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IR and the and on electronvolts, distribution band- depending several pulse energy varied typically attosecond kinetic continuously broad, the infrared very the by is intense case, imposed width, an this photoelectrons, the In with of pulse. pulse 30) laser attosecond (29, (IR) technique single “streaking” a The 28). molecules combines (27, (20–23), solids time- atoms and of in (24–26), study the processes for photoemission available resolved become ultraviolet tools extreme new attosecond range, the in (XUV) 19) (18, gases in generation phase pulses. CEP laser the the characterize of to offset direction polarization laser the to 2 National Swedish the on available 1 are paper the (https://doi.org/10.5878/dc7g-n289).y in Service discussed Data data All deposition: Data oeiaie ies . C BY-NC-ND) (CC 4.0 NoDerivatives License distributed under is article access open This interest.y competing no declare authors The University Schiller Friedrich G.G.P., paper.y and the Technology; wrote Jena. of M.G. University and Vienna A.L., J.B., S.M., Y.-C.C., Reviewers: and S.M., Y.-C.C., data; research; analyzed performed M.G. M.G. and and A.L., C.G., Y.-C.C., M.M., L.R., J.V., research; A.H., designed S.C., M.G. C.G., and L.R., S.N., A.L., S.M., C.L.A., S.N., S.M., Y.-C.C., contributions: Author owo orsodnemyb drse.Eal nelulirfsklhs or [email protected] Email: addressed. be may [email protected]. correspondence whom To work. this to equally contributed S.M. and Y.-C.C. nue rcse,uigatioe euneo attosecond of sequence photo- tailored of a control pulses. coherent using repre- domain processes, work time induced This toward circumvented. step low- be a weak can sents rules a we these atoms, and that helium pulses photoionize show to properties attosecond field laser electronic few control a frequency study Using to matter. approach of process general this conservation, a of Ruled parity provides nature. and one in quantization is processes energy photon, fastest by and high-energy fundamental a most from of the emitted is absorption electron after an matter which in effect, photoelectric The Significance hsbifdsrpino h tt fkoldeo light– of knowledge of state the of description brief This high-harmonic through produced pulses, shorter even With y a hnGuo Chen , a,2 n ahe Gisselbrecht Mathieu and , a tfnsCarlstr Stefanos , y re n ehr .Paulus) G. 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PHYSICS To the best of our knowledge, the limits of these rules in is temporally confined to approximately an IR cycle, shedding photoelectron spectroscopy, in particular concerning energy light on the possibility to control the photoelectric effect in the quantization, have not been discussed in the case of weak time domain. optical fields. In this work, we study the photoionization of helium by tai- Results lored sequences of a few attosecond pulses in the presence of Details of the experiment are presented in Fig. 2A and explained a weak IR laser field using three-dimensional (3D) momen- in Materials and Methods. Briefly, a 200-kHz repetition-rate tum electron detection, which is becoming an essential tool in CEP-stable few-cycle laser generates a few attosecond pulses attosecond science (34, 35). The principle of our experiment is separated by half of the laser period (1.3 fs) (36). Helium atoms illustrated in Fig. 1. Helium atoms interact with two (Fig. 1A) are ionized by the attosecond pulses, in the presence of a weak or three (Fig. 1B) attosecond pulses, and the IR field. EWPs fraction of the IR laser pulse. In contrast to RABBIT or streak- are emitted, which carry the phase of the ionizing attosecond ing experiments, the delay between the XUV and the IR fields is pulse and a phase modulation due to the IR field at the time of kept fixed. Charged particles are detected using a 3D momentum ionization. The resulting momentum distribution is determined spectrometer based on an electron–ion coincidence scheme (37, by the interference of these wave packets. When helium atoms 38). Fig. 2B shows an example of a 3D photoelectron momentum are photoionized by two attosecond pulses separated by half of distribution obtained in helium with XUV-only radiation. Since the laser period, the electron energy is shifted relative to the the momentum distribution has rotational symmetry along the kinetic energy for the XUV-only case by a continuous amount polarization axis, we can define the photoelectron direction with which depends on the IR light field as well as on the direction of positive (negative) pz as up (down). Simulations based on the emission. When helium atoms are photoionized by three attosec- Strong Field Approximation (39, 40) are described in Materials ond pulses, we recover discrete energies equal to the energy of and Methods. the absorbed photons minus the ionization energy. The emis- Fig. 3 shows photoelectron distributions as a function of sion direction is, however, strongly asymmetric. A theoretical angle and energy, in two cases corresponding to attosecond analysis shows that this behavior can be explained by time- pulse trains generated by IR fields with CEPs equal to π/2 slit interferences of EWPs when the light–matter interaction (Fig. 3A) and 0 (Fig. 3B). Measured and simulated results are shown in Fig. 3 C and D and Fig. 3 E and F, respectively. The XUV field, indicated by the blue solid line in Fig. 3 A and B, is obtained using a model (36) based on the three-step pic- ture of high-order harmonic generation (41, 42), with ionization A Up rates from ref. 43 and photoionization cross-sections from ref. 44. The predictions of the model have been checked against detailed experimental studies of HHG spectra as a function of dispersion (36). As shown in Fig. 3A, laser pulses with CEP equal to π/2, anti- symmetric with respect to time reversal, lead to the generation E of an even number of attosecond pulses. In our conditions, we obtain mainly two similar pulses with a phase difference of π, since they are generated by two consecutive half-cycles of the IR field. The resulting photoelectron distributions, shown in Fig. 3 C and E, are shifted toward lower energy in the up direction and higher energy in the down direction. The shift increases with kinetic energy. H17 As shown in Fig. 3B, laser pulses with CEP equal to 0, symmet- H19 Up H21 H23 ric with respect to time reversal, lead to the generation of an odd Down number of attosecond pulses, with a main central pulse. In our conditions, we obtain three pulses. The resulting photoelectron B distributions, shown in Fig. 3 D and F, depend on the direction SB20 SB22 of emission. In the down direction, photoelectrons are emitted with kinetic energies corresponding to absorption of harmon- E ics 17 to 23. In the up direction, photoabsorption of harmonics 21 and 23 is strongly reduced, while new peaks corresponding to additional absorption/emission of an IR photon appear, so- called sidebands (SB20 and SB22). In general, measurements performed with different laser CEPs show both energy shifts and asymmetric appearance of sidebands. When the CEP is equal to 3π/2 or π, very similar results to those shown in Fig. 3 C and D H17 are obtained, except that the up and down directions are now H19 H21 reversed. In all of these cases, very good agreement is found Down H23 between experiment and simulation.

Fig. 1. Principle of the experiment: Helium atoms are exposed to (A) two Discussion or (B) three XUV attosecond pulses (blue) in the presence of a weak IR laser We now examine the behavior of the photoelectron distri- field (red) at a fixed delay. EWPs (violet) are emitted with an up–down asym- bution in the two cases by using an analytical derivation metry relative to the direction of polarization, resulting in different spectra (brown and green) when recording electrons emitted in the two opposite described in Materials and Methods. Assuming two pulses with directions. In the case of two pulses (in A), the photoelectron spectrum is the same amplitude and a spectral phase difference of π, the shifted toward higher or lower energies, while, for three pulses (in B), peaks photoionization probability is proportional to at different frequencies, called sidebands, are observed, mostly in the up 2 2 direction. |a (p)| ∝ sin [πΩ/(2ω) − ηp ], [1]

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tE dt hnebtenconsecutive between change = = imπ E 0 m Nature I d p p ω m P |E + cos(ωτ stedpl moment, dipole the is Ω · eaae yhl fthe of half by separated , m m 2m A(t m p E (t (Ω 2 m m e E ) 9–9 (1960). 493–494 187, = Ω 0 E (Ω ! η m )| e ), t t p ), i (t +i .Ce.Phys. Chem. J. → Ω .Ot o.A.A Am. Soc. Opt. J. exp[imπ and ). h ore trans- Fourier The . 1713 (1979). 1127–1130 42,  − Φ I Srne cec & Science (Springer t p t IR + /~ mπ/ω − (p,t (Wiley-Blackwell, mπ F ω mπ/ω + ) ,  aebeen have + . p ,cnbe can ), 2 n.Phys. Ann. i /(2m Φ 942– 48, Eq. , is d(p) m E (Ω XUV e [4] [7] [6] [5] [3] 11, ~) )], 3 9 .Ferray M. 19. McPherson A. 18. 7 .G Paulus G. G. 17. Paulus G. G. 16. Lindner F. 15. 4 .Sali P. 14. distri- angular Laurent photoelectron G. Asymmetric 13. Smith, V. A. intense Elliott, by S. D. electrons Chen, of C. Scattering Yin, McIlrath, Y. J. 12. T. Bashkansky, M. Bucksbaum, H. P. 11. cnweg upr rmteSeihRsac oni,teEuro- Marie the the and from We ATTOPIE. Knut Council, support 793604 Agreement the discussions. acknowledges Grant Research J.V. and Sklodowska-Curie scientific PALP-339253), Foundation. Swedish Grant Wallenberg insightful (Advanced Alice the Council for Research from pean Langer support Fabian acknowledge and Sytcevich, ACKNOWLEDGMENTS. (51). Service Data National Swedish the Statement. Availability Data Eq. on based formally is Slits. Temporal Eq. is parenthesis the of square absolute The tude Pulses. Two pulses. now attosecond We three downward. and or two upward by emitted photoionization term photoelec- photoelectrons examine the the the to for spectrally, due opposite overlap asymmetric, is the become contributions num- to will two even respect spectrum the and tron with odd hand, symmetrical an other is both the photons, of IR absorption of to ber corresponding energies at ampli- of same difference the phase approximately a and have tude pulses attosecond consecutive When interaction the includes term field, second IR The the field. with laser the of harmonics order of ampli- difference same where phase the a approximately and have tude pulses attosecond consecutive When Φ Pulses. Three (Eq. that so to simplifies of |a absorption by ionization to correspond harmonics. would even-order that energies at bution, q .W introduce We 3B). (Fig. pulses satellite identical, ratio smaller, the two and pulse ±1 2 sa nee,laigtu osdbn ek ntepoolcrndistri- photoelectron the in peaks sideband to thus leading integer, an is hntetotrsd o vra spectrally, overlap not do terms two the When (p)| hs B Phys. gases. rare the in radiation Lett. ae pulses. laser tions. tv hs fee n d amnc na toeodpletrain. pulse attosecond an in (2012). harmonics 083001 odd 109, and even of phase ative processes. (1992). photoionization interfering from butions light. coherent (Ω |E 2 ) q 504(2003). 253004 91, n h hteeto pcrm hc ossso eiso peaks of series a of consists which spectrum, photoelectron the and , 0 eres − Science ` (Ω sa nee,crepnigt oiainb bopino odd- of absorption by ionization to corresponding integer, an is 3–3 (1988). L31–L35 21, r Φ pcrlphase spectral )|, = toeoddul-ltexperiment. double-slit Attosecond al., et utpehroi ovrino 04n aito nrr gases. rare in radiation nm 1064 of conversion Multiple-harmonic al. , et 1) 0 ena’ ahitga prahfritnelsrao interac- intense-laser-atom for approach path-integral Feynman’s al., et a(p) toeodcnrlo ria aiymxitreecsadterel- the and interferences mix parity orbital of control Attosecond al., et (Ω ntecs ftople (m pulses two of case the In |E Nature enwcnie he pulses, three consider now We esrmn ftepaeo e-yl ae pulses. laser few-cycle of phase the of Measurement al. , et bouepaepeoeai htinzto ihfew-cycle with photoionization in phenomena Absolute-phase al., et 0–0 (2001). 902–905 292, ial,tetmoa ltaaoymnindi h antext main the in mentioned analogy slit temporal the Finally, ±1 .W obtain We ). hs e.Lett. Rev. Phys. tde fmlihtnpouto fvacuum-ultraviolet of production multiphoton of Studies al., et = a(p) |a(p) (Ω −id a 8–8 (2001). 182–184 414, 2 )|/E (p) = a 2 (p)E 1 −id (p) = etakMru Dahlstr Marcus thank We ersnigasmo toeodEWPs. attosecond of sum a representing 5, = 0 (Ω 4|d .Ot o.A.B Am. Soc. Opt. J. η 0 −id ≈ (p)E (Ω p l aadsusdi h ae r vial on available are paper the in discussed data All )| d 4–5 (1987). 349–352 58, (p)| Φ ) (p) n h ifrnei pcrlphase spectral in difference the and  0 π 0 (Ω π e (Ω 2 (p) , X i |E , η m a ) ,adapaedfeec of difference phase a and ), p a 2 0  X smxmmwhen maximum is (p) 1 (Ω (−1) − m smxmmwhen maximum is (p) e i )| η 2re e p 2 i m 9 (1987). 595 4, sin − mπ −i e ω imπ e η Ω 2 2. −i p ω m E hs e.Lett. Rev. Phys. +is(Ω) NSLts Articles Latest PNAS = Ω η π m 2ω hs e.Lett. Rev. Phys. p Ω = E (Ω ,1 iheulampli- equal with 1) 0, +i m m ai ut,Ivan Busto, David om, − ,0 ,wt central a with 1, 0, −1, ¨ ). (Ω π cos( ω η Ω ). p p 
|a(p) π x . η ω , , Ω p = Ω p 441(2005). 040401 95, ) ∝ y = Ω  2 . hs e.Lett. Rev. Phys. p ln.I,on If, plane. 2353–2356 69, |a ≈ 2qω · (2q A π hs Rev. Phys. 0 1 | where , which , Eq. , (p)| + s(Ω f6 of 5 1)ω [12] [11] [10] 2 ) [9] [8] + = J. 7 ,

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