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arXiv:2309.13945 · Nature Photonics

Measuring the quantum state of photoelectrons

Hugo Laurell, Sizuo Luo, Robin Weissenbilder, Mattias Ammitzböll, Shahnawaz Ahmed, Hugo Söderberg, C. Leon M. Petersson, Vénus Poulain, Chen Guo, Christoph Dittel, Daniel Finkelstein‐Shapiro, Richard James Squibb, R. Feifel, Mathieu Gisselbrecht, Cord L. Arnold, Andreas Buchleitner, Eva Lindroth, Anton Frisk Kockum, Anne L’Huillier, David Busto

Published Jan 29, 2025• 36 citations
arXivHTMLPDF

Abstract

Abstract A photoelectron, emitted due to the absorption of light quanta as described by the photoelectric effect, is often characterized experimentally by a classical quantity, its momentum. However, since the photoelectron is a quantum object, its rigorous characterization requires the reconstruction of the complete quantum state, the photoelectron’s density matrix. Here we use quantum-state tomography to fully characterize photoelectrons emitted from helium and argon atoms upon absorption of ultrashort, extreme ultraviolet light pulses. While in helium we measure a pure photoelectronic state, in argon, spin–orbit interaction induces entanglement between the ion and the photoelectron, leading to a reduced purity of the photoelectron state. Our work shows how state tomography gives new insights into the fundamental quantum aspects of light-induced electronic processes in matter, bridging the fields of photoelectron spectroscopy and quantum information and offering new spectroscopic possibilities for quantum technology.

DOI
10.1038/s41566-024-01607-8

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Abstract A photoelectron, emitted due to the absorption of light quanta as described by the photoelectric effect, is often characterized experimentally by a classical quantity, its momentum. However, since the photoelectron is a quantum object, its rigorous characterization requires the reconstruction of the complete quantum state, the photoelectron’s density matrix. Here we use quantum-state tomography to fully characterize photoelectrons emitted from helium and argon atoms upon absorption of ultrashort, extreme ultraviolet light pulses. While in helium we measure a pure photoelectronic state, in argon, spin–orbit interaction induces entanglement between the ion and the photoelectron, leading to a reduced purity of the photoelectron state. Our work shows how state tomography gives new insights into the fundamental quantum aspects of light-induced electronic processes in matter, bridging the fields of photoelectron spectroscopy and quantum information and offering new spectroscopic possibilities for quantum technology.
We propose a continuous variable quantum state tomography protocol of electrons which result from the ionization of atoms or molecules by the absorption of extreme ultraviolet light pulses. Our protocol is benchmarked against a direct calculation of the quantum state of photoelectrons ejected from helium and argon in the vicinity of a Fano resonance. In the latter case, we furthermore distill ion-photoelectron entanglement due to spin-orbit splitting. This opens routes toward the investigation of quantum coherence and entanglement properties on the ultrafast timescale.
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.
There is a growing interest in reconstructing the density matrix of photoelectron wavepackets, in particular in complex systems where decoherence can be introduced either by a partial measurement of the system or through coupling with a stochastic environment. To this end, several methods to reconstruct the density matrix, quantum state tomography protocols, have been developed and tested on photoelectrons ejected from noble gases following absorption of extreme ultraviolet (XUV) photons from attosecond pulses. It remains a challenge to obtain model-free, single scan protocols that can reconstruct the density matrix with high fidelities. Current methods require extensive measurements or involve complex fitting of the signal. Efficient single-scan reconstructions would be of great help to increase the number of systems that can be studied. We propose a new and more efficient protocol that is able to reconstruct the continuous variable density matrix of a photoelectron in a single time delay scan. It is based on measuring the coherences of a photoelectron created by absorption of an XUV pulse using a broadband infrared (IR) probe that is scanned in time and a narrowband IR reference that is temporally fixed to the XUV pulse. We illustrate its performance for a Fano resonance in He as well as mixed states in Ar arising from spin-orbit splitting. We show that the protocol results in excellent fidelities and near-perfect estimation of the purity.
Summary form only given. The goal of any pulse characterization protocol is to describe how the spectral components of the electric field are changing in time. Apart from linear methods such as streak cameras, characterization techniques based on nonlinear processes have been developed. Those processes require broad spectral acceptance bandwidths, i.e. to be capable of resolving ultrashort features of the pulse. For many of those techniques, the pulses are reconstructed by iterative or deconvolution algorithms where the electric field is assumed to be fully coherent and do not account for the possibility of reduced coherence from pulse to pulse, or within a single pulse. In general, the chronocyclic Wigner function should be reconstructed in order to provide full information about an ensemble of partially coherent pulses. To make a parallel with quantum mechanics, most quantum systems cannot be considered as closed and interact with the environment, and subsequently, undergo decoherence. Therefore, a noisy quantum state cannot be described by a single pure state only but as a classical mixture of pure states.
Laser-dressed photoemission spectroscopy has established itself as the gold standard of attosecond temporal metrology.In this technique, the attosecond structure of an extreme-ultraviolet pulse is retrieved from the wave function of the electron wave packet released during photoionization.Here, we show that this electron wave packet should rather be described using the density matrix formalism, thus allowing one to account for all processes that can affect its coherence, from the attosecond pulse generation to the photoemission and the measurement processes.Using this approach, we reconstruct experimentally a partially coherent electron wave packet with a purity of 0.11 (1 for full coherence).Comparison with theoretical models then allows us to identify the origins of this decoherence and to overcome several limitations such as beam-line instabilities or spectrometer resolution.Furthermore, we show numerically how this method gives access to the coherence and eigencomponents of complex photoelectron wave packets.It thus goes beyond the current measurement of photoionization time delays and provides a general framework for the analysis and understanding of complex photoemission processes.
Quantum computation depends on quantum entanglement, a correlation between subsystems that cannot occur classically. A variety of theoretical measures exist for quantifying the degree entanglement in such schemes, all of which are functions of the system density matrix. How can the entanglement be measured experimentally? Using quantum tomography techniques developed for two photon entangled states, the density matrix can be reconstructed from the appropriate experimental data. In this case the state tomography gives the complete characterization of the physical system (for the relevant degree of freedom, such as spin or polarization). It gives information on both the degree of nonclassical correlation, that is entanglement, as well as the amount of decoherence in the system. In this proceedings we discuss the general state tomography procedure required to characterize a few qubit quantum computer, for any architecture.