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arXiv:2409.15556

About the role of short and long trajectories on the quantum optical state after high-harmonic generation

Javier Rivera-Dean

Published Sep 23, 2024• 0 citations
arXivHTMLPDF

Abstract

High-harmonic generation (HHG) involves the up-conversion of a high-intensity driving field into its harmonic orders. This process is intrinsically non-classical, requiring from quantum mechanics for a complete explanation as, under suitable conditions, involves phenomena such as particle tunneling through a potential barrier. When exposed to a high-intensity, low-frequency laser field, bound electrons ionize via tunneling, accelerate under the driving field, and recombine with the parent ion, emitting high-harmonic radiation. However, electrons can follow two distinct pathways -- short and long trajectories -- during these steps. In this work, we evaluate the signatures left by these trajectories on the quantum optical state after HHG, and observe that they lead to entanglement between the driving field and the generated harmonics. By leveraging these correlations, we use harmonic generation to herald the creation of optical Schrödinger cat-like states in the driving field. Additionally, using an ab-initio approach, we examine how propagation effects, which spatially separate the harmonic contributions from short and long trajectories, influence the non-classical characteristics of the emitted light.

DOI
10.48550/arxiv.2409.15556

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High-harmonic generation (HHG) involves the up-conversion of a high-intensity driving field into its harmonic orders. This process is intrinsically non-classical, requiring from quantum mechanics for a complete explanation as, under suitable conditions, involves phenomena such as particle tunneling through a potential barrier. When exposed to a high-intensity, low-frequency laser field, bound electrons ionize via tunneling, accelerate under the driving field, and recombine with the parent ion, emitting high-harmonic radiation. However, electrons can follow two distinct pathways -- short and long trajectories -- during these steps. In this work, we evaluate the signatures left by these trajectories on the quantum optical state after HHG, and observe that they lead to entanglement between the driving field and the generated harmonics. By leveraging these correlations, we use harmonic generation to herald the creation of optical Schrödinger cat-like states in the driving field. Additionally, using an ab-initio approach, we examine how propagation effects, which spatially separate the harmonic contributions from short and long trajectories, influence the non-classical characteristics of the emitted light.
High-harmonic generation (HHG) involves the up-conversion of a high-intensity driving field into its harmonic orders. This process is intrinsically nonclassical, requiring from quantum mechanics for a complete explanation as, under suitable conditions, involves phenomena such as particle tunneling through a potential barrier. When exposed to a high-intensity, low-frequency laser field, bound electrons ionize via tunneling, accelerate under the driving field, and recombine with the parent ion, emitting high-harmonic radiation. However, electrons can follow two distinct pathways, short and long trajectories, during these steps. In this work, we evaluate the signatures left by these trajectories on the quantum-optical state after HHG, and observe that they lead to entanglement between the driving field and the generated harmonics. By leveraging these correlations, we use harmonic generation to herald the creation of optical Schr\"odinger-cat-like states in the driving field. Additionally, using an ab initio approach, we examine how propagation effects, which spatially separate the harmonic contributions from short and long trajectories, influence the nonclassical characteristics of the emitted light.
High-harmonic generation (HHG) provides a powerful platform for exploring the interaction between intense laser fields and matter on ultrafast timescales. Beyond its conventional description in terms of emitted radiation and electron dynamics, a fully quantum treatment of HHG reveals that the nonlinear light-matter interaction can modify the quantum state of the driving field itself, establishing correlations between the fundamental and harmonic modes. This perspective opens new possibilities for using HHG as a tool to engineer and control nonclassical states of light. In this work, we investigate the geometric properties of optical Schroedinger cat states generated in HHG via conditioning and post-selection. By analyzing the coherent-state displacements induced by different structured driving fields, we characterize the resulting phase-space evolution and the associated geometric phases of the generated quantum states. Particular emphasis is placed on how the polarization and spatial-mode structure of the driving light influence the geometry and evolution of displaced coherent states. Our results demonstrate that structured light offers a versatile means of controlling the geometric dynamics of HHG-generated cat states across the parameter space. Furthermore, we discuss the prospects for realizing genuinely topological optical cat states by exploiting more complex structured light configurations.
Recently, the intersection of quantum optics and attosecond physics has attracted growing interest. Here, we study the quantum optical signatures of high-harmonic generation (HHG) from solid-state material driven by squeezed coherent states. We find that squeezed coherent states can either enhance or suppress the HHG yields compared to that driven by coherent light, depending on the photon bunching or antibunching characteristics of driving light. The analysis on semiclassical trajectories indicates that the amplitude fluctuation alters the recombination energy, while the phase fluctuation affects the birth and recombination time of electron-hole pairs. By calculating the Husimi Q distributions of HHG, we demonstrate that the squeezing of the two conjugate quadratures of driving light asymmetrically influence the squeezing phase of harmonics. Surprisingly, we find that even under coherent driving, the harmonics still exhibit squeezing due to the highly nonlinear response of solid-state HHG, which was overlooked previously. Numerical calculations of the Mandel parameter are performed to characterize the photon statistics of emitted HHG arising from different microscopic mechanisms. The results indicate that intraband radiation can exhibit a super-Poissonian distribution, while interband emission exhibits sub-Poissonian distribution under coherent driving.
Recently we have demonstrated the quantum nature of light in strongly laser driven atoms, and we have shown how the process of high harmonic generation can be used for the creation of highly non-classical light states, in particular superpositions of two coherent states, i.e., optical Schr\{o}dinger states [M. Lewenstein et al., Generation of optical Schr\odinger cat states in intense laser-matter interactions, Nat. Phys., 17 1104-1108 (2021)]. Here, we investigate the quantum optical description of the interaction, incorporating many atoms and the back-action of the high harmonic generation or above threshold ionization processes on the coherent state of the driving laser field. We show how the conditioning on high harmonic generation and above threshold ionization can lead to non-classical light states, and we discuss the key parameters that can be used for controlling and characterizing the non-classical states obtained after high harmonic generation. The theoretical results have been experimentally confirmed by demonstrating how the obtained coherent state superposition changes from an optical to kitten state by changing the number of atoms participating in the high harmonic generation process. Additionally, we experimentally verify the applicability of the approach for generating high photon number non-classical light states. This is shown by demonstrating the generation of a 9--photon optical state which, to our knowledge, is the highest photon number optical 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.
High harmonic generation (HHG) is an extremely nonlinear effect generating coherent broadband radiation and pulse durations reaching attosecond timescales. Conventional models of HHG that treat the driving and emitted fields classically are usually very successful but inherently cannot capture the quantum-optical nature of the process. Although prior work considered quantum HHG, it remains unknown in what conditions the spectral and statistical properties of the radiation depart considerably from the known phenomenology of HHG. The discovery of such conditions could lead to novel sources of attosecond light having squeezing and entanglement. Here, we present a fully-quantum theory of extreme nonlinear optics, predicting quantum effects that alter both the spectrum and photon statistics of HHG, thus departing from all previous approaches. We predict the emission of shifted frequency combs and identify spectral features arising from the breakdown of the dipole approximation for the emission. Our results show that each frequency component of HHG can be bunched and squeezed and that each emitted photon is a superposition of all frequencies in the spectrum, i.e., each photon is a comb. Our general approach is applicable to a wide range of nonlinear optical processes, paving the way towards novel quantum phenomena in extreme nonlinear optics.
Effects of extreme nonlinear optics, such as high harmonic generation (HHG), are conventionally modeled with classical electromagnetic fields: both the driving and emitted fields are treated classically. We present the fully quantum electrodynamical theory of extreme nonlinear optics and use it to predict new quantum effects in HHG. The quantum description shows new effects in both the spectral and statistical properties of HHG. We also describe how the HHG process changes in the single-atom regime and discuss experiments that can test our various predictions. Revealing the quantum-optical nature of HHG could lead to novel sources of attosecond light having intrinsically quantum statistics, such as squeezing and entanglement.