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Physical Review A

Trichromatic shaper-based quantum state holography

Kevin Eickhoff, Lea Feld, D. Köhnke, Tim Bayer, M. Wollenhaupt

Published Nov 5, 2021• 8 citations
Publisher

Abstract

Phases play an important role in ultrafast dynamics. In this paper, the authors present an ultrafast quantum state holography scheme based on the interference of photoelectron wave packets from multiphoton ionization using shaper-generated trichromatic pump-probe-reference pulse sequences. Independent control of the phase, the time delay, and the central wavelength of all three sub-pulses are demonstrated in a proof-of-concept experiment on the multiphoton ionization of potassium atoms.

DOI
10.1103/physreva.104.052805

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Phases play an important role in ultrafast dynamics. In this paper, the authors present an ultrafast quantum state holography scheme based on the interference of photoelectron wave packets from multiphoton ionization using shaper-generated trichromatic pump-probe-reference pulse sequences. Independent control of the phase, the time delay, and the central wavelength of all three sub-pulses are demonstrated in a proof-of-concept experiment on the multiphoton ionization of potassium atoms.
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.
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.
Ultrafast atomic processes, such as excitation and ionization occurring on the femtosecond or shorter time scale, were explored by employing attosecond high-harmonic pulses. With the absorption of a suitable high-harmonic photon a He atom was ionized, or resonantly excited with further ionization by absorbing a number of infrared photons. The electron wave packets liberated by the two processes generated an interference containing the information on ultrafast atomic dynamics. The attosecond electron wave packet, including the phase, from the ground state was reconstructed first and, subsequently, that from the 1s3p state was retrieved by applying the holographic technique to the photoelectron spectra comprising the interference between the two ionization paths. The reconstructed electron wave packet revealed details of the ultrafast photoionization dynamics, such as the instantaneous two-photon ionization rate.
Ultrafast pulse shapes are used to control simultaneously the optimal population transfer coefficients and rotational wave-packet quantum interferences in the $E{}^{1}{\ensuremath{\Sigma}}_{g}^{+}$ state of Li2{\mathrm{Li}}_{2}Li2​ $({\ensuremath{\nu}}_{E}=9,$ JE=27{J}_{E}=27JE​=27 and 29). By dividing the spectral bandwidth of the ultrafast pulses into multiple ``control domains'' centered on each resonant wavelength, the population transfer coefficients can be manipulated independently of the wave-packet interferences to maximize the Li2{\mathrm{Li}}_{2}Li2​ photoionization yield at arbitrary short pump-probe time delays. To investigate the population transfer coefficients with and without wave-packet interferences, respectively, the pump polarization is set to be either parallel to or at the magic angle (\ensuremath{\sim}55\ifmmode^\circ\else\textdegree\fi{}) relative to the probe polarization. A comparison is made between phases that are symmetric and antisymmetric about the resonances. The effects of resonant and nonresonant frequencies are separately established and quantified. It is estimated that up to 90% of the possible nonresonant Rabi oscillations can be brought into phase simultaneously for each rovibrational state in the wave packet, while at the same time a constant phase offset added to one of the control domains establishes the phase of the wave-packet interference.
We analyze and further develop our method of quantum-state holography for reconstructing quantum superposition states in molecules or atoms [Phys. Rev. Lett. 80, 1418 (1998)]. The technique is based on mixing the unknown object state with a known reference state generated in the same system by two delayed laser pulses, and detecting the total time- and frequency-integrated fluorescence as a function of the delay. The feasibility of the method is demonstrated by reconstructing various vibrational wave packets in sodium dimers. Both the cases of completely controlled and noisy relative phase between the laser pulses are considered. In the latter case, we use the technique of coherence observation by interference noise to recover the interference component of the fluorescence signal. Our results clearly demonstrate the robustness of quantum-state holography and the high quality of reconstruction even in the presence of the external noise.
Quantitative control and measurement of quantum entanglement are essential for advancing quantum technologies. Photoionization induced by ultrashort laser pulses provides a unique platform for studying entanglement between photoelectrons and residual ions, representing one of the most intriguing quantum phenomena in attosecond physics. Although extensive studies have focused on the coherence properties within either the emitted electrons or the ions individually, the electron-ion entanglement has remained largely unexplored. In this work, we bridge this gap by investigating the resonance-enhanced multiphoton ionization of argon atoms driven by two time-delayed ultrashort ultraviolet pulses. Employing state-of-the-art first-principles multi-electron simulations, we demonstrate the ability to reconstruct and precisely manipulate the purity of electron quantum states through detailed analysis of the photoelectron angular distributions. Our results reveal distinct scattering-phase differences among various electron configurations within the same partial wave channel, providing unequivocal evidence of electron-ion correlation and entanglement. With the fast development of free-electron lasers, this study establishes an experimentally feasible framework for directly controlling quantum entanglement in ultrafast ionization processes, offering new insights and powerful methodologies for exploring complex electron dynamics in many-electron systems.