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Attosecond science has opened up new frontiers in our understanding of processes happening on the intrinsic timescale of electrons. The ability to manipulate and observe phenomena at the attosecond level has yielded groundbreaking insights into processes such as electron dynamics and the behavior of matter under extreme conditions. This interdisciplinary field bridges various research areas such as quantum optics, quantum chemistry and quantum information science facilitating a cohesive understanding. However, despite many emerging successful applications, the discussion about intrinsic quantum effects has mainly been ignored. In this Perspective, we explore the latest advancements in quantum phenomena within attosecond science, encompassing both experimental and theoretical progress. Specifically, in the context of high-harmonic generation and above-threshold ionization, we focus on discerning genuinely quantum observations and distinguishing them from classical phenomena. Additionally, we illuminate the often overlooked yet significant role of entanglement in attosecond processes, elucidating its influence on experimental outcomes., Comment: 10 pages (with 3 figures and 2 tables), Comments welcome

High-harmonic generation has emerged as a pivotal process in strong-field physics, yielding extreme ultraviolet radiation and attosecond pulses with a wide range of applications. Furthermore, its emergent connection with the field of quantum optics has revealed its potential for generating non-classical states of light. Here, we investigate the process of high-harmonic generation in semiconductors under a quantum optical perspective while using a Bloch-based solid-state description. Through the implementation of quantum operations based on the measurement of high-order harmonics, we demonstrate the generation of non-classical light states similar to those found when driving atomic systems. These states are characterized using diverse quantum optical observables and quantum information measures, showing the influence of electron dynamics on their properties. Additionally, we analyze the dependence of their features on solid characteristics such as the dephasing time and crystal orientation, while also assessing their sensitivity to changes in driving field strength. This study provides insights into HHG in semiconductors and its potential for generating non-classical light sources., Comment: 22 pages (16 main text + 6 appendix), 7 figures (5 main text + 2 appendix)

Optical Schr\"odinger "cat" states created by superpositions of coherent light states, correspond to an optical analog of the Schr\"odinger's cat in his $\textit{Gedankenexperiment}$. These non-classical light states are generated by means of quantum state engineering methods, and they are considered as one of the main resources for fundamental tests of quantum theory and the development of new quantum technologies. However, the power of existing optical "cat" state sources is limited by their low average photon number, which prevents their use in nonlinear optics. Here, we demonstrate the generation of a femtosecond duration optical "cat" state in the infrared spectral range, with mean photon number orders of magnitude higher than those delivered by current available sources. These states exhibit intensities sufficient to induce nonlinear processes in matter. This is shown using the process of second harmonic generation in an optical crystal, in which the infrared-frequency photons of an optical "cat" state are up-converted into blue-frequency photons. We create the light states driving the second harmonic generation process, by means of conditioning operations applied on the quantum state of an intense infrared femtosecond laser field after its nonlinear interaction with atoms. Due to the presence of quantum interference between the coherent states composing the optical "cat" state, the quantum properties of the state are imprinted in the measured second-order interferometric autocorrelation traces. The findings introduce the optical "cat" states into the realm of nonlinear quantum optics, opening up exciting new paths in quantum information science., Comment: 8 pages (5 main text + 3 Methods), 5 figures (3 in main text + 2 in Methods)

Strong laser physics is a research direction that relies on the use of high-power lasers and has led to fascinating achievements ranging from relativistic particle acceleration to attosecond science. On the other hand, quantum optics has been built on the use of low photon number sources and has opened the way for groundbreaking discoveries in quantum technology, advancing investigations ranging from fundamental tests of quantum theory to quantum information processing. Despite the tremendous progress, until recently these directions have remained disconnected. This is because, the majority of the interactions in the strong-field limit have been successfully described by semi-classical approximations treating the electromagnetic field classically, as there was no need to include the quantum properties of the field to explain the observations. The link between strong laser physics, quantum optics, and quantum information science has been developed in the recent past. Studies based on fully quantized and conditioning approaches have shown that intense laser--matter interactions can be used for the generation of controllable entangled and non-classical light states. This achievement opens the way for a vast number of investigations stemming from the symbiosis of strong laser physics, quantum optics, and quantum information science. Here, after an introduction to the fundamentals of these research directions, we report on the recent progress in the fully quantized description of intense laser--matter interaction and the methods that have been developed for the generation of non-classical light states and entangled states. Also, we discuss the future directions of non-classical light engineering using strong laser fields, and the potential applications in ultrafast and quantum information science., Comment: 60 pages, 20 figures. Comments are welcome

The development of sources delivering non-classical states of light is one of the main needs for applications of optical quantum information science. Here, we demonstrate the generation of non-classical states of light using strong-laser fields driving a solid-state system, by using the process of high-order harmonic generation, where an electron tunnels out of the parent site and, later on, recombines on it emitting high-order harmonic radiation, at the expense of affecting the driving laser field. Since in solid-state systems the recombination of the electron can be delocalized along the material, the final state of the electron determines how the electromagnetic field gets affected because of the laser-matter interaction, leading to the generation of entanglement between the electron and the field. These features can be enhanced by applying conditioning operations, i.e., quantum operations based on the measurement of high-harmonic radiation. We study non-classical features present in the final quantum optical state, and characterize the amount of entanglement between the light and the electrons in the solid. The work sets the foundation for the development of compact solid-state-based non-classical light sources using strong-field physics., Comment: We present a different formulation to that of the previous version, more in line with the approach followed in our previous works. 12 pages (8 main text + 4 Methods), 4 figures. Comments are welcome

Light-matter entanglement plays a fundamental role in many applications of quantum information science. Thus, finding processes where it can be observed is an important task. Here, we address this matter by theoretically investigating the entanglement between light and electrons generated in above-threshold ionization (ATI) process. The study is based on the back-action of the ATI process on the quantum optical state of the system, and its dependence on the kinetic energy and direction of the emitted photoelectrons. Taking into account the dynamics of the process, we demonstrate the creation of hybrid entangled states. The amount of entanglement has been studied in terms of the entropy of entanglement. Additionally, we use the Wigner function of the driving field mode to motivate the entanglement characterization when considering electrons propagating in opposite directions., Comment: 20 pages (13 main text + 7 supplementary material), 8 figures (6 main text + 2 supplementary material). Comments are welcome

Quantum information science and intense laser matter interaction are two apparently unrelated fields. Here, we introduce the notion of quantum information theory to intense laser driven processes by providing the quantum mechanical description of measurement protocols for high harmonic generation in atoms. This allows to conceive new protocols for quantum state engineering of light. We explicitly evaluate conditioning experiments on individual optical field modes, and provide the corresponding quantum operation for coherent states. The associated positive operator-valued measures are obtained, and give rise to the quantum theory of measurement for the generation of high dimensional entangled states, and coherent state superposition with controllable non-classical features on the attosecond timescale. This establish the use of intense laser driven processes as a novel quantum technology platform for quantum information processing., Comment: 6 pages

Recently, intensely driven laser-matter interactions have been used to connect the fields of strong laser field physics with quantum optics by generating non-classical states of light. Here, we make a further key step and show the potential of strong laser fields for generating controllable high-photon-number coherent-state superpositions. This has been achieved by using two of the most prominent strong-laser induced processes: high-harmonic generation and above-threshold ionization. We show how the obtained coherent-state superpositions change from an optical Schr\"odinger "cat" state to a "kitten" state by changing the atomic density in the laser-atom interaction region, and we demonstrate the generation of a 9-photon shifted optical "cat" state which, to our knowledge, is the highest photon number optical "cat" state experimentally reported. Our findings anticipate the development of new methods that naturally lead to the creation of high-photon-number controllable coherent-state superpositions, advancing investigations in quantum technology., Comment: Revised version submitted to Physical Review A

We present a theoretical demonstration on the generation of entangled coherent states and of coherent state superpositions, with photon numbers and frequencies orders of magnitude higher than those provided by the current technology. This is achieved by utilizing a quantum mechanical multimode description of the single- and two-color intense laser field driven process of high harmonic generation in atoms. It is found that all field modes involved in the high harmonic generation process are entangled, and upon performing a quantum operation, leads to the generation of high photon number optical cat states spanning from the far infrared to the extreme-ultraviolet spectral region. This provides direct insights into the quantum mechanical properties of the optical field in intense laser matter interaction. Finally, these states can be considered as a new resource for fundamental tests of quantum theory, quantum information processing or sensing with non-classical states of light., Comment: 5 pages (3 figures) + 4 pages supplement (2 figures)

Recently, using conditioning approaches on the high-harmonic generation process induced by intense laser-atom interactions, we have developed a new method for the generation of optical Schr\"odinger cat states (M. Lewenstein et al., arXiv:2008.10221 (2020)). These quantum optical states have been proven to be very manageable as, by modifying the conditions under which harmonics are generated, one can interplay between $\textit{kitten}$ and $\textit{genuine cat}$ states. Here, we demonstrate that this method can also be used for the development of new schemes towards the creation of optical Schr\"odinger cat states, consisting of the superposition of three distinct coherent states. Apart from the interest these kind of states have on their own, we additionally propose a scheme for using them towards the generation of large cat states involving the sum of two different coherent states. The quantum properties of the obtained superpositions aim to significantly increase the applicability of optical Schr\"odinger cat states for quantum technology and quantum information processing., Comment: 13 pages (12 main text + 1 appendix), 8 figures. This paper has been submitted to the JCEL Special Issue on Wigner Functions in Computational Electronics and Photonics. Comments are welcome

Quantum-optical spectrometry is a recently developed shot-to-shot photon correlation-based method, namely using a quantum spectrometer (QS), that has been used to reveal the quantum optical nature of intense laser-matter interactions and connect the research domains of quantum optics (QO) and strong laser-field physics (SLFP). The method provides the probability of absorbing photons from a driving laser field towards the generation of a strong laser-field interaction product, such as high-order harmonics. In this case, the harmonic spectrum is reflected in the photon number distribution of the infrared (IR) driving field after its interaction with the high harmonic generation medium. The method was implemented in non-relativistic interactions using high harmonics produced by the interaction of strong laser pulses with atoms and semiconductors. Very recently, it was used for the generation of non-classical light states in intense laser-atom interaction, building the basis for studies of quantum electrodynamics in strong laser-field physics and the development of a new class of non-classical light sources for applications in quantum technology. Here, after a brief introduction of the QS method, we will discuss how the QS can be applied in relativistic laser-plasma interactions and become the driving factor for initiating investigations on relativistic quantum electrodynamics.

The physics of intense laser-matter interactions is described by treating the light pulses classically, anticipating no need to access optical measurements beyond the classical limit. However, the quantum nature of the electromagnetic fields is always present. Here, we demonstrate that intense laser-atom interactions may lead to the generation of highly non-classical light states. This was achieved by using the process of high-harmonic generation in atoms, in which the photons of a driving laser pulse of infrared frequency are up-converted into photons of higher frequencies in the extreme ultraviolet spectral range. The quantum state of the fundamental mode after the interaction, when conditioned on the high-harmonic generation, is a so-called Schr\"odinger cat state, which corresponds to a superposition of two distinct coherent states: the initial state of the laser and the coherent state reduced in amplitude that results from the interaction with atoms. The results open the path for investigations towards the control of the non-classical states, exploiting conditioning approaches on physical processes relevant to high-harmonic generation., Comment: We dedicate this work to the memory of Roy J. Glauber, the inventor of coherent states