Attosecond photoionization dynamics with stimulated core-valence transitions

Jhih-An You, Nina Rohringer, and Jan Marcus Dahlström

Phys. Rev. A 93, 033413 – Published 21 March 2016

Abstract

We investigate ionization of neon atoms by an isolated attosecond pump pulse in the presence of two coherent extreme ultraviolet or x-ray probe fields. The probe fields are tuned to a core-valence transition in the residual ion and induce spectral shearing of the photoelectron distributions. We show that the photoelectron-ion coincidence signal contains an interference pattern that depends on the temporal structure of the attosecond pump pulse and the stimulated core-valence transition. Many-body perturbation theory is used to compute “atomic response times” for the processes and we find strikingly different behavior for stimulation to the outer-core hole $(2 p \leftrightarrow 2 s)$ and stimulation to the inner-core hole $(2 p \leftrightarrow 1 s)$ . The response time of the inner-core transition is found to be comparable to that of state-of-the-art laser-based characterization techniques for attosecond pulses.

Received 4 August 2015

DOI:https://doi.org/10.1103/PhysRevA.93.033413

Physics Subject Headings (PhySH)

Single- and few-photon ionization & excitation Ultrashort pulses

Ultrafast pump-probe spectroscopy

Atomic, Molecular & Optical

Authors & Affiliations

Jhih-An You^1,2,3, Nina Rohringer^1,2,3,*, and Jan Marcus Dahlström^1,2,4,†

¹Center for Free-Electron Laser Science, Luruper Chaussee 149, 22761 Hamburg, Germany
²Max Planck Institute for the Physics of Complex Systems, Noethnitzerstrasse 38, 01187 Dresden, Germany
³Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
⁴Department of Physics, Stockholm University, AlbaNova University Center, SE-106 91 Stockholm, Sweden

^*nina.rohringer@mpsd.mpg.de
^†marcus.dahlstrom@fysik.su.se

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Vol. 93, Iss. 3 — March 2016

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Images

Figure 1
(a) Photoionization processes in neon: (1) photoelectron replica of attosecond pulse by one-photon absorption from $2 p$ state; (S+) nonsequential two-photon processes generating spectrally sheared replicas by stimulated ionic transitions with a final hole in the $2 s$ state. (b) Sketch of the proposed experiment where an IR laser field is split into two parts for generation of the XUV pump (1) and XUV probe (2,3) fields by HHG. Photoionization of neon atoms is then studied with electron-ion coincidence detection. (c) Photoelectron spectrum with residual hole in $2 p$ state and (d) photoelectron spectrum with residual hole in $2 s$ state, both computed by one-dimensional time-dependent configuration interaction singles (within an independent-particle model). See main text for the labeled spectroscopic structures.
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Figure 2
(a)–(c) Normalized photoelectron distribution of the (S+) peak in Fig. 1 as a function of phase difference between probe fields, $ϕ_{32}$ . Data are computed using 1D-TDCIS (within an independent-particle model). (a) Fourier-limited pump pulse; (b) linear chirp; and (c) quadratic chirp of pump pulse. (d)–(f) Same as (a)–(c), but with normalization at each individual kinetic energy. The left vertical axis labels the relative phase in radians, while the right axis labels the extracted group delay of the attosecond pulse in femtoseconds defined in Eq. (2), shown by the dashed white curve.
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Figure 3
Detailed study of the “response time” of the (S+) peak for three different detuning of the probe field given an unchirped pump pulse $(α = β = 0)$ . In accordance with Eq. (5), the response time, $τ_{p b}$ , is extracted by making a cosine fit to the phase-dependent oscillations of the photoelectron probability, e.g., the modulations shown in Fig. 2 (where $δ ω = 1$ eV). The raw data (not shown) has been fitted to a line in order to extract the $α$ parameter of the pump pulse. Standard deviation of the linear fit is indicated by the error bars. The data were computed by the 1D time-dependent independent-particle model discussed in the Appendix.
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Figure 4
(a) Squared matrix elements, $| M_{p b, f} |^{2}$ , for final $s$ -wave (dotted) and $d$ -wave (dashed), including both stimulated hole and electron paths in the bold lines and only electron paths in the thin lines. (b) Response time for photoemission along polarization axis, $s$ -wave and $d$ -wave. Data presented in (a) and (b) are computed by a 3D independent-particle model of neon. (c) Response time for photoemission along the polarization axis (within a correlated model including both time orderings) for the stimulated valence hole $(2 p \to 2 s)$ and core hole $(2 p \to 1 s)$ transitions. The streak-camera delay from the initial $2 p$ $(2 s)$ state [38] is shown for reference.
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Figure 5
(a) Two-photon diagram for stimulated hole transition, $2 p \to 2 s$ , after photoemission from outer state, $2 p \to k s, k d$ . (b) Two-photon diagram for stimulated electron continuum transition from an inner valence state, $2 s \to k^{'} p \to k s, k d$ . (c) Two-photon diagram for stimulated virtual electron transition from a core state, $1 s \to n^{'} p \to k s, k d$ .
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