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arXiv:2403.15337 · Nature Physics

High-harmonic generation by a bright squeezed vacuum

Andrei Rasputnyi, Zhaopin Chen, Michael Birk, Oren Cohen, Ido E. Kaminer, Michael B. Kruger, Denis V. Seletskiy, Maria V. Chekhova, Francesco Tani

Published Oct 2, 2024• 84 citations
arXivHTMLPDF

Abstract

Abstract High-harmonic generation has been driving the development of attosecond science and sources. More recently, high-harmonic generation in solids has been adopted by other communities as a method to study material properties. However, so far high-harmonic generation has only been driven by classical light, despite theoretical proposals to do so with quantum states of light. Here we observe non-perturbative high-harmonic generation in solids driven by a macroscopic quantum state of light, a bright squeezed vacuum, which we generate in a single spatiotemporal mode. The process driven by a bright squeezed vacuum is considerably more efficient in the generation of high harmonics than classical light of the same mean intensity. Due to its broad photon-number distribution, covering states from 0 to 2 × 10 13 photons per pulse, and strong subcycle electric field fluctuations, a bright squeezed vacuum gives access to free carrier dynamics within a much broader range of peak intensities than accessible with classical light.

DOI
10.1038/s41567-024-02659-x

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Abstract High-harmonic generation has been driving the development of attosecond science and sources. More recently, high-harmonic generation in solids has been adopted by other communities as a method to study material properties. However, so far high-harmonic generation has only been driven by classical light, despite theoretical proposals to do so with quantum states of light. Here we observe non-perturbative high-harmonic generation in solids driven by a macroscopic quantum state of light, a bright squeezed vacuum, which we generate in a single spatiotemporal mode. The process driven by a bright squeezed vacuum is considerably more efficient in the generation of high harmonics than classical light of the same mean intensity. Due to its broad photon-number distribution, covering states from 0 to 2 × 10 13 photons per pulse, and strong subcycle electric field fluctuations, a bright squeezed vacuum gives access to free carrier dynamics within a much broader range of peak intensities than accessible with classical light.
Abstract Attosecond quantum light, formed by the superposition of high-order harmonics driven by intense quantum light, opens new routes to probe quantum-mechanical correlations in matter. In this study, we have investigated the macroscopic propagation effects of quantum high-order harmonics generated by the combination of strong coherent and weak bright squeezed vacuum (BSV) lasers interacting with atomic gas. Our results reveal that the pressure-dependent intensity of harmonics arising from absorbing or emitting BSV photons differs from that of harmonics generated using only strong coherent pulses. Macroscopic propagation simulations indicate that the action phase of harmonics is perturbed by the weak BSV pulses. This perturbation modulates the phase mismatch of sub-cycle attosecond bursts and affects their quantum properties when the gas pressure varies. The ability to generate bright quantum high-order harmonics lays a foundation for the establishment and application of attosecond quantum spectroscopy.
High-harmonic generation (HHG) driven by intense quantum light has recently emerged as a new frontier in strong-field physics. Yet, the mechanism underlying HHG with nonclassical fields such as bright squeezed vacuum (BSV) light—characterized by a vanishing mean electric field—remains elusive. In this work, we develop a fully quantum theory for HHG under arbitrary quantum driving fields. We show that the fluctuation component of the dipole correlation operator plays a central role in HHG with quantum light and is essential for BSV-driven HHG. Furthermore, our framework reveals the photon statistics distribution within individual harmonics and across different harmonics, demonstrating that the statistics inherit the statistical properties of the driving field. This theory overcomes key limitations of existing approaches and uncovers new quantum features of HHG in the presence of nonclassical light.
Attosecond quantum light, formed by the superposition of high-order harmonics driven by intense quantum light, opens new routes to probe quantum-mechanical correlations in matter. In this study, we have investigated the macroscopic propagation effects of quantum high-order harmonics generated by the combination of strong coherent and weak bright squeezed vacuum (BSV) lasers interacting with atomic gas. Our results reveal that the pressure-dependent intensity of harmonics arising from absorbing or emitting BSV photons differs from that of harmonics generated using only strong coherent pulses. Macroscopic propagation simulations indicate that the action phase of harmonics is perturbed by the weak BSV pulses. This perturbation modulates the phase mismatch of sub-cycle attosecond bursts and affects their quantum properties when the gas pressure varies. The ability to generate bright quantum high-order harmonics lays a foundation for the establishment and application of attosecond quantum spectroscopy.
High harmonic generation (HHG) is a highly nonlinear optical process in which radiation from a strong driving field is up-converted into its high-order harmonics. In atomic systems, this nonlinearity manifests itself through the intensity scaling of the emitted harmonics with the driving field strength. Despite the highly nonlinear nature of HHG, when the driving field is prepared in a classical Gaussian state and atomic depletion remains negligible, the quantum statistical properties of the generated harmonics retains classical Gaussian quantum statistics. Driving HHG with bright squeezed vacuum (BSV) light challenges this paradigm, as its enhanced field fluctuations can modify the statistical properties of the generated harmonics. In this work, we investigate the conditions under which BSV-driven HHG gives rise to non-classical Gaussian states, and identify the regimes where this Gaussian description breaks down. For bichromatic driving by a strong coherent field at frequency ωωω and a perturbative BSV field at 2ω2ω2ω, the even-harmonic response is approximately linear in the BSV quadrature, leading to non-classical multimode Gaussian entanglement in the harmonic field. We show that this state can be described as a distributed collective squeezed mode over the even-harmonic manifold, and characterize its covariance matrix, entanglement structure, and quantum teleportation fidelity as an operational benchmark. Our results highlight the potential of non-classically driven HHG as a platform for engineering Gaussian and non-Gaussian states of light in the extreme ultraviolet regime.
The extreme light-matter interaction has brought unique tools for the subfemtosecond control of electron dynamics [1] and ultra-fast spectroscopy [2]. Until recently, the strong-field regime was accessible only with coherent states of light, which can be well described by classical electric fields when many photons are present (Fig. 1a). With the use of intense states of non-classical light, this situation has changed. New opportunities emerge with bright squeezed vacuum (BSV), which can be generated from optical parametric amplification of quantum vacuum fluctuations. Unlike classical light, BSV is a quantum superposition of coherent states with an amplitudes spanning a range from zero to very high values, up to ~1 TW/cm2[3]. BSV has a zero mean electric field and the variance of the electric field oscillates at the double carrier frequency (Fig. 1a). How such a non-classical electric field can affect the dynamics of photoemitted electrons was theoretically demonstrated recently [4]. Furthermore, the photon-number distribution of BSV has a very long tail in contrast to coherent light. These photon-number distributions can be imprinted onto the photon statistics of optical harmonics [3] and the statistics of electrons [5].