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arXiv:2406.10443 · Physical Review A

Attosecond pulse synthesis from high-order harmonic generation in intense squeezed light

ShiJun Wang, XuanYang Lai, XiaoJun Liu

Published Jul 2, 2025• 6 citations
arXivHTMLPDF

Abstract

High-order harmonic generation (HHG) provides a broad spectral bandwidth for synthesizing attosecond pulses. However, in the current HHG schemes, only part of the harmonics can be phase-locked, which limits the ability to achieve shorter attosecond pulses. Here, we study attosecond pulse synthesis from HHG of an atom driven by an intense quantum light, i.e., squeezed light. It is interestingly found that the harmonics in the whole spectrum can be phase-locked and, by using these harmonics, the width of the synthesized attosecond pulse is greatly reduced. By developing strong-field approximation theory in squeezed light, the physics of the phase-locked harmonic generation throughout the HHG spectrum is revealed and is found to be independent of the target system. Furthermore, we uncover the dependence of the synthesized attosecond pulse width on the squeezing parameter of the squeezed light. Our findings provide a robust tool for obtaining phase-locked harmonics throughout the HHG spectrum for synthesizing short attosecond pulses.

DOI
10.1103/4x11-phs2

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High-order harmonic generation (HHG) provides a broad spectral bandwidth for synthesizing attosecond pulses. However, in the current HHG schemes, only part of the harmonics can be phase-locked, which limits the ability to achieve shorter attosecond pulses. Here, we study attosecond pulse synthesis from HHG of an atom driven by an intense quantum light, i.e., squeezed light. It is interestingly found that the harmonics in the whole spectrum can be phase-locked and, by using these harmonics, the width of the synthesized attosecond pulse is greatly reduced. By developing strong-field approximation theory in squeezed light, the physics of the phase-locked harmonic generation throughout the HHG spectrum is revealed and is found to be independent of the target system. Furthermore, we uncover the dependence of the synthesized attosecond pulse width on the squeezing parameter of the squeezed light. Our findings provide a robust tool for obtaining phase-locked harmonics throughout the HHG spectrum for synthesizing short attosecond pulses.
For decades, most research of high harmonic generation (HHG) considered matter as quantum but light as classical. Recently, HHG driven by quantum states of light such as bright squeezed vacuum was predicted to reach beyond the classical HHG cutoff. Moreover, in squeezed coherent illumination, it was shown that the underlying dynamics are significantly modified by the photon statistics effective force. Here we show that HHG driven by quantum light results in quantum high harmonics. We derive a formula for the quantum state of the high harmonics, when driven by arbitrary quantum light states, and then explore specific cases of experimental relevance. Specifically, for a moderately squeezed pump, HHG driven by squeezed coherent light results in squeezed high harmonics. Harmonic squeezing is optimized by syncing ionization times with the pump's squeezing phase. Beyond this regime, as pump squeezing is increased, the harmonics initially acquire squeezed thermal photon statistics, and then occupy an intricate quantum state which strongly depends on the semiclassical nonlinear response function of the interacting system. Our results pave the way for generation of squeezed extreme-ultraviolet ultrashort pulses, and more generally, quantum frequency conversion into previously inaccessible spectral ranges, which may enable ultrasensitive attosecond metrology. Published by the American Physical Society 2024
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.
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 conventionally understood to produce attosecond pulse trains only when the emitted harmonics are mutually phase-locked, in accordance with the classical theory of mode-locking. Such locking is necessary for pulse synthesis when the harmonic field is in a separable multimode quantum state. This requirement, however, can be circumvented entirely for harmonic combs exhibiting intermodal entanglement. We introduce a novel family of multimode quantum states, termed attoquants: states associated with highly structured pulse trains that are inherently insensitive to relative phases. As a concrete example, we analyse the coherent permanent state, constructed as a completely symmetric superposition of products of coherent states over all permutations of a fixed parameter set. It is shown analytically that its electric-field expectation value is a locked Fourier superposition of the driving-field harmonics, yielding an attosecond pulse train without requiring mode-locking. We further calculate the photon statistics, the Wigner function, and the logarithmic negativity of this state, confirming it to be genuinely nonclassical and entangled. Finally, we offer a phenomenological interpretation for the generation of such entangled states during HHG, as a consequence of multi-atom effects. Since the coherence volume of the driving field greatly exceeds that of its harmonics, a collectively-driven cluster of atoms can radiate the individual harmonics as spatially resolved, but fundamentally indistinguishable sources. This can generate the permutation-symmetric entanglement structure of an attoquant.
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.
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.