Phase-of-the-phase electron momentum spectroscopy on single metal atoms in helium nanodroplets
B. Krebs, V. A. Tulsky, L. Kazak, M. Zabel, D. Bauer, J. Tiggesbäumker
aa r X i v : . [ phy s i c s . a t m - c l u s ] F e b Phase-of-the-phase electron momentum spectroscopy on single metal atomsin helium nanodroplets
B. Krebs, V. A. Tulsky, L. Kazak, M. Zabel, D. Bauer, and J. Tiggesb¨aumker
1, 2, ∗ Institute of Physics, University of Rostock, 18059 Rostock, Germany Department “Life, Light and Matter”,University of Rostock, 18059 Rostock, Germany
Abstract
Magnesium atoms fully embedded in helium nanodroplets are exposed to two-color laser pulses in or-der to exemplarily study the contribution of a dense and finite medium on multiphoton-triggered above-threshold ionization (ATI). The angular-resolved photoelectron spectra show striking differences with re-spect to results obtained on free atoms. Scattering of the Mg photoelectrons, when traversing the heliumenvironment, causes the angular distribution to become almost isotropic. Furthermore, we observe a markedincrease in the ATI order, pointing out the impact of the helium environment on the concerted electron emis-sion process. Phase-of-the-phase spectroscopy, however, reveals a marked loss in the 2 ω - ω phase depen-dence of the electron signal. Taking into account sideband formation on a quantitative level, a Monte-Carlosimulation which includes laser-assisted electron scattering can reproduce the experimental spectra and giveinsights into the strong field-induced electron emission from disordered systems. ∗ [email protected]
1n strong field ionization, the interaction of the liberated electron with the remaining ion hasdrawn considerable attention [1–3]. In particular, the intensity regime differentiating multipho-ton and field-driven ionization is of interest [4]. This is because tunneling in concert with there-scattering of the freed electron with the parent ion [5] results in the generation of high har-monics [6]. The wealth of information encoded in the light signal permits to probe matter on theshortest spatial and temporal scales [7]. Complementary information is provided by the photo-electrons [8] as the different birth times of the electron wave packets lead to interferences, whichcan be analyzed by recording the photoelectron angular distribution (PAD). Examples are carpetstructures [9] or holographic side lobes [10]. In addition, multiphoton ionization can be investi-gated, which provides information about the ultrafast electron dynamics away from the tunnelingregime.In order to fully resolve the electron dynamics experimentally, the driving laser field has to beadjusted on a time scale shorter than an optical cycle. Experiments using two-color pulses areappealing, since the superimposed laser fields allows for a control of the relative intensity andphase as well as polarization [11–13]. For resolving phase dependencies covering the entire PAD,phase-of-the-phase electron momentum spectroscopy ( P o P ) has been introduced recently [14]. P o P enables to work out cooperative effects. A prime example with respect to coherent phenom-ena is above-threshold ionization (ATI) [2, 15]. The corresponding clearly structured pattern in thephotoelectron signals provides a sensitive marker to resolve interfering influences on the electrontrajectories. Moreover, the impact on the emission process itself can be studied. In order to reachthis goal, P o P utilizes the precise control of the relative phase between the two-color componentsand the differentiation into phase-dependent and phase-independent contributions to the electronsignals. The power of the P o P has been demonstrated in strong field ionization of atoms andmolecules [13, 14, 16–18]. Even relativistic two-color-field-induced pair production in vacuumhas been discussed on a theoretical level [19].In the present study, the P o P method is applied to the strong field-induced photoemission fromatomic impurities within a medium of bulk density, see Fig. 1. More precisely, multiphoton ion-ization from single atoms enclosed by a size-limited dense medium is investigated. So far, sucha phase-sensitive ionization scenario has not been experimentally considered. As surroundingmedium, we choose helium nanodroplets, which offer unique low-temperature conditions [20] forspectroscopy. We refer to [21–23] for recent reviews in the field. The strong field response ofhelium nanodroplets has been studied in context of the nanoplasma response and gives insights2nto, e.g., collective effects [24, 25] and relaxation dynamics [26, 27]. In the present investigation,we inspect the multiphoton intensity regime and focus on the signatures of ATI in the ionization ofmagnesium atoms embedded in helium nanodroplets. ATI originates from electron waves period-ically emitted at different cycles of the laser pulse. Only events separated by an integer number ofthe optical cycle interfere constructively. The corresponding pattern has been found in atoms andmolecules and show up as regularly spaced features separated by the laser photon energy [2]. Inthe following, we will show that in comparison to free atoms, the two-color photoelectron studiesfrom embedded atoms reveal severe changes in the angular pattern and the appearance of side-band features, which point at laser-assisted electron-helium scattering. Further these findings areaccompanied by a complete loss in phase-dependencies, as P o P reveals.The experiment used to investigate the strong field electron dynamics of atoms embedded inhelium nanodroplets is depicted in Fig. 1. Briefly, a molecular beam of droplets is produced bysupersonic expansion of pre-cooled helium gas (10 . N avg =
54 000. On its wayto the interaction region the molecular beam passes a resistively heated oven filled with magne-sium. The average number of Mg impurities per droplet is about 0.1. This establishes single-atomdoping conditions and ensures that contributions from dimer formation to be negligible. In addi-tion, a mechanical shutter is installed between the droplet source and the pick-up region allowingto block the droplet beam and conduct measurements on free Mg atoms, while all other conditionsremain unchanged. After the pick-up chamber, the droplet beam enters the velocity-map-imaging
FIG. 1. Schematic view of the experimental setup to study phase-dependencies in the photoemission fromsingle metal atoms embedded in helium nanodroplets triggered by strong linearly polarized two-color laserfields. Momentum-resolved electron signals are obtained by velocity map imaging (VMI). The expandedview on the ionization dynamics inside the droplets highlights photoemission pathways taken into accountin the computational analysis. ω is produced in a BBO-II crystal and propagates co-linearly with the fundamental. The temporal overlap between 2 ω and ω pulses is controlled by anarray of calcite plates, leading to the formation of two-color pulses. Focusing onto the target isachieved through a f =
250 mm metallic mirror. In contrast to generic setups, the 2 ω componentserves to ionize the target, whereas ω modifies the pulse shape. The intensities of the harmonicsare set equal to I ω = . · W cm − and I ω = . · I ω , respectively, and correspond to the Mgmultiphoton ionization regime. These conditions ensure to suppress dopand-induced nanoplasmaformation [29, 30]. The relative phase shift ϕ between the 2 ω - ω laser components, responsible forthe asymmetry of the laser field, is controlled with sub-cycle precision by a pair of movable fusedsilica wedges installed in front of the experimental chamber. We recorded 200 PADs at variousvalues of ϕ , equally distributed between 0 and 6 π .In order to obtain the P o P spectra, the PADs are Fourier-transformed with respect to ϕ . Dueto the I ω / I ω ratio being small, this Fourier decomposition can be well represented by the twoleading terms: Y ( p , ϕ ) ≃ Y ( p ) + Y ( p ) cos [ ϕ + Φ ( p )] . (1)Here, Y ( p ) represents the phase-averaged momentum spectrum (PA) and bundles the informa-tion about the processes taking place in the two-color laser field disregarding possible phase-dependencies. Conceptionally, the result compares to few-cycle experiments, which are conductedwithout phase stabilization or phase tracing [31]. The second term in Eq. (1) includes Y ( p ) and Φ ( p ) , which equal the relative-phase-contrast (RPC) and phase-of-the-phase (PP) spectra, re-spectively. RPC and PP provide momentum-resolved information about the degree of phase de-pendencies encoded in distinct features (see, e.g., [14] for more details).The decomposition process (Eq. 1) is demonstrated by measuring the P o P spectra of freemagnesium atoms, see Fig. 2. The PA ( Y ) shows a clear ATI pattern, whereas the signals isenhanced along the laser polarization axis. Although the photon energy of the stronger lasercomponent is 2 ~ ω = .
10 eV, the ATI features are spaced by ~ ω = .
55 eV, which corresponds tothe photon energy of the weaker component. The odd rings, however, are relatively weaker thanthe even ones, being enforced by the 2 ω field (see Fig. 2 (d)).Inspecting the PP reveals that the phase-of-the-phase signals for positive and negative momentadiffer by a phase shift of π . Other phase shifts represent different ionization pathways, which4 + | | | FIG. 2. (color online) P o P spectra (a: PA ( Y ), b: RPC ( Y ), c: PP ( Φ ) of atomic magnesium extractedfrom the photoelectron spectra obtained by phase-sensitive two-color ionization ( ~ ω = .
55 eV, I ω = . · W cm − , I ω = . · I ω ). Due to symmetry reasons, it is sufficient to display only quarter segmentsof the spectra. The PA and RPC signals are normalized to the maximum of Y . PP values are not shown,whenever the corresponding RPC result drops below 10 − . The arrow indicates the polarization axis of the2 ω - ω laser field. (d) Angle-integrated PA yield as function of electron energy, showing the developmentof ATI peaks. Even and odd ATI orders are emphasized by (+) and ( | ), respectively. Note the logarithmicscaling in the yields. v v v v v v v v v v v FIG. 3. P o P spectra of single magnesium atoms embedded in helium droplets, obtained under laserconditions as indicated in Fig. 2. The PA spectrum (a) shows nearly an almost isotropic electron emission.Another finding compared to free Mg is the appearance of higher-order ATI features. In addition, we notea complete loss in the phase-dependencies between 2 ω - ω laser field and electron momentum, which showsup as an unphysical granular phase signal in the RPC and PP spectra. ω - ω field conditions. From this finding one can deduce, that the information imprinted on thelaunched electron wave packet by the asymmetrical laser field is preserved until detection. Theclearly discernible signals therefore reflect an almost full coherence process, which can be linkedto the 2 ω - ω phase shift. A full analysis of the magnesium two-color ionization in the multiphotonregime is a task on its own. For the further treatment, however, it is relevant that the multiphotonionization process under study exhibits a strong dependence on ϕ , which is expressed in clear RPCand PP signals.Based on these studies, experiments on magnesium embedded in helium droplets were carriedout under identical laser conditions. The results presented in Fig. 3 can be summarized as follows:(i) The angular distribution becomes nearly isotropic (cf. Figs. 2 (a) and 3 (a));(ii) A careful check of the experimental spectra reveals no evidence, that phase-dependent fea-tures are still present (cf. Figs. 2 (b,c) and 3 (b,c));(iii) The ATI peaks extend to higher energies. Up to 12 ATI peaks can now be resolved (cf.Figs. 2 (d) and 3 (d));(iv) No pronounced energy shifts of the ATIs are obtained.With regard to the PA, there are indications in the PP and RPC spectra on signals of largermomentum. However, in comparison to free Mg, the RPC to PA ratio in droplets diminishes byat least one order of magnitude, which manifests in an unphysical granular structure in the RPCand PP spectra obtained from embedded Mg. One can draw the conclusion, that all features ofphase-dependencies have disappeared and thus the previously observed coherence of the processhas been completely lost. It is rather unlikely, that the 2 ω - ω laser field no longer has an impacton the ionization pathways in embedded Mg. Therefore, subsequent processes taking place in thepropagation of the electron wave packet through the enclosing medium have to be considered todecipher the underlying physics.For further processing of the data, the target conditions have to be clarified. It is known that Mgatoms reside near the center of the droplet [33]. Hence, the dopand is enclosed by a spherical shellof helium atoms. Further, underpinned by the considerable difference in the ionization potentialsbetween Mg and He and the lack of low-energy helium excitation levels [34], electron emission7olely originates from the dopand. Observing no photoemission from pure droplets under the cho-sen laser conditions proves this assertion. These special properties suggest to divide the ionizationdynamics in droplets into independent processes, that is multiphoton ionization from the impurityatoms and scattering of the electrons when transversing the enclosing helium shell. On the basisof these considerations we analyzed the change in the distribution of photoelectrons emitted fromdoped Mg within a Monte-Carlo (MC) simulation based on [13] and extended by including laser-assisted electron scattering [35]. The latter has a severe impact, as it leads to significantly reducedscattering cross sections [36]. A detailed description of the MC simulation procedure can be foundin the Supplementary material at URL.The results of the corresponding simulation are presented in Fig. 4 (c-e) and are comparedto the VMI measurements being subject to an inverse Abel transform using the onion peelingprocedure [37]. Based on the strong anisotropy obtained for Mg (Fig. 4 (a)), e-He scattering turnsout to be the crucial factor determining the final emission direction. The simulation predicts amean value of h N sc i = IG. 4. Inverse Abel transformed photoelectron spectra of free Mg (a) and embedded Mg (b) plotted inenergy and angle axes. (c) Result of a Monte-Carlo simulation as described in the text. Correspondingangular distributions (d) and energy spectra (e): free Mg, red; embedded Mg, black; MC simulation, blue.
The increased occurrence of ATI peaks suggests, that the helium environment obviously en-hances the energy exchange between the strong laser field and photoelectrons through laser-assisted scattering at He atoms. One might expect, that the ATI progression changes if excitedstates of helium are involved or if direct ionization can take place. However, no marked change inthe slope or resonance-enhanced ATI orders (e.g., through Freeman resonances [2]) are observedabove 19 . P o P allows insight into the strong field ionization dynamics that takes placein a dense environment. As an example, we studied above-threshold ionization of isolated Mgatoms and Mg atoms embedded in He nanodroplets. The resulting spectra differ substantially. Theinspection of the angular-resolved electron momentum spectra and accompanying Monte-Carlosimulations reveal that the electron trajectories are modified by multiple laser-assisted scatteringwith the helium environment, which enhances the isotropy. Moreover, phase-of-the-phase spec-troscopy reveals the complete loss of the 2 ω - ω phase dependency. The perhaps most striking resultis the enhancement of the ATI peaks because of the multiple elastic scattering of photoelectrons onhelium during which additional photons can be absorbed. With these experiments, we tackle thechallenge to bridge the gap between the rather well understood strong field laser physics of freeatoms in vacuum and the much more complex physics of photoelectron emission from atoms em-bedded in a condensed, nanometer-size environment, in that way paving the way towards atto-nanoscience [38, 39].The Deutsche Forschungsgemeinschaft (BA 2190/ 10, TI 210/ 7, TI 210/ 8) is gratefully ac-knowledged for financial support. [1] L. Gallmann, C. Cirelli, and U. Keller, “Attosecond Science: Recent Highlights and Future Trends,”Ann. Rev. Phys. Chem. , 447–469 (2012).[2] K Amini, J Biegert, F Calegari, A Chac´on, M F Ciappina, A Dauphin, D K Efimov, C F de Moris-son Faria, K Giergiel, P Gniewek, A S Landsman, M Lesiuk, M Mandrysz, A S Maxwell,R Moszy´nski, L Ortmann, J A P´erez-Hern´andez, A Pic´on, E Pisanty, J Prauzner-Bechcicki, K Sacha,N Su´arez, A Za¨ır, J Zakrzewski, and M Lewenstein, “Symphony on strong field approximation,”Rep. Prog. Phys. , 116001 (2019).[3] E. Lindroth, F. Calegari, L. Young, M. Harmand, N. Dudovich, N. Berrah, and O. Smirnova, “Chal-lenges and opportunities in attosecond and xfel science,” Nature Rev. Phys. , 107–111 (2019).
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B. Krebs, V. A. Tulsky, L. Kazak, M. Zabel, D. Bauer, and J. Tiggesb¨aumker
1, 2, ∗ Institute of Physics, University of Rostock, 18059 Rostock, Germany Department “Life, Light and Matter”,University of Rostock, 18059 Rostock, Germany ∗ [email protected] . MONTE-CARLO SIMULATION The procedure to conduct the Monte-Carlo calculation is described in [1] and adapted to thepresent scenario. With respect to the qualitative nature of the model and due to the azimuthalsymmetry of the photoelectron distribution as a result of the linearly polarized laser field, thesimulations are restricted to only two dimensions.
A. Initial condition
According to density functional theory [2], Mg resides at the center of the droplet, which inthe following defines the origin of each ionization event ( N e = electrons in total) in the sim-ulation. The initial velocity is chosen according to the distribution recorded for free Mg atoms inthe considered laser field which we obtain from data shown in Fig. 2 (a) by performing the decon-volution via polar onion peeling [3]. This procedure gives the spectrum of electrons within theplane parallel to the laser polarization (shown in Fig. 4(a)) and validates the 3D →
2D reductionof our model. In order to suppress signals originating from residual gas in the interaction region,we restrict our analysis to electron energies E = p / m > . | p | > .
12 atomic units).The droplet size is chosen individually for each electron according to a log-normal droplet sizedistribution [4] P ( N He ) = √ π N He δ exp (cid:20) − ( ln N He − µ ) δ (cid:21) (1)with parameters µ = ln N avg − δ / δ =0.626 (corresponding to an average number of N avg =54 000helium atoms per droplet, which corresponds to a mean radius 8 .
18 nm for empty droplets). Thenumber of dopand atoms being captured per a droplet of mean size is λ = .
08 and in general isknown to obey the Poisson distribution [5, 6], thus, the final distribution of number of atoms N He in a helium droplet that embeds a single Mg atom reads P ( N He ) = P ( N He ) · λ e − λ (2)where the Poisson distribution parameter λ reads λ = π R Ln Mg , R = [ N He / ( π n He )] / = . N / [ ˚A ] . (3)Basically, it reflects the number of Mg atoms that are in the geometrical volume that a droplet ofsize N He covers in the pickup chamber. In our case, L = .
35 cm and n Mg = . · cm − .2e note, however, that the influence of the droplet size distribution on the final results had only aminor effect. B. Random walk in a droplet
Subsequently, the random walk of each electron within the droplet is treated by calculating theprobability of scattering after traveling a certain spatial distance s as w ( s , E ) = − exp ( − n He σ ( E ) s ) (4)where σ ( E ) denotes the total scattering cross section. The concentration of helium n He is assumedto be homogeneous and equal to the bulk value of n He = . · cm − [7]. The spatial distancebetween scattering events s = − n He σ ( E ) ln X (5)is obtained by choosing a random number X uniformly distributed in the range [ , ) . If s is smallerthan the current distance to the surface of the droplet, scattering takes place. The scattering angle θ is then chosen according to the differential cross section d σ ( θ , ε ) / d Ω .In extending the model of [1], the impact of the laser field on the electron-helium scatteringprocess, i.e., formation of the sidebands, is introduced by scaling the cross sections σ ( E ) withthe asymptotic expression of the Kroll-Watson formula [8] for n = d σ ( θ , ε ) / d Ω in the presence of the laser field is evaluated via the laser-free value taken at the off-shell energy ε ( θ , E ) depending on the number of photons involved ina process, and direction of scattering and weighted with the asymptotic expression of the Kroll-Watson formula. Laser-free cross sections are taken from [9]. [1] V A Tulsky, B Krebs, J Tiggesb¨aumker, and D Bauer, “Revealing laser-coherent electron features usingphase-of-the-phase spectroscopy,” J. Phys. B , 074001 (2020).[2] A. Hernando, M. Barranco, R. Mayol, M. Pi, and F. Ancilotto, “Density functional theory of thestructure of magnesium-doped helium nanodroplets,” Phys. Rev. B , 184515 (2008).[3] G. M. Roberts, J. L. Nixon, J. Lecointre, E. Wrede, and J. R. R. Verlet, “Toward real-time charged-particle image reconstruction using polar onion-peeling,” Rev. Sci. Instr. , 053104 (2009).
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