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 2024For 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

arXiv:2311.11257Physical Review ResearchJul 17, 202443 citations

Resonant high-order harmonic generation driven by quantum light

Zhi-Hong Jiao, Qianqian Li, Jin-Xu Du +2 more

Abstract We theoretically demonstrate ultra-wideband resonant high-order harmonic generation (HHG) driven by quantum light. The resonant HHG spectra generated by the bright squeezed vacuum (BSV) state exhibit nearly twice the bandwidth compared to typical non-resonant HHG driven by BSV, enabling the cutoff to approach approximately 400 eV. The underlying mechanism of this significant broadening is analyzed by examining the yield of fluctuation amplitude-dependent coherent harmonics. We find that this broadening results from the weak sensitivity of the coherent harmonic yield to the fluctuation amplitude of BSV. Furthermore, by analyzing the dependence of the cutoff energy of resonant HHG on the BSV intensity and wavelength, we propose a revised formula for estimating the cutoff energy of BSV-driven resonant HHG.Abstract We theoretically demonstrate ultra-wideband resonant high-order harmonic generation (HHG) driven by quantum light. The resonant HHG spectra generated by the bright squeezed vacuum (BSV) state exhibit nearly twice the bandwidth compared to typical non-resonant HHG driven by BSV, enabling the cutoff to approach approximately 400 eV. The underlying mechanism of this significant broadening is analyzed by examining the yield of fluctuation amplitude-dependent coherent harmonics. We find that this broadening results from the weak sensitivity of the coherent harmonic yield to the fluctuation amplitude of BSV. Furthermore, by analyzing the dependence of the cutoff energy of resonant HHG on the BSV intensity and wavelength, we propose a revised formula for estimating the cutoff energy of BSV-driven resonant HHG.

Chinese Physics BOct 19, 20260 citations

Photon bunching in high-harmonic emission controlled by quantum light

Samuel Lemieux

Optical and Quantum Sensing and Precision Metrology IIMar 19, 20250 citations

Emergence of Gaussian entanglement and non-Gaussianity in high-harmonic generation driven by bright squeezed light

J. Rivera-Dean, M. Even-Tzur, M. F. Ciappina +3 more

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 $ω$ and a perturbative BSV field at $2ω$ , 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.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 $ω$ and a perturbative BSV field at $2ω$, 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.

quant-pharXiv:2606.22714Journal of Physics B Atomic Molecular and Optical PhysicsJun 23, 20260 citations

ω

and a perturbative BSV field at

2ω

, 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.