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arXiv:1503.08308 · Physical Review A

Maximum-information photoelectron metrology

Paul Hockett, Christian Lux, M. Wollenhaupt, Thomas Baumert

Published Jul 13, 2015• 16 citations
arXivHTMLPDF

Abstract

Photoelectron interferograms, manifested in photoelectron angular distributions (PADs), are high-information, coherent observables. In order to obtain the maximum information from angle-resolved photoionization experiments it is desirable to record the full, three-dimensional (3D), photoelectron momentum distribution. Here we apply tomographic reconstruction techniques to obtain such 3D distributions from multiphoton ionization of potassium atoms, and fully analyze the energy and angular content of the 3D data. The PADs obtained as a function of energy indicate good agreement with previous 2D data and detailed analysis [Hockett et al., Phys. Rev. Lett. 112, 223001 (2014)] concerning the main spectral features, but also indicate unexpected symmetry breaking in certain regions of momentum space, thus revealing additional continuum interferences which cannot otherwise be observed. These observations reflect the presence of additional ionization pathways and, most generally, illustrate the power of maximum-information measurements of coherent observables for quantum metrology of complex systems.

DOI
10.1103/physreva.92.013412

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Photoelectron interferograms, manifested in photoelectron angular distributions (PADs), are high-information, coherent observables. In order to obtain the maximum information from angle-resolved photoionization experiments it is desirable to record the full, three-dimensional (3D), photoelectron momentum distribution. Here we apply tomographic reconstruction techniques to obtain such 3D distributions from multiphoton ionization of potassium atoms, and fully analyze the energy and angular content of the 3D data. The PADs obtained as a function of energy indicate good agreement with previous 2D data and detailed analysis [Hockett et al., Phys. Rev. Lett. 112, 223001 (2014)] concerning the main spectral features, but also indicate unexpected symmetry breaking in certain regions of momentum space, thus revealing additional continuum interferences which cannot otherwise be observed. These observations reflect the presence of additional ionization pathways and, most generally, illustrate the power of maximum-information measurements of coherent observables for quantum metrology of complex systems.
Abstract We present a three-dimensional (3D) photoelectron wave packet holography scheme based on polarization-tailored trichromatic femtosecond laser pulses for the determination of quantum phases in atomic multiphoton ionization (MPI). Experimentally, we combine supercontinuum polarization pulse shaping with photoelectron tomography for the reconstruction of the 3D photoelectron momentum distribution (PMD). To demonstrate the 3D photoelectron holography scheme, we superimpose a sculptured wave packet encoding a relative continuum phase with a reference wave packet. In particular, we create a sculptured angular momentum superposition wave packet by (2 + 1) resonance-enhanced MPI of potassium atoms using a counter-rotating circularly polarized bichromatic pulse sequence. The sculptured wave packet, consisting of states with different orbital angular momentum quantum numbers, interferes with the reference wave packet generated by direct three-photon ionization with a circularly polarized pulse of the third color. Depending on the circularity of the reference pulse, interference of both wave packets gives rise to 3D photoelectron holograms with c 2 or c 4 rotational symmetry in the laser polarization plane, i.e., in the azimuthal direction. In the polar direction, the azimuthal interference pattern undergoes a phase-shift revealing the relative quantum phase between the p- and f-type continuum partial waves in the sculptured wave packet. We determine the relative continuum phase by fitting the parameters of an analytical model of the hologram to the measured 3D PMD and confirm the result by direct extraction of the continuum phase difference from the polar-angle-dependent azimuthal phase-shift of the photoelectron angular distribution.
The feasibility of complete photoionization experiments, in which the full set of photoionization matrix elements is determined, using multiphoton ionization schemes with polarization-shaped pulses has recently been demonstrated [P. Hockett et al., Phys. Rev. Lett. 112, 223001 (2014)]. Here we extend our previous work to discuss further details of the numerics and analysis methodology utilized and compare the results directly to new tomographic photoelectron measurements, which provide a more sensitive test of the validity of the results. In so doing we discuss in detail the physics of the photoionization process and suggest various avenues and prospects for this coherent multiplexing methodology.
Coherent control over photoelectron wavepackets, via the use of polarization-shaped laser pulses, can be understood as a time and polarization-multiplexed process, where the final (time-integrated) observable coherently samples all instantaneous states of the light–matter interaction. In this work, we investigate this multiplexing via computation of the observable photoelectron angular interferograms resulting from multi-photon atomic ionization with polarization-shaped laser pulses. We consider the polarization sensitivity of both the instantaneous and cumulative continuum wavefunction; the nature of the coherent control over the resultant photoelectron interferogram is thus explored in detail. Based on this understanding, the use of coherent control with polarization-shaped pulses as a methodology for a highly multiplexed coherent quantum metrology is also investigated, and defined in terms of the information content of the observable.
Abstract Angle-resolved (AR) RABBITT measurements offer a high information content measurement scheme, due to the presence of multiple, interfering, ionization channels combined with a phase-sensitive observable in the form of angle and time-resolved photoelectron interferograms. In order to explore the characteristics and potentials of AR-RABBITT, a perturbative 2-photon model is developed; based on this model, example AR-RABBITT results are computed for model and real systems, for a range of RABBITT schemes. These results indicate some of the phenomena to be expected in AR-RABBITT measurements, and suggest various applications of the technique in photoionization metrology.
We present the unambiguous determination of quantum phases in the multiphoton ionization (MPI) of potassium atoms by using a multichannel photoelectron interferometry scheme based on trichromatic pulse shaping. The colors of the laser field are chosen to produce three energetically separated photoelectron interferograms in the continuum. While the red pulse is two-photon resonant with the 3d3d3d state resulting in a (2+1)(2+1)(2+1) resonance-enhanced MPI (REMPI), a (1+2)(1+2)(1+2) REMPI occurs via the nonresonant intermediate 4p4p4p state with an initial green or blue pulse. We show that ionization via a nonresonant intermediate state lifts the degeneracy of photoelectron interferograms from pathways consisting of permutations of the colors. The analysis of the interferograms reveals a phase shift of $\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2$ depending on the sign of the detunings in the (1+2)(1+2)(1+2) REMPI pathways. In addition, we demonstrate that the photoionization time delay in the resonant (2+1)(2+1)(2+1) REMPI pathway gives rise to a linear spectral phase in the photoelectron spectra. Insights into the underlying MPI processes are gained through an analytic perturbative description and numerical simulations of a trichromatic driven three-level system coupled to the continuum.
We theoretically study the photoelectron angular distribution (PAD) from the two-photon single ionization of H and He by femtosecond and attosecond extreme-ultraviolet pulses, based on the time-dependent perturbation theory and simulations with the full time-dependent Schrodinger equation. The PAD is formed by the interference of the s and d continuum wave packets, and, thus, contains the information on the relative phase and amplitude ratio between them. We find that, when a spectrally broadened femtosecond pulse is resonant with an excited level, the PAD substantially changes with pulse width, since the competition between resonant and nonresonant ionization paths, leading to distinct from the scattering phase shift difference, changes with it. In contrast, when the Rydberg manifold is excited, and for the case of above-threshold two-photon ionization, and the PAD do not depend much on pulse width, except for the attosecond region. Thus, the Rydberg manifold and the continuum behave similarly in this respect. For a high-harmonic pulse composed of multiple harmonic orders, while the value is different from that for a single-component pulse, the PAD still rapidly varies with pulse width. The present results illustrate a new way to tailor the continuum wave packet.