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, and Reinhard Dörner

Phys. Rev. Lett. 114, 143001 – Published 6 April 2015

Abstract

We investigate electron momentum distributions from single ionization of Ar by two orthogonally polarized laser pulses of different color. The two-color scheme is used to experimentally control the interference between electron wave packets released at different times within one laser cycle. This intracycle interference pattern is typically hard to resolve in an experiment. With the two-color control scheme, these features become the dominant contribution to the electron momentum distribution. Furthermore, the second color can be used for streaking of the otherwise interfering wave packets establishing a which-way marker. Our investigation shows that the visibility of the interference fringes depends on the degree of the which-way information determined by the controllable phase between the two pulses.

Received 3 December 2014

DOI:https://doi.org/10.1103/PhysRevLett.114.143001

Authors & Affiliations

Martin Richter^1,*, Maksim Kunitski¹, Markus Schöffler¹, Till Jahnke¹, Lothar P. H. Schmidt¹, Min Li^2,†, Yunquan Liu^2,3, and Reinhard Dörner¹

¹Institut für Kernphysik, Goethe-Universität Frankfurt, 60438 Frankfurt am Main, Germany
²State Key Laboratory for Mesoscopic Physics and Department of Physics, Peking University, Beijing 100871, People’s Republic of China
³Collaborative Innovation Center of Quantum Matter, Beijing 100871, China

^*richter@atom.uni-frankfurt.de
^†minli@pku.edu.cn

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Vol. 114, Iss. 14 — 10 April 2015

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Images

Figure 1
(a) The vector potential of the second-harmonic field relative to the ionizing 780-nm electric field and the electron trajectories ID (indirect) and D (direct) at two different phases between the colors [see Eq. (1)]. Though the fields are perpendicularly polarized in the experiment, here they are drawn in parallel for a more intuitive understanding of the streaking dynamics. For $ϕ = - π / 2$ , both trajectories are streaked in the same direction, allowing them to interfere in momentum space. For the phase $ϕ = 0$ trajectories, A and B are streaked in opposite directions which extinguishes the interference. (b) A sketched spatial analog where a double slit (depicted with two holes in a disk) transforms an incoming plane wave into two coherent spherical waves (for the sake of simplicity, shown with curved lines). These waves are then steered into the same direction by two plane deflectors (capacitors) of equal polarity, resulting in an interference pattern. This corresponds to the phase $ϕ = - π / 2$ . (c) The case for $ϕ = 0$ where the two waves are deflected in opposite directions, showing no interference.
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Figure 2
Electron momentum distribution from strong-field single ionization of argon. The data are integrated over an angular range $ϑ = 90 ° \pm 15 °$ , where $ϑ = acos (p_{x} / \sqrt{p_{x}^{2} + p_{y}^{2} + p_{z}^{2}})$ is the angle between the electron momentum vector and the normal to the $(p_{z}, p_{y})$ plane. (a) Experiment with 780-nm ( $1.4 \times 10^{14} W / {cm}^{2}$ , 40 fs) pulse only. The laser polarization direction is shown by an arrow. (b) $780 − nm / 390 − nm$ orthogonal two-color pulse with an intensity ratio $I_{390} / I_{780} = 0.09$ and a phase difference $ϕ = - π / 2$ . The polarizations of the 780 and 390-nm lights are shown by red and blue arrows, respectively. The field-driven momentum $p = - A (t_{0})$ is shown by the dashed line. The fingerlike structure results from the intracycle interference. (c) QMTC calculation for the same laser parameters as in (b).
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Figure 3
In (a) the time windows are shown where the electron trajectories ID (blue) and D (red) are born in the electric 780-nm field. (b)-(d) represent the QTMC-calculated momentum spectra for these trajectories at a streaking field phase of $ϕ = - π / 2$ . In (b) only the electrons tunneling during the blue marked quarter cycle are plotted. These indirect trajectories are driven back to the core by the laser field but only weakly interact with it because of streaking. The direct nonreturning trajectories originate from the red marked quarter cycle and are shown in (c). Adding up the trajectories from both quarter cycles coherently (d) leads to the same intracycle interference pattern as in the experiment.
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Figure 4
Dependence of the intracycle interferences on the phase $ϕ$ between the fields of the two colors [see Eq. (1)]. (a) $\cos (α) = p_{z} / p_{total}$ with $p_{total} = \sqrt{p_{x}^{2} + p_{y}^{2} + p_{z}^{2}}$ is plotted against the phase $ϕ$ . To improve the interference contrast, there is an additional restriction in momentum $0.32 a . u . < p_{total} < 0.4 a . u .$ and $p_{y} < 0$ which gives a half spherical shell in momentum space [shown in (c) in gray], and again, as in Fig. 2, the data are integrated over an angular range $ϑ = 90 ° \pm 15 °$ . Three projections along the $\cos (α)$ axis for the phases $- π / 2$ (black), 0 (red), and $π / 2$ (green) are shown in (b). The gray dashed curve is from our QTMC calculation at $- π / 2$ and agrees very well with the experiment. In (c), the OTC field’s negative vector potentials corresponding to the field-driven final momenta are shown. The blue and red curves correspond, respectively, to the quarter cycle time windows where trajectories ID and D originate (see Fig. 3).
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