Streaking temporal double slit interference by an orthogonal two-color laser field
Martin Richter, Maksim Kunitski, Markus Schöffler, Till Jahnke, Lothar P.H. Schmidt, Min Li, Yunquan Liu, Reinhard Dörner
SStreaking temporal double slit interference by an orthogonal two-color laser field
Martin Richter, ∗ Maksim Kunitski, Markus Sch¨offler, Till Jahnke, Lothar P.H. Schmidt, Min Li, † Yunquan Liu,
2, 3 and Reinhard D¨orner Institut f¨ur Kernphysik, Goethe-Universit¨at Frankfurt, 60438 Frankfurt am Main, Germany State Key Laboratory for Mesoscopic Physics and Department of Physics,Peking University, Beijing 100871, People’s Republic of China Collaborative Innovation Center of Quantum Matter, Beijing 100871, China (Dated: November 12, 2018)We investigate electron momentum distributions from single ionization of Ar by two orthogonallypolarized laser pulses of different color. The two-color scheme is used to experimentally control theinterference between electron wave packets released at different times within one laser cycle. Thisintracycle interference pattern is typically hard to resolve in an experiment. With the two-colorcontrol scheme these features become the dominant contribution to the electron momentum distri-bution. Furthermore the second color can be used for streaking of the otherwise interfering wavepackets establishing a which-way marker. Our investigation shows that the visibility of the inter-ference fringes depends on the degree of the which-way information determined by the controllablephase between the two pulses.
Electron wave packets launched from a sample at dif-ferent positions [1–3] or at different times [4, 5] give riseto interference effects in the final electron momentumdistribution whenever the wave packets cannot be distin-guished by a measurement. Any which-way informationwill destroy the interference. There are at least two waysto record such which-way information. One is to storeit in another particle by entanglement of the electronwith that particle [2, 6] or the environment [7–9]. Thesecond is by marking the which-way information in theelectron itself, either in a spin degree of freedom [10] or ina motional degree of freedom like one of the momentumcomponents.A versatile scenario to create electron wave packets forwhich several prominent interference effects have beenidentified in recent years is strong-field ionization in anultrashort laser pulse. There the wave packets are re-leased by strong-field tunnel ionization during the laserpulse and are subsequently driven by this optical field(see Fig. 1a). The interference fringes are then observedin the final electron momentum distribution long afterthe laser pulse. In the present work we show how one ofthese strong-field ionization interference patterns can bemade visible and switched on and off. We have achievedthis by using a second, phase locked orthogonal laser fieldof doubled frequency which encodes the which-way infor-mation in one momentum component.The most prominent interference fringes emerging instrong-field ionization are the equidistant peaks in theelectron energy distribution. These above threshold ion-ization (ATI) peaks are spaced by the photon energy.They result from the interference of wave packets bornperiodically in time at subsequent laser cycles. In ex-periments at higher laser intensities these structures arewashed out by the averaging over the different intensitiesin the focus since the energy offset of this comb dependson the laser intensity. Much less striking and only discov- ered in 2005 [4] are additional fringes resulting from theinterference between wave packets born within one cy-cle at times where the vector potential is the same, butthe direction of the electric field is opposite (trajectoriesID and D in Fig. 1a). We refer to this channel in thefollowing as intracycle interference. These interferenceshave been seen first in an experiment using three-cycle(6 fs, 760 nm) laser pulses [4]. In a later experiment two-color pulses have been used to characterize the phasedifference between the two wave packets after tunneling[11]. Most of the works discussing the intracycle inter-ferences are theoretical [12–14]. The main reason is thatin experiments with linearly polarized multi-cycle pulsesthese interference structures are buried in a wealth ofother, more prominent structures. They show up onlyas a height modulation of the ATI peaks [11, 15]. ATIand intracycle interferences would occur even without theinfluence of the ionic potential. The unavoidable pres-ence of this potential gives rise to further structures inthe momentum distribution of electrons upon strong-fieldionization, which also obscure the intracycle interferencefringes. The key physical effect behind these additionalstructures is that electron trajectories (labeled with ID inFig. 1a) which escape in one direction, are turned aroundby the oscillating laser field and they are deflected bypassing the ionic core. This deflection gives rise to whathas been named ”Coulomb focusing” [16] leading to anarrowing of the momentum distribution perpendicularto the field direction [17]. They also lead to spider-legshaped structures [18–20] (labeled with S in Fig. 2a).In the present work we show that orthogonally polar-ized two-color pulses (OTC) [21–23] can be used to turnthe typically faint intracycle interference fringes into adominating structure in the electron momentum distri-bution and at the same time can be used as a control-lable which-way marker allowing to efface the interfer-ences. The OTC pulses are shown in Fig. 1a. We use a r X i v : . [ phy s i c s . a t o m - ph ] M a r FIG. 1. (a) The vector potential of the second harmonic fieldrelative to the ionizing 780 nm electric field and the elec-tron trajectories ID (indirect) and D (direct) at two differentphases between the colors (see eq. 1). Though the fieldsare perpendicularly polarized in the experiment, here theyare drawn in parallel for a more intuitive understanding ofthe streaking dynamics. For φ = − π/ φ = 0 trajectories A and Bare streaked to opposite directions which extinguishes the in-terference. (b) is a sketched spatial analogue where a doubleslit (depicted with two holes in a disk) transforms an incom-ing plane wave into two coherent spherical waves (for the sakeof simplicity shown with curved lines). These waves are thensteered into the same direction by two plane deflectors (ca-pacitors) of equal polarity resulting in an interference pattern.This corresponds to the phase φ = − π/
2. (c) is the case for φ = 0 where the two waves are deflected in opposite directionsshowing no interference. a strong 780 nm pulse (1 . · W/cm ) and a weak(1 . · W/cm ) 390 nm pulse. The conditions are cho-sen such that the tunneling is mainly caused by the 780nm pulse while the orthogonal 390 nm field mildly streaksthe electron wave packet. By changing the phase betweenthe two colors we can adjust the vector potential of the390 nm laser field which causes the streaking such thatit is the same for trajectories ID and D (Fig. 1a, left).In this case ID and D are indistinguishable, there is nowhich-way information and we expect the intracycle in-terference to occur. Alternatively, the phase between the390 and 780 nm laser pulses can be chosen such that thevector potential of the 390 nm laser field is opposite atpoints ID and D (Fig. 1a, right). In this case the 390nm laser field marks the slits in time and makes the wave packets distinguishable switching off the interference.A spatial analogue of this scenario is shown in Figs. 1band 1c. An electron wave traverses a double slit wherebehind each slit a pair of deflector plates is mounted.The deflection is orthogonal to the interference fringes.If the deflectors behind both slits are biased with thesame polarity they both deflect the electron wave packetto the same direction and an interference pattern occurs.If however, the polarity is opposite, one deflects upward,one downward. The which-slit information is then im-printed in the momentum component orthogonal to theinterference fringes and no double slit interference occurs.In the experiment the OTC field (cid:126)E = E z, cos( ωt ) (cid:126)e z + E y, cos(2 ωt + φ ) (cid:126)e y (1)is used, where φ is the tunable phase between the two col-ors. The three-dimensional electron momenta were mea-sured in coincidence with argon ions using COLTRIMS[24, 25]. Further experimental details are given in [26].The momentum distribution of electrons originatingfrom single ionization of Argon by a single-color 780 nmpulse with an intensity of 1 . · W/cm is shown in Fig.2a. The distribution exhibits the features which are wellknown from the literature [17, 18, 27]. Namely, it shows acutoff at a momentum of approx. p cutoffz = 1 .
08 au whichis the maximum momentum p z an electron can acquire inthe 780 nm field at this intensity without rescattering atthe nucleus. A decrease of intensity at this momentumis visible in Fig. 2a (note the logarithmic color scale).Electrons at larger momenta than p cutoffz originate frombackscattering at the nucleus and form what is knownas the “plateau” in the energy spectrum [28]. The ATIpeaks are visible as rings. In the regime of energies below2 U P (momenta below p cutoffz ) the dominating emissionis along the polarization axis with small transverse mo-menta. This feature is caused by the Coulomb focusingof electrons which pass the nucleus (e.g. trajectory ID inFig. 1a). Also the spider-leg shape holographic interfer-ence features can be seen (feature marked with S) [18–20].The intracycle interferences, however, are not visible inthis figure without a detailed analysis. They are buriedbelow the other, much more prominent structures.By adding a weak 390 nm streaking field orthogonal tothe 780 nm field with a phase shift of φ = − π/
2, a strongfinger-like structure appears in the lower half of the graph(Fig. 2b) in which the field driven momentum is repre-sented by the dashed line. For these experimental param-eters we performed a quantum-trajectory Monte Carlo(QTMC) simulation shown in panel (c). This simula-tion describes the strong-field ionization semiclassicallyby combining Ammosov-Delone-Krainov (ADK) theoryand Feynman’s path integral approach (see [29] for de-tails). In ADK-theory the ionization rate, the tunnel exitand the momentum distribution are prescribed [30]. Dur-ing the laser pulse electron trajectories are launched witha probability and a transverse momentum distribution
FIG. 2. Electron momentum distribution from strong-fieldsingle ionization of Argon. The data are integrated over an an-gular range ϑ = 90 ± ◦ where ϑ = acos( p x / (cid:112) p x + p y + p z )is the angle between the electron momentum vector and thenormal to the ( p z , p y ) plane. (a) Experiment with 780 nm(1 . · W/cm , 40 fs) pulse only. The laser polarization di-rection is shown by an arrow. (b) 780 nm/390 nm orthogonaltwo-color pulse with an intensity ratio I /I = 0 .
09 anda phase difference φ = − π/
2. The polarizations of the 780nm and 390 nm lights are shown by red and blue arrows, re-spectively. The field driven momentum p = − A ( t ) is shownby the dashed line. The finger-like structure results from theintracycle interference. (c) QMTC calculation for same laserparameters as in (b). given by ADK-theory. These electrons are propagatedclassically in the laser field and the Coulomb field of theionic core and the action integral along the trajectoryis calculated for each electron. Using this phase infor-mation the contributions from different trajectories canbe added coherently. Experiment and theory both showthe finger-like lines which, in contrast to the spider-legstructure, do not end at ( p z , p y ) = (0 , p y = 0 visible in theexperiment. This might be due to the fact that in theexperiment the spatial and temporal overlap of the 780nm and 390 nm pulse is never as perfect as assumed inthe calculation (i.e. due to imperfect beam profiles). Theintensity in the calculation is averaged over the focal vol-ume. This realistic focal averaging is essential for visualcomparison with the experiment to reduce the otherwisedominating contribution of the ATI peaks. FIG. 3. In (a) the time windows are shown where the elec-tron trajectories ID (blue) and D (red) are born in the electric780 nm field. (b)-(d) represent the QTMC-calculated momen-tum spectra for these trajectories at a streaking field phaseof φ = − π/
2. In (b) only the electrons tunneling during theblue marked quarter cycle are plotted. These indirect trajec-tories are driven back to the core by the laser field but onlyweakly interact with it because of streaking. The direct non-returning trajectories originate from the red marked quartercycle and are shown in (c). Adding up the trajectories fromboth quarter cycles coherently (d) leads to the same intracycleinterference pattern as in the experiment.
With the help of the QTMC calculation we show thatthe new finger-like structures are indeed intracycle inter-ference fringes (Fig. 3). We separate the trajectories inthose starting in the quarter cycles marked in blue andred. The blue part of the trajectories are driven back bythe 780 nm field and pass nearby the ion. The deflectionof these trajectories leads to a partial focusing as visiblein panel b. The trajectories from the red quarter cycleescape directly without recollision. They lead to a finalmomentum which is defined by the vector potential atthe instant of ionization and is broadened by the initialtransverse momentum distribution after tunneling. Sep-arately, none of the two distributions from the quartercycles show any finger-like structure. Adding the trajec-tories from both coherently, i.e. allowing for interferencebetween wave packets from both quarter cycles (Fig. 3d),yields the finger-like structure which is visible in the ex-periment.
FIG. 4. Dependence of the intracycle interferences on thephase φ between the fields of the two colors (see eq. 1). (a)cos( α ) = p z /p total with p total = (cid:112) p x + p y + p z is plottedagainst the phase φ . To improve the interference contrastthere is an additional restriction in momentum 0 .
32 au