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Physical Review A

Quantum-optical analysis of high-order harmonic generation in H 2 + molecules

Javier Rivera-Dean, Philipp Stammer, Andrew Maxwell, Theocharis Lamprou, Emilio Pisanty, P. Tzallas, Maciej Lewenstein, Marcelo F. Ciappina

Published Mar 8, 2024• 15 citations
Publisher

Abstract

We present a comprehensive theoretical investigation of high-order harmonic generation in ${\mathrm{H}}_{2}{}^{+}$ molecules within a quantum-optical framework. Our study focuses on characterizing various quantum-optical and quantum-information measures stemming from the correlations established between light and matter. We demonstrate the emergence of entanglement between electron and light states after the laser-matter interaction. We also identify the possibility of obtaining nonclassical states of light in targeted frequency modes by conditioning on specific electronic quantum states, which turn out to be crucial in the generation of highly nonclassical entangled states between distinct sets of harmonic modes. Our findings open up avenues for studying strong-laser-field-driven interactions in molecular systems under a fully quantum-mechanical framework.

DOI
10.1103/physreva.109.033706

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Quantum optical analysis of high-order harmonic generation in H2+_2^+2+​ molecular ions
We present a comprehensive theoretical investigation of high-order harmonic generation in H2+_2^+2+​ molecular ions within a quantum optical framework. Our study focuses on characterizing various quantum optical and quantum information measures, highlighting the versatility of HHG in two-center molecules towards quantum technology applications. We demonstrate the emergence of entanglement between electron and light states after the laser-matter interaction. We also identify the possibility of obtaining non-classical states of light in targeted frequency modes by conditioning on specific electronic quantum states, which turn out to be crucial in the generation of highly non-classical entangled states between distinct sets of harmonic modes. Our findings open up avenues for studying strong-laser field-driven interactions in molecular systems, and suggest their applicability to quantum technology applications.
We present an analytical framework for the emergence of nonclassical radiation in strongly laser-driven quantum systems, with a focus on high-order harmonic generation (HHG). Starting from a Pauli-Fierz description, we employ a parametric factorization of the coupled light-matter wavefunction that reduces the dynamics to coupled equations for a field-driven electronic state and a quantized light mode. Within this framework, we identify a simple and predictive mechanism for nonclassicality: it originates from the nonlinear dependence of the electronic dipole response on the light-mode coordinate. An approximately constant dipole yields coherent radiation, a linear dependence produces squeezing, and higher-order nonlinearities give rise to Wigner-function negativity. We illustrate this mechanism for atomic and molecular model systems and analyze its scaling in multi-emitter configurations, indicating routes toward high-photon-number nonclassical radiation in HHG. Our results provide a transparent connection between strong-field dynamics and quantum-optical properties of emitted light, offering a basis for engineering nonclassical states in intense laser-matter interactions.
High-order harmonic generation (HHG) is a significant nonlinear phenomenon triggered by the interaction of intense laser fields with matter. As a high-quality coherent light source, it has found extensive applications in areas such as attosecond pulse generation and ultrafast spectroscopy. Recent studies have revealed the prevalent existence of nonclassical effects in high-harmonic radiation, including nonclassical photon statistics, intermodal correlations, and entanglement. It holds broad development prospects in directions including the generation of nonclassical states with high photon numbers, precise control of entanglement in solid-state systems, and integration with cavity quantum electrodynamics. This review systematically summarizes the research progress concerning the nonclassical effects in HHG. It begins with an overview of the semiclassical model and strong-field quantum theory, clarifying the differences in the quantum properties of harmonic fields when driven by coherent states versus nonclassical states. Subsequently, it focuses on various physical schemes for generating nonclassical optical field states, such as optical cat states and squeezed states, via this process. Research on strong-field HHG not only deepens our understanding of the fundamental nature of intense laser physics but also opens new avenues for the generation and application of quantum light sources in the extreme ultraviolet to X-ray spectral regions.
High-harmonic generation (HHG) has recently emerged as a promising method for generating nonclassical states of light with frequencies spanning from the infrared up to the extreme ultraviolet regime. In this work, we theoretically investigate the generation of squeezed states of light through HHG processes in atomic systems that were initially driven to their first excited state. Our study reveals significant single-mode squeezing in both the driving field and low-order harmonic modes. Additionally, we characterize two-mode squeezing features in the generated states, both between fundamental and harmonic modes, and among the harmonic modes themselves. Using these correlations, we demonstrate the generation of optical Schr\"odinger kitten states through heralding measurements, specifically via photon subtraction in one of the modes influenced by two-mode squeezing.
The generation of higher-order harmonic radiation originating from the interaction of intense laser pulses with matter is typically described semiclassically: While the electronic structure and dynamics of matter is described quantum mechanically, the intense light field is described classically---and accordingly the generated harmonic radiation. However, pioneering experiments on quantum optical properties of high-order harmonic generation (HHG) in atomic gases from the group of P. Tzallas [I. Gonoskov et al., Sci. Rep. 6, 32821 (2016) and N. Tsatrafyllis et al., Nat. Commun. 8, 15170 (2017)], and theoretical investigations from the group of M. Lewenstein [M. Lewenstein et al., Nat. Phys. 17, 1104 (2021) and P. Stammer et al., Phys. Rev. Lett. 128, 123603 (2022)] have impressively demonstrated that light's quantum properties are observable in the strong-field realm. In this paper, we develop a quantum optical description of HHG in a bulk semiconductor originating from the nonlinear Bloch current. This mechanism of HHG, known as the intraband current, constitutes the major contribution to the emission spectrum for harmonic with energies of quanta roughly below the bandgap. Under certain approximations, employing a quantum description of both light and matter, we obtain analytical solutions, which allow us to analyze the classical and quantum optical characteristics of the fundamental mode of light and the harmonic modes. We find intricate but sufficiently mild modifications of the photon statistics of the fundamental mode and coherent displacements depending on the parameters of the driving laser field. Similar to high-harmonic generation in atoms, the fundamental and emitted harmonic field modes are entangled. Moreover, our analytical model predicts parameter ranges where these quantum optical properties will be most pronounced, allowing protocols for quantum information processing with high photon numbers over a large range of frequencies.