Overall Objectives

Attosecond science, which is the science of generation and application of attosecond light pulses, has become a well-established research field that goes across several traditional areas such as Ultrafast and Nonlinear Optics, Atomic and Molecular Physics, and Condensed Matter Physics. Attosecond pulses have been first produced through the phenomenon of high-order harmonic generation (HHG) in gases. Nowadays, they can also be produced in plasmas produced by high-power lasers, and very recently using free electron lasers. Their duration varies from a few tens to a few hundred attoseconds, while the central photon energy goes from the extreme ultraviolet (XUV) to the X-ray domain. Matter exposed to these ultrashort XUV light pulses ionizes and temporally-confined coherent electron wave packets are created.  
The aim of the QPAP project is to perform quantum optics experiments, not with photons as in conventional quantum optics, but with photoelectrons created by absorption of attosecond light pulses. In other words, we aim at developing “attosecond quantum electronics”, quantum electronics not referring here to the physics of few-level systems in a laser medium, but to the quantum behavior of ultrashort electron wavepackets created by the absorption of attosecond light pulses. 

This research lies at the crossing between three different areas of atomic, molecular, and optical (AMO) physics: attosecond science, photoionization /dissociation of atoms and molecules, and quantum information. These fields have been largely disconnected in the past.  Attosecond science emerged at the beginning of the millennium, with the main emphasis first on the generation of attosecond pulses. Photoionization processes in atoms and molecules have been traditionally studied with synchrotron radiation. Quantum information has preferentially considered simpler systems than electrons in atoms or molecules like photons, ions in a trap, cold atoms, superconducting circuits, etc.

Progress in the performances of the attosecond sources, in particular regarding repetition rate, now enables us to perform photoionization studies of atoms and molecules using the advanced coincidence/three-dimensional momentum techniques developed by scientists for synchrotron radiation experiments. Adding phase information, thanks to interferometric techniques, we hope to be able to follow in time the quantum properties of the created photoelectrons, like coherence and entanglement. In addition, we will study the interaction of matter with a controlled sequence of a few attosecond pulses, with a variable number of pulses and pulse separation, in the presence of a weak and well-characterized dressing field. We will study the properties of the electronic states created by interferences of the electron wavepackets and their temporal evolution.

Our objectives are

• to characterize and study the quantum coherence of attosecond electron wavepackets,
• to control quantum interferences of electron wavepackets using a small number of attosecond pulses, and
• to create and follow in time entangled two-electron attosecond wavepackets.

Major Achievements

Our first objective is to characterize electron wavepackets created by photoionization. When this wavepacket is fully coherent, its phase can be determined by an interference technique (named RABBIT) involving two-photon transitions: two-photon absorption of a high-order harmonic and a laser photon, and absorption of the next harmonic close to the resonance and emission of a laser photon, leading to the creation of a sideband. When the delay between the harmonics and the laser is
varied, the sideband intensity oscillates. The phase variation of the ionizing wavepacket is imprinted in the measured phase. This technique has been applied to different topics, resonant two-photon photoionization in He, both below and above the threshold, and non-resonant photoionization of neon over a broad energy range with angular resolution. 

A new algorithm for the quantum state tomography of photoelectrons, named KRAKEN, has been derived, numerically verified and experimentally implemented. We photoionize atoms using short extreme ultraviolet pulses and probe the emitted electron with a delayed, spectrally tunable, bichromatic infrared pulse. By varying the frequency separation of the two spectral components of the probe pulse, we determine the populations and coherences of the density matrix. We apply this method to measure the quantum state of photoelectrons originating from helium and argon atoms. In helium, the density matrix is close to that of a pure state, while in argon, the density matrix describes a mixed state. The reduced purity is due to entanglement between the ion and the electron, induced by the spin-orbit interaction .A PhD thesis has been successfully defended on this subject (Hugo Laurell, June 2023). It is one of the major achievements of this project. 

Key to objectives two and three of the project is the combination of a high-repetition-rate, few-cycle laser source, with the possibility to reach high photon energy, a specially designed gas target for efficient high harmonic generation, and an advanced three-dimensional photoelectron/ion momentum detector. Progress has been made in all three parts of the experiment. A large effort has been made to improve the capabilities of our laser system toward efficiency, flexibility, and reliability, needed for the planned experiments. The possibility of using post-compression techniques directly after the output from our ytterbium fiber amplifier has been explored. A few-cycle short-wave-infrared light source working at a wavelength of 1.8 um, at a 200 kHz repetition rate, and with a duration of two cycles has been successfully built. 

The requirement of Career Envelope Phase (CEP) stability has led to a novel detector, allowing the measurement in a single shot and at a high repetition rate, of the CEP offset of ultrashort laser pulses. The spectral fringes resulting from nonlinear interferometry, encoding the CEP, are evaluated completely optically via optical Fourier transform. For demonstration, the CEP of a 200 kHz, few-cycle laser system based on optical parametric chirped pulse amplification was measured. The proposed method shows excellent agreement with simultaneous measurement of the spectral fringes by a fast line-scan camera. We have filed a patent application, submitted an article for publication, and written a Proof-of-Concept proposal, which has just been accepted.

The requirement for a high XUV photon flux has led us to re-examine how to optimize high-order harmonic generation. Our findings constitute one (unexpected) major result of this project. High-order harmonic generation, which is at the basis of the formation of attosecond pulses, depends on many parameters, and there is still no consensus on how to choose the target geometry to optimize the source efficiency. We find that efficient HHG can be realized over a large range of pressures and
medium lengths if these follow a certain hyperbolic equation. This explains the large versatility of gas target designs for efficient HHG and provides design guidance for future high-flux XUV sources. Our prediction has also been validated in experimental studies, partly performed at the Extreme Light Infrastructure ELI-ALPS in Szeged, Hungary.

Finally, progress has been made regarding the efficient utilization of the three-dimensional electron detector. Analysis routines have been developed and calibration procedures implemented.