Photoelectron Circular Dichroism with Two Overlapping Laser Pulses of CarrierFrequencies ω and 2ω Linearly Polarized in Two Mutually Orthogonal Directions

Philipp V Demekhin Anton N Artemyev Alexander Kastner and Thomas Baumertdagger

Institute of Physics and CINSaT University of Kassel Heinrich-Plett-Straszlige 40 34132 Kassel Germany

(Received 22 June 2018 revised manuscript received 9 August 2018 published 18 December 2018)

Using a model methanelike chiral system we theoretically demonstrate a possibility to accessphotoelectron circular dichroism (PECD) by a single experiment with two overlapping laser pulses ofcarrier frequencies ω and 2ω which are linearly polarized in two mutually orthogonal directionsDepending on the relative phase the resulting electric field can be tailored to have two different rotationaldirections in the upper and lower hemispheres along the polarization of the ω pulse We predict a strongforward-backward asymmetry in the emission of photoelectrons from randomly oriented samples whichhas an opposite sign in the upper and lower hemispheres The predicted PECD effect is phase andenantiomer sensitive providing new insight in this fascinating fundamental phenomenon The effect can beoptimized by varying relative intensities of the pulses

DOI 101103PhysRevLett121253201

In 1976 it was theoretically predicted that the photo-ionization of chiral molecules is sensitive to the helicity ofionizing light [1] The effect already emerges in theelectric-dipole approximation and it manifests itself as aforward-backward asymmetry in the emission of photo-electrons from randomly oriented chiral molecules in thegas phase It took about 25 years to verify these theoreticalpredictions experimentally [23] Later on this enantiomer-and helicity-selective effect was termed as photoelectroncircular dichroism (PECD) [4] During the last decade one-photon ionization of chiral molecules by circularly polar-ized radiation and the emerging PECD effects was studiedin numerous experimental and theoretical works (see egreview articles [5ndash8])Recently [910] a similar PECD effect has been observed

in the multiphoton ionization of chiral molecules by circu-larly polarized laser pulses Since then extensive exper-imental studies provided many important details on themultiphoton PECD like eg its dependence on the pulseintensity and ellipticity [11ndash13] the enantiomeric excess ofthe target [1415] or the intermediate electronic statesinvolved in different multiphoton ionization schemes[1617] In addition the impact of the nuclear and electrondynamics during the multiphoton ionization of chiralmolecules has been demonstrated by pump-probe experi-ments [18ndash21] Theoretical approaches to describe themultiphoton PECD range from the time-independentperturbative ab initio calculation of the two-photonabsorption followed by the one-photon ionization in thehydrogenic continuum spectrum [22] to nonperturbativetime-dependent methods [2324]Employing overlapping bichromatic laser pulses is a

particularly important example of coherent control schemes[2526] Here interference between the n-photon route of

one of the fields and the m-photon route of the other fieldcan be controlled through the relative phase According tothe selection rules for multiphoton transitions in atomsthere are two control scenarios [25] If n and m are bothodd or even numbers the integral and differential crosssection can be controlled In the case where n and m areeither odd or even only the differential cross section iethe photoemission in different angles can be controlledThe latter effect can also be understood in terms of thesymmetry breaking of the total electric field of two pulsesThe simplest realization of such an interference is theutilization of integer multiples of frequency components ofa fundamental laser field [27ndash36]Polarization- and phase-locked bichromatic pulses have

been successively used to control angular emission dis-tribution of photoproducts in molecules [3738] and thephotocurrent in semiconductors [3940] and on metalsurfaces [41] Here we demonstrate the possibility ofutilizing bichromatic pulses to control PECD For thispurpose we propose an experiment on the photoionizationof chiral molecules by two temporally-overlappinglaser pulses with carrier frequencies of ω and 2ω whichare polarized linearly along two perpendicular directionsDepending on the relative phase ϕ the resulting electricfield

EethtTHORN frac14 exExgethtTHORN coseth2ωtTHORN thorn eyEygethtTHORN cosethωtthorn ϕTHORN eth1THORN

can have a strong asymmetry in the xy plane Here Ex andEy are the field amplitudes and gethtTHORN is the time-envelope ofthe pulses For instance for ϕ frac14 0 or ϕ frac14 ethπ=2THORN thefield EethtTHORN has a ldquohorseshoerdquo form which is asymmetricalong the x axis For the case of ϕ frac14 ethπ=4THORN the resulting

PHYSICAL REVIEW LETTERS 121 253201 (2018)

0031-9007=18=121(25)=253201(6) 253201-1 copy 2018 American Physical Society

electric field has a ldquobutterflyrdquo form which is orientedalong the y axis (see the upper right part of Fig 1) In thelatter case the resulting field is mirrored with respect to thex axis and it exhibits two different rotational directions forpositive and negative values of yThe geometry of the presently proposed experiment is

illustrated in Fig 1 In the upper hemisphere (y gt 0) thebichromatic electric field (1) points upward and has one ofthe rotational directions In the lower hemisphere (y lt 0) itpoints downward and has an opposite rotational directionDuring photoionization photoelectrons are released alongthe electric field in the upper (lower) hemispheres and willsubsequently be projected on the respective up (down) partof the velocity map imaging (VMI [4243]) detector placedin the yz plane Such a polarization state allows for a singleand simultaneous measurement with two different rota-tional directions in the upper and lower hemispheres Achiral target acts as a ldquogearboxrdquo [544] that transforms therotational motion of the electric field in the translationmotion of the photoelectron along the pulse propagationdirection (z axis) Thus one can expect a different sign ofthe forward-backward (z gt 0=z lt 0) asymmetry in thephotoelectron angular distribution images on the upperor lower (y gt 0=y lt 0) parts of the detector Such anexperiment can be performed by combining the fundamen-tal and its second harmonic driving two-red-photon vs one-blue-photon ionization of a chiral molecule

In order to verify this hypothesis we simulated theproposed experiment theoretically Calculations were car-ried out by the time-dependent single center (TDSC)method and code [2324] It consists of the propagationof the wave packet of a single active electron which isdriven in the potential of a chiral ion by an intense shortlaser pulse The TDSCmethod accounts for the light-matterinteraction nonperturbatively via the numerical solution ofthe time-dependent Schroumldinger equation Details of themethod can be found in Ref [23] There it was applied tostudy PECD in the one-photon ionization and two-photonabove-threshold ionization of a model methanelike chiralsystem by short intense high-frequency laser pulsesIn the present Letter we use the methanelike model

chiral system from Ref [23] (see Fig 1 there) and similarhigh-frequency laser pulses In particular we utilize shortGaussian-shaped pulses of gethtTHORN frac14 expethminusetht minus t0THORN2=τ2THORN withτ frac14 1 fs The carrier frequency of the ldquoredrdquo pulse is set toω frac14 1105 eV such that the absorption of one ldquobluerdquophoton of energy 2ω frac14 221 eV results in the ionization ofthe system with the ionization potential of 183 eV [23]We thus realize the two-red-photon vs one-blue-photonionization scheme by the ω and 2ω pulses All of thecomputational details and parameters can be found in ourprevious work [23] except that here the photoelectronwave packets were projected on Coulomb waves (not onplane waves) in order to obtain final momentum distribu-tions [45ndash48] In Ref [23] it was demonstrated that theone-photon ionization spectrum of this model system by acircularly polarized 2ω frac14 221 eV pulse exhibits a sizablePECD effect of about 156 For the ω frac14 1105 eVcircularly polarized pulse the two-photon PECD computedhere amounts to about 84Owing to the chosen high frequencies these short

pulses support about 10 and 20 optical cycles for the ωand 2ω components respectively Therefore any attoclockasymmetry effects in the dipole plane due to the carrier-envelope phase can be neglected The field (1) possesses noaxial symmetry along the pulse propagation directionTherefore in order to simulate the gas phase experimentionization spectra computed at different molecular orien-tations should be averaged over all rotational Eulerangles (α β γ) for the transformation from the molecularto the laboratory frame The orientation intervals α γ isinfrac120 2πTHORN and β isin frac120 π were covered with the steps ofΔα frac14 Δβ frac14 Δγ frac14 01π Finally owing to the same reasonthe photoelectron angular distribution images recorded byeg a VIM detector cannot be Abel inverted Thereforewe theoretically simulate these images by projecting (byintegrating over the x coordinate) the computed three-dimensional angular distributions on the detector yz plane(see Fig 1)The main set of the present calculations was performed

for the equal peak intensities of two pulses Ix frac14 Iy frac141014 W=cm2 (see below) An overview of the total electron

FIG 1 Scheme of the experiment with bichromatic laser pulsesEq (1) The pulses propagate along the z axis For the relativephase ϕ frac14 thornethπ=4THORN the resulting electric field rotates counter-clockwise in the upper and clockwise in the lower parts of the xyplane from the point of view of the emitter During measure-ments photoelectrons are projected on the yz plane of eg aVMI detector Thereby photoelectrons released by the fieldpointing in the upper (lower) hemispheres are projected ontothe upper (lower) part of the detector (labeled as ldquoUpDownrdquo)For a chiral target in the gas phase it is expected that velocity mapimages recorded by the detector will exhibit an opposite sign ofthe forward-backward asymmetry (of the PECD) on its upper andlower parts

PHYSICAL REVIEW LETTERS 121 253201 (2018)

253201-2

spectrum computed for ϕ frac14 thornethπ=4THORN and integrated overall molecular orientations is shown in Fig 2(a) It exhibitsthree main features The strongest threshold peak I at aboutε frac14 38 eV is produced by the competition of two-photonionization by the red pulse and one-photon ionization bythe blue pulse At the chosen pulse intensities the indi-vidual contribution to this peak I from the red pulsebecomes noticeable compared to the contribution fromthe blue pulse [see Fig 2(b)] The weak features II and III inFig 2(a) represent electrons released by the above-thresh-old ionization processes Peak II at about ε frac14 1485 eV isproduced either by the absorption of one blue and one redphoton or by three red photons The very weak peak III atε frac14 259 eV is due to the absorption of two blue photonsone blue and two red photons or four red photons

Figure 2(c) depicts the projection of the three-dimensional photoelectron angular distribution on thedetector yz plane One can see that the computed imageexhibits a sizable forward-backward asymmetry (along thepulse propagation direction kz axis) The asymmetry ispresent in peaks I II and III Very importantly thisasymmetry is opposite for positive and negative valuesof ky momentum (ie in the upper and lower hemispheres)In order to set this effect on a quantitative scale weintroduce PECD as the difference between the two signalsIethky kzTHORN minus Iethminusky kzTHORN Figure 2(d) illustrates the effect inpercent of the maximal intensity One can see that thecomputed PECD has a different sign for ky gt 0 and ky lt 0Peak I exhibits the strongest asymmetry about 20 whilethe above-threshold ionization peaks II and III show asmaller PECD of 11 and 6 respectively The differencein size and angular dependence of chiral asymmetryobserved for peaks I II and III is dictated by theinterference between the respectively involved n- and m-photon ionization routes [25]In order to confirm the chiral origin of this effect we

performed a set of calculations for different relative phasesand for another enantiomer of the model chiral systemResults of these calculations are summarized in Fig 3which depicts the detector images and the respective PECDsfor the threshold peak I The data in Fig 3(a) obtained forϕ frac14 thornethπ=4THORN are the same as those in Figs 2(c) and 2(d)Figure 3(b) demonstrates that switching the rotationaldirections of the field to the opposite ones by changingthe phase to ϕ frac14 minusethπ=4THORN results in the opposite effect of thesame size In addition switching the enantiomer but keepingthe phase ϕ frac14 thornethπ=4THORN coincides with keeping the enan-tiomer and switching the phase to ϕ frac14 minusethπ=4THORN [compareFigs 3(b) and 3(c)]For the relative phase ϕ frac14 0 the resulting electric field

(1) possesses two different rotational directions for equalperiods of time in each of the hemispheres (see upper rightpart of Fig 1) Such a horseshoe-shaped field thus exhibitsno preferable rotational direction in the upper or lowerhemispheres As is evident from Fig 3(d) the detectorimage computed for ϕ frac14 0 is almost forward-backward andup-down symmetric A very weak asymmetry seen forϕ frac14 0 is within the error of the present integration overmolecular orientations due to finite intervals Δα Δβ andΔγ Finally the three-dimensional photoelectron angulardistribution computed for ϕ frac14 0 is strongly asymmetricalong the x axis (not shown here) owing to the respectiveasymmetry of the electric field (1)As a final point we demonstrate that the maximal chiral

asymmetry achieved at ϕ frac14 ethπ=4THORN can be optimized byvarying the field amplitudes of two pulses Indeed theeffect demonstrated here depends not only on the asym-metry of the total electric field but also on intrinsicelectronic properties of a chiral target ie on the respectivetransition amplitudes for the one-photon and two-photon

FIG 2 Panel (a) total photoelectron spectrum computed forthe model chiral system exposed to the bichromatic field (1) withthe ϕ frac14 thornethπ=4THORN butterfly form Note the logarithmic scale of thevertical axis Peak I is produced by the absorption of either oneblue photon or two red photons peak IImdashby either one blue andone red photon or by three red photons peak IIImdashby either twoblue photons or one blue and two red photons or four red photonsPanel (b) individual contributions to the total spectrum [solidcurve the same as in panel (a)] from each of the linearly polarizedpulses with carrier frequencies 2ω and ω (see legend) Panel (c)projection of the photoelectron angular distribution on thedetector yz plane Maximal pixel intensity in each spectrum isset to 100 Note that two outer rings are shown on the enhancedscales as indicated by the factors times42 and times1300 in this panelPanel (d) the photoelectron circular dichroism in percent of thetotal intensity of the signal Note from panels (c) and (d) that theforward-backward asymmetry in the emission of photoelectrons(along the kz axis) has different signs in the upper and lowerhemispheres (along the ky axis)

PHYSICAL REVIEW LETTERS 121 253201 (2018)

253201-3

ionization pathways In the previous example the peakintensities of two pulses were equivalent and the relativecontribution of the two-photon ionization was rather smallcompared to the one-photon ionization [see Fig 2(b)]What happens if the two contributions will be madecomparable This can be achieved by enhancing the Ey

component of the field (1)Figure 4 depicts computational results obtained for the

peak intensities Ix frac14 1013 and Iy frac14 4 times 1013 W=cm2 and

relative phase ϕ frac14 thornethπ=4THORN Thereby the Ey component istwo times larger than Ex and the resulting butterfly field isstretched along the y axis Now the individual contribu-tions to the total spectrum from the one-photon and two-photon ionization processes are made comparable [see

FIG 3 Projections of the photoelectron angular distributions on the detector yz plane (upper panels) and the respective PECDs (lowerpanels) computed for the model chiral system and different phases in Eq (1) (a) ϕ frac14 thornethπ=4THORN butterfly form (b) ϕ frac14 minusethπ=4THORN butterflyform and (d) ϕ frac14 0 horseshoe form Only the contribution from peak I is shown Results computed for another enantiomer of the systemand phase ϕ frac14 thornethπ=4THORN (butterfly form) are shown in panel (c) Switching the phase ϕ from thornethπ=4THORN to minusethπ=4THORN is thus equivalent toswitching enantiomers which confirms a chiral origin of the effect Note that color scales of all upper panels (and separately of all lowerpanels) are identical An asymmetry of about 1 seen in panel (d) can be considered as the accuracy of the present integration overdifferent molecular orientations

FIG 4 Computational results obtained for the case of nonequalfield amplitudes Ex and Ey (see text) Panel (a) individualcontributions to the total spectrum from each of the pulses withcarrier frequencies 2ω and ω (see legend) Panel (b) the PECD inpercent of the total intensity of the signal The observed maximalasymmetry of about 25 is larger than that of 20seen from Fig 3 One can conclude that in order to maximizethe effect it is important as a general rule to maximize theinterference between the n- and m-photon routes by making theircontributions to the spectrum comparable

FIG 5 Projections of the photoelectron angular distributionson the detector yz plane (upper panels) and the respectivePECDs (lower panels) computed for the case of six-red-photonvs three-blue-photon ionization of the model chiral system bybichromatic pulses with ω frac14 34 eV and 2ω frac14 68 eV of equalpeak intensities of Ix frac14 Iy frac14 1013 W=cm2 and pulse durations ofτ frac14 3 fs The observed chiral asymmetry is phase sensitive(a) ϕ frac14 thornethπ=4THORN and (b) ϕ frac14 minusethπ=4THORN It is however somewhatsmaller than that shown in Figs 2ndash4 for the two-red-photon vsone-blue-photon ionization scheme

PHYSICAL REVIEW LETTERS 121 253201 (2018)

253201-4

Fig 4(a)] The respective PECD computed for the thresholdphotoelectron peak I is shown in Fig 4(b) The chiral effectin this figure is very similar to that obtained for equal peakintensities of two pulses [see Fig 3(a)] However thePECD in Fig 4(b) is larger than that in Fig 3(a) This mayprovide a higher sensitivity in the enantiomeric excessdetermination [1415]In conclusion we demonstrate the possibility of studying

the PECD phenomenon by a single experiment with twoorthogonally-polarized laser pulses of frequenciesω and 2ωOur simulations show a sizable forward-backward asym-metry which depends on the enantiomer and the rotationaldirection of the field We generalize the traditional PECD toany kind of rotationally-tailored laser pulses whose electricfields exhibit circulation and we propose that this effectdoes not rely on the photon-electron angular momentumtransfer Bichromatic pulses can be generated in manyexperimental laboratories in the optical [27ndash41] and evenXUV regimes [49] The present results open a new avenuefor future PECDexperiments with tailored bichromatic laserpulses and they represent a challenge for the development ofthe required theory Particularly enticing are approaches inthe optical regime thatmake use of higher-ordermultiphotonionization schemes Additional calculations performed inthis work on the same model chiral system confirm thepossibility of generating a notable effect by such schemesAs an example the results for the six-red-photon vs three-blue-photon ionization scheme are displayed in Fig 5

The authors thank T Ring C Sarpe H Braun ASenftleben and D Reich for fruitful discussions This workwas supported by the Deutsche Forschungsgemeinschaft(DFG) within the Sonderforschungsbereich SFBndash1319ldquoExtreme Light for Sensing and Driving MolecularChiralitymdashELCHrdquo and the Schwerpunktprogramme SPPndash1840 ldquoQuantum Dynamics in Tailored Intense FieldsmdashQUTIFrdquo (Project No 281051436)

demekhinphysikuni-kasseldedaggerbaumertphysikuni-kasselde

[1] B Ritchie Phys Rev A 13 1411 (1976)[2] N Boumlwering T Lischke B Schmidtke N Muumlller T

Khalil and U Heinzmann Phys Rev Lett 86 1187 (2001)[3] G A Garcia L Nahon M Lebech J C Houver D

Dowek and I Powis J Chem Phys 119 8781 (2003)[4] L Nahon G A Garcia C J Harding E Mikajlo and I

Powis J Chem Phys 125 114309 (2006)[5] I Powis Adv Chem Phys 138 267 (2008)[6] L Nahon and I Powis in Chiral Recognition in the Gas

Phase edited by A Zehnacker (CRC Press Boca RatonFL 2010)

[7] L Nahon G A Garcia and I Powis J Electron SpectroscRelat Phenom 204 322 (2015)

[8] S Turchini J Phys Condens Matter 29 503001 (2017)

[9] C Lux M Wollenhaupt T Bolze Q Liang J Koumlhler CSarpe and T Baumert Angew Chem Int Ed Engl 515001 (2012)

[10] C S Lehmann N B Ram I Powis and M H M JanssenJ Chem Phys 139 234307 (2013)

[11] C Lux M Wollenhaupt C Sarpe and T Baumert ChemPhys Chem 16 115 (2015)

[12] C Lux A Senftleben C Sarpe M Wollenhaupt and TBaumert J Phys B 49 02LT01 (2016)

[13] SBeaulieuA Ferre RGeneauxRCanongeDDescampsB Fabre N Fedorov F Legare S Petit T RuchonV Blanchet Y Mairesse and B Pons New J Phys 18102002 (2016)

[14] A Kastner C Lux T Ring S Zuumlllighoven C Sarpe ASenftleben and T Baumert Chem Phys Chem 17 1119(2016)

[15] J Miles D Fernandes A Young C M M Bond S WCrane O Ghafur D Townsend J Saacute and J B GreenwoodAnal Chim Acta 984 134 (2017)

[16] MM Rafiee Fanood M H M Janssen and I PowisJ Chem Phys 145 124320 (2016)

[17] A Kastner T Ring B C Kruumlger G B Park T Schaumlfer ASenftleben and T Baumert J Chem Phys 147 013926(2017)

[18] S Beaulieu S Comby B Fabre D Descamps A FerreG Garcia R Geneaux F Legare L Nahon S Petit TRuchon B Pons V Blanchet and Y Mairesse FaradayDiscuss 194 325 (2016)

[19] A Comby S Beaulieu M Boggio-Pasqua D Descamps FLegaree L Nahon S Petit B Pons B Fabre Y Mairesseand V Blanchet J Phys Chem Lett 7 4514 (2016)

[20] S Beaulieu A Comby A Clergerie J Caillat D DescampsN Dudovich B Fabre R Geneaux F Legare S Petit BPons G Porat T Ruchon R Taeb V Blanchet and YMairesse Science 358 1288 (2017)

[21] S Beaulieu A Comby D Descamps B Fabre G AGarcia R Geneaux A G Harvey F Legare Z Mašiacuten LNahon A F Ordonez S Petit B Pons Y Mairesse OSmirnova and V Blanchet Nat Phys 14 484 (2018)

[22] R E Goetz T A Isaev B Nikoobakht R Berger and C PKoch J Chem Phys 146 024306 (2017)

[23] A N Artemyev A D Muumlller D Hochstuhl and Ph VDemekhin J Chem Phys 142 244105 (2015)

[24] A D Muumlller A N Artemyev and Ph V DemekhinJ Chem Phys 148 214307 (2018)

[25] M Shapiro and P Brumer Quantum Control of MolecularProcesses (Wiley-VCH Berlin 2011)

[26] M Wollenhaupt and T Baumert Faraday Discuss 153 9(2011)

[27] H G Muller P H Bucksbaum DW Schumacher and AZavriyev J Phys B 23 2761 (1990)

[28] Y Y Yin C Chen D S Elliott and A V Smith Phys RevLett 69 2353 (1992)

[29] DW Schumacher F Weihe H G Muller and P HBucksbaum Phys Rev Lett 73 1344 (1994)

[30] Y Y Yin D S Elliott R Shehadeh and E R Grant ChemPhys Lett 241 591 (1995)

[31] Z M Wang and D S Elliott Phys Rev Lett 87 173001(2001)

PHYSICAL REVIEW LETTERS 121 253201 (2018)

253201-5

spectrum computed for ϕ frac14 thornethπ=4THORN and integrated overall molecular orientations is shown in Fig 2(a) It exhibitsthree main features The strongest threshold peak I at aboutε frac14 38 eV is produced by the competition of two-photonionization by the red pulse and one-photon ionization bythe blue pulse At the chosen pulse intensities the indi-vidual contribution to this peak I from the red pulsebecomes noticeable compared to the contribution fromthe blue pulse [see Fig 2(b)] The weak features II and III inFig 2(a) represent electrons released by the above-thresh-old ionization processes Peak II at about ε frac14 1485 eV isproduced either by the absorption of one blue and one redphoton or by three red photons The very weak peak III atε frac14 259 eV is due to the absorption of two blue photonsone blue and two red photons or four red photons

Figure 2(c) depicts the projection of the three-dimensional photoelectron angular distribution on thedetector yz plane One can see that the computed imageexhibits a sizable forward-backward asymmetry (along thepulse propagation direction kz axis) The asymmetry ispresent in peaks I II and III Very importantly thisasymmetry is opposite for positive and negative valuesof ky momentum (ie in the upper and lower hemispheres)In order to set this effect on a quantitative scale weintroduce PECD as the difference between the two signalsIethky kzTHORN minus Iethminusky kzTHORN Figure 2(d) illustrates the effect inpercent of the maximal intensity One can see that thecomputed PECD has a different sign for ky gt 0 and ky lt 0Peak I exhibits the strongest asymmetry about 20 whilethe above-threshold ionization peaks II and III show asmaller PECD of 11 and 6 respectively The differencein size and angular dependence of chiral asymmetryobserved for peaks I II and III is dictated by theinterference between the respectively involved n- and m-photon ionization routes [25]In order to confirm the chiral origin of this effect we

performed a set of calculations for different relative phasesand for another enantiomer of the model chiral systemResults of these calculations are summarized in Fig 3which depicts the detector images and the respective PECDsfor the threshold peak I The data in Fig 3(a) obtained forϕ frac14 thornethπ=4THORN are the same as those in Figs 2(c) and 2(d)Figure 3(b) demonstrates that switching the rotationaldirections of the field to the opposite ones by changingthe phase to ϕ frac14 minusethπ=4THORN results in the opposite effect of thesame size In addition switching the enantiomer but keepingthe phase ϕ frac14 thornethπ=4THORN coincides with keeping the enan-tiomer and switching the phase to ϕ frac14 minusethπ=4THORN [compareFigs 3(b) and 3(c)]For the relative phase ϕ frac14 0 the resulting electric field

(1) possesses two different rotational directions for equalperiods of time in each of the hemispheres (see upper rightpart of Fig 1) Such a horseshoe-shaped field thus exhibitsno preferable rotational direction in the upper or lowerhemispheres As is evident from Fig 3(d) the detectorimage computed for ϕ frac14 0 is almost forward-backward andup-down symmetric A very weak asymmetry seen forϕ frac14 0 is within the error of the present integration overmolecular orientations due to finite intervals Δα Δβ andΔγ Finally the three-dimensional photoelectron angulardistribution computed for ϕ frac14 0 is strongly asymmetricalong the x axis (not shown here) owing to the respectiveasymmetry of the electric field (1)As a final point we demonstrate that the maximal chiral

asymmetry achieved at ϕ frac14 ethπ=4THORN can be optimized byvarying the field amplitudes of two pulses Indeed theeffect demonstrated here depends not only on the asym-metry of the total electric field but also on intrinsicelectronic properties of a chiral target ie on the respectivetransition amplitudes for the one-photon and two-photon

FIG 2 Panel (a) total photoelectron spectrum computed forthe model chiral system exposed to the bichromatic field (1) withthe ϕ frac14 thornethπ=4THORN butterfly form Note the logarithmic scale of thevertical axis Peak I is produced by the absorption of either oneblue photon or two red photons peak IImdashby either one blue andone red photon or by three red photons peak IIImdashby either twoblue photons or one blue and two red photons or four red photonsPanel (b) individual contributions to the total spectrum [solidcurve the same as in panel (a)] from each of the linearly polarizedpulses with carrier frequencies 2ω and ω (see legend) Panel (c)projection of the photoelectron angular distribution on thedetector yz plane Maximal pixel intensity in each spectrum isset to 100 Note that two outer rings are shown on the enhancedscales as indicated by the factors times42 and times1300 in this panelPanel (d) the photoelectron circular dichroism in percent of thetotal intensity of the signal Note from panels (c) and (d) that theforward-backward asymmetry in the emission of photoelectrons(along the kz axis) has different signs in the upper and lowerhemispheres (along the ky axis)

PHYSICAL REVIEW LETTERS 121 253201 (2018)

253201-3

ionization pathways In the previous example the peakintensities of two pulses were equivalent and the relativecontribution of the two-photon ionization was rather smallcompared to the one-photon ionization [see Fig 2(b)]What happens if the two contributions will be madecomparable This can be achieved by enhancing the Ey

component of the field (1)Figure 4 depicts computational results obtained for the

peak intensities Ix frac14 1013 and Iy frac14 4 times 1013 W=cm2 and

relative phase ϕ frac14 thornethπ=4THORN Thereby the Ey component istwo times larger than Ex and the resulting butterfly field isstretched along the y axis Now the individual contribu-tions to the total spectrum from the one-photon and two-photon ionization processes are made comparable [see

FIG 3 Projections of the photoelectron angular distributions on the detector yz plane (upper panels) and the respective PECDs (lowerpanels) computed for the model chiral system and different phases in Eq (1) (a) ϕ frac14 thornethπ=4THORN butterfly form (b) ϕ frac14 minusethπ=4THORN butterflyform and (d) ϕ frac14 0 horseshoe form Only the contribution from peak I is shown Results computed for another enantiomer of the systemand phase ϕ frac14 thornethπ=4THORN (butterfly form) are shown in panel (c) Switching the phase ϕ from thornethπ=4THORN to minusethπ=4THORN is thus equivalent toswitching enantiomers which confirms a chiral origin of the effect Note that color scales of all upper panels (and separately of all lowerpanels) are identical An asymmetry of about 1 seen in panel (d) can be considered as the accuracy of the present integration overdifferent molecular orientations

FIG 4 Computational results obtained for the case of nonequalfield amplitudes Ex and Ey (see text) Panel (a) individualcontributions to the total spectrum from each of the pulses withcarrier frequencies 2ω and ω (see legend) Panel (b) the PECD inpercent of the total intensity of the signal The observed maximalasymmetry of about 25 is larger than that of 20seen from Fig 3 One can conclude that in order to maximizethe effect it is important as a general rule to maximize theinterference between the n- and m-photon routes by making theircontributions to the spectrum comparable

FIG 5 Projections of the photoelectron angular distributionson the detector yz plane (upper panels) and the respectivePECDs (lower panels) computed for the case of six-red-photonvs three-blue-photon ionization of the model chiral system bybichromatic pulses with ω frac14 34 eV and 2ω frac14 68 eV of equalpeak intensities of Ix frac14 Iy frac14 1013 W=cm2 and pulse durations ofτ frac14 3 fs The observed chiral asymmetry is phase sensitive(a) ϕ frac14 thornethπ=4THORN and (b) ϕ frac14 minusethπ=4THORN It is however somewhatsmaller than that shown in Figs 2ndash4 for the two-red-photon vsone-blue-photon ionization scheme

PHYSICAL REVIEW LETTERS 121 253201 (2018)

253201-4

Fig 4(a)] The respective PECD computed for the thresholdphotoelectron peak I is shown in Fig 4(b) The chiral effectin this figure is very similar to that obtained for equal peakintensities of two pulses [see Fig 3(a)] However thePECD in Fig 4(b) is larger than that in Fig 3(a) This mayprovide a higher sensitivity in the enantiomeric excessdetermination [1415]In conclusion we demonstrate the possibility of studying

the PECD phenomenon by a single experiment with twoorthogonally-polarized laser pulses of frequenciesω and 2ωOur simulations show a sizable forward-backward asym-metry which depends on the enantiomer and the rotationaldirection of the field We generalize the traditional PECD toany kind of rotationally-tailored laser pulses whose electricfields exhibit circulation and we propose that this effectdoes not rely on the photon-electron angular momentumtransfer Bichromatic pulses can be generated in manyexperimental laboratories in the optical [27ndash41] and evenXUV regimes [49] The present results open a new avenuefor future PECDexperiments with tailored bichromatic laserpulses and they represent a challenge for the development ofthe required theory Particularly enticing are approaches inthe optical regime thatmake use of higher-ordermultiphotonionization schemes Additional calculations performed inthis work on the same model chiral system confirm thepossibility of generating a notable effect by such schemesAs an example the results for the six-red-photon vs three-blue-photon ionization scheme are displayed in Fig 5

The authors thank T Ring C Sarpe H Braun ASenftleben and D Reich for fruitful discussions This workwas supported by the Deutsche Forschungsgemeinschaft(DFG) within the Sonderforschungsbereich SFBndash1319ldquoExtreme Light for Sensing and Driving MolecularChiralitymdashELCHrdquo and the Schwerpunktprogramme SPPndash1840 ldquoQuantum Dynamics in Tailored Intense FieldsmdashQUTIFrdquo (Project No 281051436)

demekhinphysikuni-kasseldedaggerbaumertphysikuni-kasselde

[1] B Ritchie Phys Rev A 13 1411 (1976)[2] N Boumlwering T Lischke B Schmidtke N Muumlller T

Khalil and U Heinzmann Phys Rev Lett 86 1187 (2001)[3] G A Garcia L Nahon M Lebech J C Houver D

Dowek and I Powis J Chem Phys 119 8781 (2003)[4] L Nahon G A Garcia C J Harding E Mikajlo and I

Powis J Chem Phys 125 114309 (2006)[5] I Powis Adv Chem Phys 138 267 (2008)[6] L Nahon and I Powis in Chiral Recognition in the Gas

Phase edited by A Zehnacker (CRC Press Boca RatonFL 2010)

[7] L Nahon G A Garcia and I Powis J Electron SpectroscRelat Phenom 204 322 (2015)

[8] S Turchini J Phys Condens Matter 29 503001 (2017)

[9] C Lux M Wollenhaupt T Bolze Q Liang J Koumlhler CSarpe and T Baumert Angew Chem Int Ed Engl 515001 (2012)

[10] C S Lehmann N B Ram I Powis and M H M JanssenJ Chem Phys 139 234307 (2013)

[11] C Lux M Wollenhaupt C Sarpe and T Baumert ChemPhys Chem 16 115 (2015)

[12] C Lux A Senftleben C Sarpe M Wollenhaupt and TBaumert J Phys B 49 02LT01 (2016)

[13] SBeaulieuA Ferre RGeneauxRCanongeDDescampsB Fabre N Fedorov F Legare S Petit T RuchonV Blanchet Y Mairesse and B Pons New J Phys 18102002 (2016)

[14] A Kastner C Lux T Ring S Zuumlllighoven C Sarpe ASenftleben and T Baumert Chem Phys Chem 17 1119(2016)

[15] J Miles D Fernandes A Young C M M Bond S WCrane O Ghafur D Townsend J Saacute and J B GreenwoodAnal Chim Acta 984 134 (2017)

[16] MM Rafiee Fanood M H M Janssen and I PowisJ Chem Phys 145 124320 (2016)

[17] A Kastner T Ring B C Kruumlger G B Park T Schaumlfer ASenftleben and T Baumert J Chem Phys 147 013926(2017)

[18] S Beaulieu S Comby B Fabre D Descamps A FerreG Garcia R Geneaux F Legare L Nahon S Petit TRuchon B Pons V Blanchet and Y Mairesse FaradayDiscuss 194 325 (2016)

[19] A Comby S Beaulieu M Boggio-Pasqua D Descamps FLegaree L Nahon S Petit B Pons B Fabre Y Mairesseand V Blanchet J Phys Chem Lett 7 4514 (2016)

[20] S Beaulieu A Comby A Clergerie J Caillat D DescampsN Dudovich B Fabre R Geneaux F Legare S Petit BPons G Porat T Ruchon R Taeb V Blanchet and YMairesse Science 358 1288 (2017)

[21] S Beaulieu A Comby D Descamps B Fabre G AGarcia R Geneaux A G Harvey F Legare Z Mašiacuten LNahon A F Ordonez S Petit B Pons Y Mairesse OSmirnova and V Blanchet Nat Phys 14 484 (2018)

[22] R E Goetz T A Isaev B Nikoobakht R Berger and C PKoch J Chem Phys 146 024306 (2017)

[23] A N Artemyev A D Muumlller D Hochstuhl and Ph VDemekhin J Chem Phys 142 244105 (2015)

[24] A D Muumlller A N Artemyev and Ph V DemekhinJ Chem Phys 148 214307 (2018)

[25] M Shapiro and P Brumer Quantum Control of MolecularProcesses (Wiley-VCH Berlin 2011)

[26] M Wollenhaupt and T Baumert Faraday Discuss 153 9(2011)

[27] H G Muller P H Bucksbaum DW Schumacher and AZavriyev J Phys B 23 2761 (1990)

[28] Y Y Yin C Chen D S Elliott and A V Smith Phys RevLett 69 2353 (1992)

[29] DW Schumacher F Weihe H G Muller and P HBucksbaum Phys Rev Lett 73 1344 (1994)

[30] Y Y Yin D S Elliott R Shehadeh and E R Grant ChemPhys Lett 241 591 (1995)

[31] Z M Wang and D S Elliott Phys Rev Lett 87 173001(2001)

PHYSICAL REVIEW LETTERS 121 253201 (2018)

253201-5

ionization pathways In the previous example the peakintensities of two pulses were equivalent and the relativecontribution of the two-photon ionization was rather smallcompared to the one-photon ionization [see Fig 2(b)]What happens if the two contributions will be madecomparable This can be achieved by enhancing the Ey

component of the field (1)Figure 4 depicts computational results obtained for the

peak intensities Ix frac14 1013 and Iy frac14 4 times 1013 W=cm2 and

relative phase ϕ frac14 thornethπ=4THORN Thereby the Ey component istwo times larger than Ex and the resulting butterfly field isstretched along the y axis Now the individual contribu-tions to the total spectrum from the one-photon and two-photon ionization processes are made comparable [see

FIG 3 Projections of the photoelectron angular distributions on the detector yz plane (upper panels) and the respective PECDs (lowerpanels) computed for the model chiral system and different phases in Eq (1) (a) ϕ frac14 thornethπ=4THORN butterfly form (b) ϕ frac14 minusethπ=4THORN butterflyform and (d) ϕ frac14 0 horseshoe form Only the contribution from peak I is shown Results computed for another enantiomer of the systemand phase ϕ frac14 thornethπ=4THORN (butterfly form) are shown in panel (c) Switching the phase ϕ from thornethπ=4THORN to minusethπ=4THORN is thus equivalent toswitching enantiomers which confirms a chiral origin of the effect Note that color scales of all upper panels (and separately of all lowerpanels) are identical An asymmetry of about 1 seen in panel (d) can be considered as the accuracy of the present integration overdifferent molecular orientations

FIG 4 Computational results obtained for the case of nonequalfield amplitudes Ex and Ey (see text) Panel (a) individualcontributions to the total spectrum from each of the pulses withcarrier frequencies 2ω and ω (see legend) Panel (b) the PECD inpercent of the total intensity of the signal The observed maximalasymmetry of about 25 is larger than that of 20seen from Fig 3 One can conclude that in order to maximizethe effect it is important as a general rule to maximize theinterference between the n- and m-photon routes by making theircontributions to the spectrum comparable

FIG 5 Projections of the photoelectron angular distributionson the detector yz plane (upper panels) and the respectivePECDs (lower panels) computed for the case of six-red-photonvs three-blue-photon ionization of the model chiral system bybichromatic pulses with ω frac14 34 eV and 2ω frac14 68 eV of equalpeak intensities of Ix frac14 Iy frac14 1013 W=cm2 and pulse durations ofτ frac14 3 fs The observed chiral asymmetry is phase sensitive(a) ϕ frac14 thornethπ=4THORN and (b) ϕ frac14 minusethπ=4THORN It is however somewhatsmaller than that shown in Figs 2ndash4 for the two-red-photon vsone-blue-photon ionization scheme

PHYSICAL REVIEW LETTERS 121 253201 (2018)

253201-4

Fig 4(a)] The respective PECD computed for the thresholdphotoelectron peak I is shown in Fig 4(b) The chiral effectin this figure is very similar to that obtained for equal peakintensities of two pulses [see Fig 3(a)] However thePECD in Fig 4(b) is larger than that in Fig 3(a) This mayprovide a higher sensitivity in the enantiomeric excessdetermination [1415]In conclusion we demonstrate the possibility of studying

the PECD phenomenon by a single experiment with twoorthogonally-polarized laser pulses of frequenciesω and 2ωOur simulations show a sizable forward-backward asym-metry which depends on the enantiomer and the rotationaldirection of the field We generalize the traditional PECD toany kind of rotationally-tailored laser pulses whose electricfields exhibit circulation and we propose that this effectdoes not rely on the photon-electron angular momentumtransfer Bichromatic pulses can be generated in manyexperimental laboratories in the optical [27ndash41] and evenXUV regimes [49] The present results open a new avenuefor future PECDexperiments with tailored bichromatic laserpulses and they represent a challenge for the development ofthe required theory Particularly enticing are approaches inthe optical regime thatmake use of higher-ordermultiphotonionization schemes Additional calculations performed inthis work on the same model chiral system confirm thepossibility of generating a notable effect by such schemesAs an example the results for the six-red-photon vs three-blue-photon ionization scheme are displayed in Fig 5

The authors thank T Ring C Sarpe H Braun ASenftleben and D Reich for fruitful discussions This workwas supported by the Deutsche Forschungsgemeinschaft(DFG) within the Sonderforschungsbereich SFBndash1319ldquoExtreme Light for Sensing and Driving MolecularChiralitymdashELCHrdquo and the Schwerpunktprogramme SPPndash1840 ldquoQuantum Dynamics in Tailored Intense FieldsmdashQUTIFrdquo (Project No 281051436)

demekhinphysikuni-kasseldedaggerbaumertphysikuni-kasselde

[1] B Ritchie Phys Rev A 13 1411 (1976)[2] N Boumlwering T Lischke B Schmidtke N Muumlller T

Khalil and U Heinzmann Phys Rev Lett 86 1187 (2001)[3] G A Garcia L Nahon M Lebech J C Houver D

Dowek and I Powis J Chem Phys 119 8781 (2003)[4] L Nahon G A Garcia C J Harding E Mikajlo and I

Powis J Chem Phys 125 114309 (2006)[5] I Powis Adv Chem Phys 138 267 (2008)[6] L Nahon and I Powis in Chiral Recognition in the Gas

Phase edited by A Zehnacker (CRC Press Boca RatonFL 2010)

[7] L Nahon G A Garcia and I Powis J Electron SpectroscRelat Phenom 204 322 (2015)

[8] S Turchini J Phys Condens Matter 29 503001 (2017)

[9] C Lux M Wollenhaupt T Bolze Q Liang J Koumlhler CSarpe and T Baumert Angew Chem Int Ed Engl 515001 (2012)

[10] C S Lehmann N B Ram I Powis and M H M JanssenJ Chem Phys 139 234307 (2013)

[11] C Lux M Wollenhaupt C Sarpe and T Baumert ChemPhys Chem 16 115 (2015)

[12] C Lux A Senftleben C Sarpe M Wollenhaupt and TBaumert J Phys B 49 02LT01 (2016)

[13] SBeaulieuA Ferre RGeneauxRCanongeDDescampsB Fabre N Fedorov F Legare S Petit T RuchonV Blanchet Y Mairesse and B Pons New J Phys 18102002 (2016)

[14] A Kastner C Lux T Ring S Zuumlllighoven C Sarpe ASenftleben and T Baumert Chem Phys Chem 17 1119(2016)

[15] J Miles D Fernandes A Young C M M Bond S WCrane O Ghafur D Townsend J Saacute and J B GreenwoodAnal Chim Acta 984 134 (2017)

[16] MM Rafiee Fanood M H M Janssen and I PowisJ Chem Phys 145 124320 (2016)

[17] A Kastner T Ring B C Kruumlger G B Park T Schaumlfer ASenftleben and T Baumert J Chem Phys 147 013926(2017)

[18] S Beaulieu S Comby B Fabre D Descamps A FerreG Garcia R Geneaux F Legare L Nahon S Petit TRuchon B Pons V Blanchet and Y Mairesse FaradayDiscuss 194 325 (2016)

[19] A Comby S Beaulieu M Boggio-Pasqua D Descamps FLegaree L Nahon S Petit B Pons B Fabre Y Mairesseand V Blanchet J Phys Chem Lett 7 4514 (2016)

[20] S Beaulieu A Comby A Clergerie J Caillat D DescampsN Dudovich B Fabre R Geneaux F Legare S Petit BPons G Porat T Ruchon R Taeb V Blanchet and YMairesse Science 358 1288 (2017)

[21] S Beaulieu A Comby D Descamps B Fabre G AGarcia R Geneaux A G Harvey F Legare Z Mašiacuten LNahon A F Ordonez S Petit B Pons Y Mairesse OSmirnova and V Blanchet Nat Phys 14 484 (2018)

[22] R E Goetz T A Isaev B Nikoobakht R Berger and C PKoch J Chem Phys 146 024306 (2017)

[23] A N Artemyev A D Muumlller D Hochstuhl and Ph VDemekhin J Chem Phys 142 244105 (2015)

[24] A D Muumlller A N Artemyev and Ph V DemekhinJ Chem Phys 148 214307 (2018)

[25] M Shapiro and P Brumer Quantum Control of MolecularProcesses (Wiley-VCH Berlin 2011)

[26] M Wollenhaupt and T Baumert Faraday Discuss 153 9(2011)

[27] H G Muller P H Bucksbaum DW Schumacher and AZavriyev J Phys B 23 2761 (1990)

[28] Y Y Yin C Chen D S Elliott and A V Smith Phys RevLett 69 2353 (1992)

[29] DW Schumacher F Weihe H G Muller and P HBucksbaum Phys Rev Lett 73 1344 (1994)

[30] Y Y Yin D S Elliott R Shehadeh and E R Grant ChemPhys Lett 241 591 (1995)

[31] Z M Wang and D S Elliott Phys Rev Lett 87 173001(2001)

PHYSICAL REVIEW LETTERS 121 253201 (2018)

253201-5

Fig 4(a)] The respective PECD computed for the thresholdphotoelectron peak I is shown in Fig 4(b) The chiral effectin this figure is very similar to that obtained for equal peakintensities of two pulses [see Fig 3(a)] However thePECD in Fig 4(b) is larger than that in Fig 3(a) This mayprovide a higher sensitivity in the enantiomeric excessdetermination [1415]In conclusion we demonstrate the possibility of studying

the PECD phenomenon by a single experiment with twoorthogonally-polarized laser pulses of frequenciesω and 2ωOur simulations show a sizable forward-backward asym-metry which depends on the enantiomer and the rotationaldirection of the field We generalize the traditional PECD toany kind of rotationally-tailored laser pulses whose electricfields exhibit circulation and we propose that this effectdoes not rely on the photon-electron angular momentumtransfer Bichromatic pulses can be generated in manyexperimental laboratories in the optical [27ndash41] and evenXUV regimes [49] The present results open a new avenuefor future PECDexperiments with tailored bichromatic laserpulses and they represent a challenge for the development ofthe required theory Particularly enticing are approaches inthe optical regime thatmake use of higher-ordermultiphotonionization schemes Additional calculations performed inthis work on the same model chiral system confirm thepossibility of generating a notable effect by such schemesAs an example the results for the six-red-photon vs three-blue-photon ionization scheme are displayed in Fig 5

The authors thank T Ring C Sarpe H Braun ASenftleben and D Reich for fruitful discussions This workwas supported by the Deutsche Forschungsgemeinschaft(DFG) within the Sonderforschungsbereich SFBndash1319ldquoExtreme Light for Sensing and Driving MolecularChiralitymdashELCHrdquo and the Schwerpunktprogramme SPPndash1840 ldquoQuantum Dynamics in Tailored Intense FieldsmdashQUTIFrdquo (Project No 281051436)

demekhinphysikuni-kasseldedaggerbaumertphysikuni-kasselde

[1] B Ritchie Phys Rev A 13 1411 (1976)[2] N Boumlwering T Lischke B Schmidtke N Muumlller T

Khalil and U Heinzmann Phys Rev Lett 86 1187 (2001)[3] G A Garcia L Nahon M Lebech J C Houver D

Dowek and I Powis J Chem Phys 119 8781 (2003)[4] L Nahon G A Garcia C J Harding E Mikajlo and I

Powis J Chem Phys 125 114309 (2006)[5] I Powis Adv Chem Phys 138 267 (2008)[6] L Nahon and I Powis in Chiral Recognition in the Gas

Phase edited by A Zehnacker (CRC Press Boca RatonFL 2010)

[7] L Nahon G A Garcia and I Powis J Electron SpectroscRelat Phenom 204 322 (2015)

[8] S Turchini J Phys Condens Matter 29 503001 (2017)

[9] C Lux M Wollenhaupt T Bolze Q Liang J Koumlhler CSarpe and T Baumert Angew Chem Int Ed Engl 515001 (2012)

[10] C S Lehmann N B Ram I Powis and M H M JanssenJ Chem Phys 139 234307 (2013)

[11] C Lux M Wollenhaupt C Sarpe and T Baumert ChemPhys Chem 16 115 (2015)

[12] C Lux A Senftleben C Sarpe M Wollenhaupt and TBaumert J Phys B 49 02LT01 (2016)

[13] SBeaulieuA Ferre RGeneauxRCanongeDDescampsB Fabre N Fedorov F Legare S Petit T RuchonV Blanchet Y Mairesse and B Pons New J Phys 18102002 (2016)

[14] A Kastner C Lux T Ring S Zuumlllighoven C Sarpe ASenftleben and T Baumert Chem Phys Chem 17 1119(2016)

[15] J Miles D Fernandes A Young C M M Bond S WCrane O Ghafur D Townsend J Saacute and J B GreenwoodAnal Chim Acta 984 134 (2017)

[16] MM Rafiee Fanood M H M Janssen and I PowisJ Chem Phys 145 124320 (2016)

[17] A Kastner T Ring B C Kruumlger G B Park T Schaumlfer ASenftleben and T Baumert J Chem Phys 147 013926(2017)

[18] S Beaulieu S Comby B Fabre D Descamps A FerreG Garcia R Geneaux F Legare L Nahon S Petit TRuchon B Pons V Blanchet and Y Mairesse FaradayDiscuss 194 325 (2016)

[19] A Comby S Beaulieu M Boggio-Pasqua D Descamps FLegaree L Nahon S Petit B Pons B Fabre Y Mairesseand V Blanchet J Phys Chem Lett 7 4514 (2016)

[20] S Beaulieu A Comby A Clergerie J Caillat D DescampsN Dudovich B Fabre R Geneaux F Legare S Petit BPons G Porat T Ruchon R Taeb V Blanchet and YMairesse Science 358 1288 (2017)

[21] S Beaulieu A Comby D Descamps B Fabre G AGarcia R Geneaux A G Harvey F Legare Z Mašiacuten LNahon A F Ordonez S Petit B Pons Y Mairesse OSmirnova and V Blanchet Nat Phys 14 484 (2018)

[22] R E Goetz T A Isaev B Nikoobakht R Berger and C PKoch J Chem Phys 146 024306 (2017)

[23] A N Artemyev A D Muumlller D Hochstuhl and Ph VDemekhin J Chem Phys 142 244105 (2015)

[24] A D Muumlller A N Artemyev and Ph V DemekhinJ Chem Phys 148 214307 (2018)

[25] M Shapiro and P Brumer Quantum Control of MolecularProcesses (Wiley-VCH Berlin 2011)

[26] M Wollenhaupt and T Baumert Faraday Discuss 153 9(2011)

[27] H G Muller P H Bucksbaum DW Schumacher and AZavriyev J Phys B 23 2761 (1990)

[28] Y Y Yin C Chen D S Elliott and A V Smith Phys RevLett 69 2353 (1992)

[29] DW Schumacher F Weihe H G Muller and P HBucksbaum Phys Rev Lett 73 1344 (1994)

[30] Y Y Yin D S Elliott R Shehadeh and E R Grant ChemPhys Lett 241 591 (1995)

[31] Z M Wang and D S Elliott Phys Rev Lett 87 173001(2001)

PHYSICAL REVIEW LETTERS 121 253201 (2018)

253201-5

[32] R Yamazaki and D S Elliott Phys Rev Lett 98 053001(2007)

[33] S Kerbstadt L Englert T Bayer and M WollenhauptJ Mod Opt 64 1010 (2017)

[34] S Kerbstadt D Timmer L Englert T Bayer and MWollenhaupt Opt Express 25 12518 (2017)

[35] S Kerbstadt D Pengel L Englert T Bayer and MWollenhaupt Phys Rev A 97 063402 (2018)

[36] O Kfir et al Nat Photonics 9 99 (2015)[37] X Gong P He Q Song Q Ji H Pan J Ding F He

H Zeng and J Wu Phys Rev Lett 113 203001(2014)

[38] J Wu A Vredenborg L Ph H Schmidt T Jahnke ACzasch and R Doumlrner Phys Rev A 87 023406 (2013)

[39] E Dupont P B Corkum H C Liu M Buchanan andZ R Wasilewski Phys Rev Lett 74 3596 (1995)

[40] A Hache Y Kostoulas R Atanasov J L P Hughes J ESipe and H M VanDriel Phys Rev Lett 78 306 (1997)

[41] J Guumldde M Rohleder T Meier S W Koch and U HoumlferScience 318 1287 (2007)

[42] A T J B Eppink and D H Parker Rev Sci Instrum 683477 (1997)

[43] O Ghafur W Siu P Johnsson M F Kling M Drescherand M J J Vrakking Rev Sci Instrum 80 033110 (2009)

[44] M Tia et al J Phys Chem Lett 8 2780 (2017)[45] L B Madsen L A A Nikolopoulos T K Kjeldsen and J

Fernaacutendez Phys Rev A 76 063407 (2007)[46] Ph V Demekhin A Ehresmann and V L Sukhorukov

J Chem Phys 134 024113 (2011)[47] S A Galitskiy A N Artemyev K Jaumlnkaumllauml B M Lagutin

and Ph V Demekhin J Chem Phys 142 034306 (2015)[48] S Gozem A O Gunina T Ichino D L Osborn J F

Stanton and A I Krylov J Phys Chem Lett 6 4532(2015)

[49] Home page of FERMI at Elettra in Trieste Italy httpwwwelettratriesteitlightsourcesfermimachinehtml

PHYSICAL REVIEW LETTERS 121 253201 (2018)

253201-6