work. The light pulses Ž530–580 nm. were generated by sum frequency generation of the idler and pump waves from an optical parametric amplifier ŽTOPAS, Light Conversion. pumped by the amplified output of a titanium:sapphire femtosecond laser Ž1 kHz pulse repetition rate.. Characteristically, the pulses had an autocorrelation halfwidth of 190–200 fs ŽSHG in BBO crystal. and a spectral halfwidth of 230 cmy1 . The pulses were split into two and, after introducing a time separation between the two fractions, focussed into the ionisation region of the mass spectrometer by a cylindrical Ž f s q30 cm. lens with the focal line perpendicular to the molecular beam propagation direction. The pulse energies at the entrance of the vacuum chamber was 5 and 3 mJ, respectively, corresponding to a peak intensity in the order of 10 GWrcm2 . The linear polarisation vectors of the two pulses were parallel to each other and perpendicular to the molecular beam direction. The NaK molecular beam was produced in a two-chamber oven. A mixture of sodium and potassium metal in the oven’s reservoir compartment was heated to around 700 K, while the exit part of the oven with its 150 mm diameter nozzle was kept at about 750 K. As no seed gas was employed, we estimate that the molecular beam is effusive or only mildly expansion-cooled, and the temperature of the molecules is therefore in the calculations below assumed to be 700 K. The molecular beam entered the ionisation region of the mass spectrometer parallel to the spectrometer’s flight path and the signal of the wanted species was collected by a boxcar integrator. Typically, the ion signals were averaged over 3000 laser shots. Single pulses were used in the frequency resolved experiment in which the pulse intensity was set constant at 5 mJ over the whole spectral region and the total yield of NaKq was measured as a function of the light frequency. For the time resolved measurements, the yields of NaKq and Kq Žfrom twophoton non-resonant ionisation of potassium atoms. were acquired simultaneously as a function of time delay between the pulses.

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3. Results and discussion The issue of this Letter is to illustrate the utility of Rydberg state-mediated photoionisation in ultrafast spectroscopy. To this end, the NaKq yield was measured as a function of time and wavelength as NaK molecules were irradiated by femtosecond laser pulses at wavelengths of 530 to 580 nm Ž18 870– 17 240 cmy1 .. In this wavelength range two electronic states are accessible from the ground X1 Sq state in electric dipole allowed transitions with appreciable Franck–Condon factors – the BŽ1.1 P and CŽ3.1 Sq states. As the adiabatic ionisation limit of NaK is 35 620 cmy1 w10x, both of these states may at wavelengths shorter than 561.5 nm be ionised by absorption of a second photon Žfor molecules initially in the vibrational ground state., either directly,

Fig. 2. Normalised measured spectra using ns- and fs-pulses, respectively. The ns spectroscopic data are from Ref. w11x.

or indirectly via Rydberg states that may autoionise or be photoionised in the high photon-density field of the femtosecond laser pulses. The relevant potential energy curves and the experimental scheme are illustrated in Fig. 1 and results of the measurements are shown in Figs. 2 and 3. All bound-bound and bound-free radial nuclear matrix elements needed for the analysis below are calculated by the LEVEL 6.1 w12x and BCONT 1.4 w13x software packages. 3.1. Verification of intermediate state

Fig. 1. Experimental scheme and relevant potential energy curves of the NaK molecule. A pump photon transfers the molecule to the B state above the dissociation limit Ždashed horizontal line.. Absorption of another photon brings the system to Rydberg levels Žthe dashed curve represents the RUU . ns 6 state above the adiabatic ionisation limit, and the dashed arrows symbolise the two open ionisation pathways, auto- and photoionisation.

To shed light on the probe mechanism of the photoionisation process, we first have to clarify which of the two possible intermediate states is active. As illustrated in Fig. 2, our measured photoionisation probability as a function of wavelength is distinctly different to the resonance-enhanced two-photon ionisation ŽR2PI. spectrum Barrows et al. w11x obtained using nanosecond laser pulses and which they assigned to the C state. The small residual signal at the short wavelength side of the femtosecond spectrum is indeed due to a resonance with the C state w14x, but, even though the calculated absorption spectrum of the C X transition at 700 K has a long-wavelength tail extending over the whole measured spectral range, the large shift between the two spectra is only possible to reconcile with that they for the most

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As a final remark on the B X transition, we note that the strong intensity of it relative to the C X band in the femtosecond photoionisation spectrum most likely is due to the large difference in electronic transition dipole moments for the corresponding transitions; w m ŽB X.rmŽC X.x2 f 13 at reŽX. according to the calculations by Ratcliff et al. w15x Žsee also Ref. w16x..

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3.2. Rydberg state-mediated probing

Fig. 3. Measured Žpoints. and simulated Žsolid line. time-resolved NaKq signal. Dashed curves reproduce the contributions from the two probe positions to the simulated signal. Inset: visual fit of the calculated autocorrelation trace Žsolid line. to the measured Kq signal Žpoints.. The latter trace has a FWHM identical to that of the autocorrelation trace in BBO, i.e. 200"10 fs.

part sample different electronic states, i.e., that the femtosecond spectrum involves primarily the B state. In accordance with this conclusion, the calculated B X absorption band at 700 K exhibits a maximum at 560 nm. The final energy level for the main part of the calculated B X absorption spectrum is however above the asymptotic dissociation level of the B state at about 18 300 cmy1 , which explains why the B state is not observed in the nanosecond R2PI spectrum. The high photon density in femtosecond pulses, on the other hand, facilitates detection of transient states, and, if a probe position is located close enough to the start location of the wave packet generated by the ultrafast pulse, these dissociating states will be detectable in a single-pulse experiment. The dissociative nature of the intermediate state is indeed clearly seen in Fig. 3, where the time-dependence of the photoionisation at l s 555 nm is shown, as no oscillatory component characteristic of bound motion is discernible in the signal. A distinct broadening of the cross-correlation signal around zero time delay is obtained, though, that confirms the resonance-enhanced character of the photoionisation. The details of the time dependent signal are discussed below, as is also the probe step.

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Let us return to the main theme of the present work – the mechanism of ionisation behind the spectrum in Fig. 2. As noted above, the total energy acquired by a NaK molecule upon absorption of two photons is exceeding the adiabatic ionisation potential for all wavelengths shorter than 561.5 nm, a threshold that is extended to somewhat longer wavelength by the high temperature of the molecules. The effective direct two-photon ionisation potential is however higher than the adiabatic one. This fact is easily recognised by applying the classical difference potential concept by Mulliken w17x to the direct photoionisation process. This method was originally developed for purely radiative transitions, but is straight-forwardly extended to photoionisation, by making the common assumption that the electronic transition dipole moment varies slowly enough with the excess electron energy to be approximated by a constant value. Then the effect of the electron is reduced to mainly ‘seek’ the final ionic level with the highest FCF, i.e., in the classical limit, to decrease the total energy deposited in the ion such that it matches the difference potential of the transition at the particular internuclear separation, r. The difference potential for a direct Xq 2 Sq 1 B P photoionisation is shown as the uppermost curve in Fig. 4. It is from this curve immediately clear that a direct photoionisation from the B state is improbable at all wavelengths above 540 nm, which is the range in which our ion signal peaks. A direct photoionisation can thus be ruled out as the mechanism of photoionisation of the B state. There is, however, a range of molecular Rydberg states with effective principle quantum numbers n, here depicted RUU n , converging to the ionic ground state. These states have for sufficiently high n values potential energy curves of nearly the same shape as

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Fig. 4. Difference potential energy curves of the RUU B1 P and n Xq 2 Sq B1 P transitions. The Rydberg series Ž ns6–20. converges to the Xq 2 Sq state and the Rydberg state predominantly contributing to the signal, RUU ns 8 , is shown as the dashed curve. The horizontal line corresponds to the photon energy 18 000 cmy1 Ž555 nm. and the vertical line represents the initial position of the wave packet in the B state.

that of the state they converge to. The related difference potential curves then have the same shape as that involving the ionic state and are shifted down in energy compared to it. Furthermore, they correspond to ‘normal’ bound–bound molecular transitions, for which the classical transition points are well-defined. The difference potential range spanned by the Rydberg states with n 0 6 is indicated in Fig. 4, and evidently the wavelength region in which we observe ionisation is characteristic of resonant transitions from the B state to intermediate-to-high-n Rydberg states. To calculate an approximate femtosecond singlepulse photoionisation spectrum, SRŽ Õ ., resulting from resonant transitions to the Rydberg manifold, we assume that all electronic transition dipole moments are independent of r. Moreover, as the rotational motion of the molecule is essentially frozen on the timescale encountered here, only a single rotational state is considered, namely J s 50, the most probable rotational state at 700 K. Then, SR Ž Õ . A

Ý

ny3 D R Ž n, n R . HP X Ž Õ, EX .

n, n R

=r Ž Õ . <² cnRR < c EX X :< 2 d EX ,

Ž 1.

where Õ is the frequency of the light, r Ž Õ . is the spectral density of the laser pulse, which here is

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assumed to follow a Gaussian distribution. The radial nuclear wavefunctions cnRR and c EX X correspond to the bound vibrational levels, n R , in the Rydberg states and the continuum states at energies EX of the dissociative part of the B state, respectively. D RŽ n, n R . is the detection efficiency of the individual Rydberg levels. The ny3 factor arises from the n-dependence of the electronic transition dipole moment of transitions between deep valence and Rydberg states w18x. Furthermore, the unknown quantum defect is arbitrarily set to zero in the calculations, as its precise value is insignificant to the model presented here. The population transferred from the molecular ground state to the level EX in the dissociation continuum of the B state, P X Ž Õ, EX ., is given by P X Ž Õ, EX . A Ý P Y Ž n Y . r Ž Õ . <² c EX X < cnYY :< 2 .

Ž 2.

nY

Here, P Y Ž n Y . is the thermal population of the n Y vibrational level in the X1 Sq state, and cnYY is the corresponding wavefunction. The detection probabilities D RŽ n, n R . of the Rydberg levels in Ž1. depend critically on the mechanism for their ionisation Žwe assume identical detection probability of all produced ions.. According to Fig. 4, the range of Rydberg states that have to be considered in the photoionisation does not encompass very-high-n Rydberg states, and we can exclude field ionisation as a mechanism of ionisation. Two alternatives then remain. First, the Rydberg states may autoionise, provided the total energy is above the adiabatic ionisation potential. Second, they may be photoionised during the femtosecond laser pulse. The autoionisation rate is in general a complicated function of the detailed interactions a specific Rydberg level is subject to w19x. However, if predissociation is ignored and if the autoionisation rate is large enough to for all levels to efficiently compete with fluorescence, or alternatively the rate is approximately the same for all levels, then the ion signal is independent of n and of the autoionisation rate. The cause of this is that both the fluorescence and the autoionisation rates scale in the same way with the effective principal quantum number, that is as ny3 , and only the total autoionisation yield after long time is measured, not the rate. Consequently, the autoionisation yield of the levels within each Rydberg state is mainly determined by the FCF:s for the populating

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tra. The different n-dependencies of the detection processes gives, however, a distinction in the prediction of the most important Rydberg state. The autoionisation mechanism favours n f 8–9, whereas photoionisation shifts the focus to n f 6, and this difference has consequences for the time-dependent signal, as discussed in Section 3.3. For reference, Fig. 5 also displays the spectrum we expect for a direct photoionisation process obtained, under the same assumptions as above, as Sd Ž Õ . A HP X Ž Õ, EX . r Ž Õ .

Ý

<² cnq < c EX :< 2 d EX .

q

n

q ( nmax

Ž 3. Fig. 5. Normalised measured Ždots. and simulated spectra assuming either direct ionisation Ždashed line. or indirect ionisation by autoionisation of Rydberg Žsolid line.. The computation is restricted to states with 6 ( n( 20 and 0 ( n R (100. Hulburt– Hirschfelder functions are used for the molecular X1 Sq w23x and C1 Sq states w11x, whereas the B1 P curve is from the calculations by Magnier and Millie´ w24x. The curve of the Xq 2 Sq state is calculated with the Gaussian94 QCISD method Žall electrons. w25x with the 6-311qqGŽ3df,3dp. and 6-311GŽ2df,2pd. basis sets for Na w26–29x and K w30x, respectively.

In this equation, cnq is the vibrational wavefuncq tion of the level nq, and nmax is the highest energetically accessible level in the molecular ion ground state. Obviously, the qualitative result of the extended difference potential analysis, that the photoionisation is predominantly proceeding via the B state and resonant transitions involving Rydberg states, is confirmed. 3.3. WaÕe packet dynamics

transition. This qualitative behaviour of autoionisation was observed for the alkali molecules Li 2 w20x, Na 2 w10x, and K 2 w21x. We assume that the same holds for NaK and accordingly approximate D RŽ n, n R . for autoionisation with a constant value. Photoionisation, on the other hand, is only possible while the femtosecond pulse is on, that is the instantaneous population of the Rydberg levels is probed. The cross-section for photoionisation of Rydberg states varies as ny3 w22x, but, with the same arguments as in the previous section, is constant for all levels within a specific Rydberg state. Thus, we arrive at D RŽ n, n R . A ny3 for photoionisation. Despite the different n-dependencies of the two detection mechanisms, they yield similar photoionisation spectra that agree well with the experimental data ŽFig. 5.. This indicates that the initial resonance with the B state is the determining factor for the overall shape of the photoionisation spectrum, and, as indicated already in Section 3.1, the calculated spectrum for the B X transition indeed looks much the same as the two calculated photoionisation spec-

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If the Franck–Condon factors in Ž1. peak strongly for a certain Rydberg state or narrow range of Rydberg states, we can expect to be able to use the Rydberg stateŽs. as probe window stateŽs. in measurements on molecular wave packet dynamics. This effect was qualitatively inferred from experimental observations in Refs. w1,2,8x, but in neither work was made a detailed analysis, which is done here. It is from the simulations of femtosecond photoionisation spectrum not possible to identify which ionisation mechanism is effective for the Rydberg states. Anyhow, both of the mechanisms considered, autoionisation and photoionisation, yield pronounced population maxima for certain n:s, although not the same ones. This leads to that we for l s 555 nm, as in Fig. 3, in either case expect to have two probe positions, which is exemplified in Fig. 4 by the crossings of the difference potential curve for n s 8 Ždashed line. and the horizontal line representing the ˚ for photon energy. For n s 8, we get 3.2 and 5.6 A; ˚ ˚ n s 9, 3.3 and 5.3 A; and for n s 6, 2.7 and 7.8 A.

R. Andersson et al.r Chemical Physics Letters 322 (2000) 439–446

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Furthermore, inspection of the difference potential of the BŽ EX . XŽ n Y . transition yields for the same laser wavelength a single, within reach from the ˚ bound part of the ground state, crossing at 3.17 A Žvertical line in Fig. 4., which corresponds to the initial position of the wave packet in the B state. The widely different predicted probe positions of the wave packet facilitates a clear identification of the Rydberg state ionisation mechanism. First, note that there is only one predicted probe position for ˚ is not within photoionisation mechanism, as 2.7 A reach of the wave packet in the B state, whereas both of the probe points of the autoionisation mechanism are available to the wave packet. Thus, the two ionisation mechanisms predict qualitatively different time-dependence of the probe signal as the molecule dissociates – photoionisation would give a single peak at rather long time, 270 fs, whereas the autoionisation would yield one peak at t s 0 and a second one with delays of 150 and 170 fs for n s 8 and n s 9, respectively. These delay times were obtained by calculating the classical trajectory of a NaK molecule moving under the influence of the B1 P ˚ to the respective potential energy curve from 3.17 A outer probe points. Now, the signal in Fig. 3 definitely has a contribution at t s 0 and a shoulder indicating a second probe process at a later time, as expected for autoionisation. The single contribution signal anticipated by the photoionisation mechanism would be easily resolved in our experiment as two distinct peaks symmetric about t s 0. Thus, autoionisation seems to be the more likely process. With this qualitative conclusion in mind, we assume that the pump–probe signal as a function of the pulse delay, Spp Žt ., can be described as a sum of two independent cross-correlation functions, one at zero delay and one at delay t 0 Žnote, t 0 s q
Spp Ž t . s

Hy`a I Ž t . I Ž t y t . q b I Ž t y t 1

2

=I2 Ž t y t . d t ,

1

0

. Ž 4.

where I1Ž t . and I2 Ž t . are the instantaneous intensities of the two pulses, assumed to be of Gaussian shape ŽFWHMs tp . and equal intensity, and a and b are proportionality factors. This approximation is

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equivalent to the single-trajectory pulse-longer-thandephasing ŽPLD. approximation of Fried and Mukamel w31x. The best fit of Ž4. to the experimental data with t 0 , a, and b as fit parameters and tp as adjustable parameter is shown as the solid curve in Fig. 3. The optimal tp is found to be 115 fs Žthe autocorrelation signal corresponding to this pulse width is compared to the Kq signal in the inset of Fig. 3., which yields t 0 f 160 fs, in agreement with the prediction of 150–170 fs of the autoionisation assumption. We thus conclude that the n s 8–9 Rydberg states indeed provide appropriate FCF windows for monitoring the wave packet evolution on the B state. In addition, we find that autoionisation is the mechanism of ionisation of the Rydberg states. The latter finding is not trivially explainable, as autoionisation of NaK Rydberg states with n s 9 requires transitions with D n ) 15, in sharp contrast to the often observed and expected D n s 1 propensity rule for pure vibrational autoionisation w32–34x. Large D n transitions have been observed before w21x in autoionisation of K 2 , however, and even though we do not attain direct information on the actual autoionisation mechanism, we strongly believe that couplings via Žthe several. nearby non-Rydberg electronic states are responsible for the obviously high autoionisation probability we observe for the intermediate-n Rydberg states.

4. Conclusion We have here shown that Rydberg state-mediated photoionisation ŽRYMPI. is a viable method for monitoring molecular wave packet dynamics. The principle behind RYMPI is to use intermediate-tohigh-n Rydberg states, n f 10, as Franck–Condon windows for the probe step in ultrafast pump–probe spectroscopy. In contrast to the very-high-n states employed in ZEKE spectroscopy, the Rydberg states used here are not field-ionisable. Instead, the population of the window states are detected by measuring the ions produced in autoionisation. The full capabilities and limitations of RYMPI remain to be explored, but the method seems to offer in general a good compromise between nuclear configuration resolution and detection sensitivity.

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Acknowledgements We thank Sylvie Magnier and Phillippe Millie´ for making their unpublished adiabatic potential curves from the calculations in Ref. w24x available to us. This work was supported by the Swedish Natural Science Research Council ŽNFR. and the Knut and Alice Wallenberg Foundation.

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