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Physical Review Research

Effect of photon quantum statistics on electrons in above-threshold ionization

Zijian Lyu, Feng-Xiao Sun, Yiqi Fang, Qiongyi He, Yunquan Liu

Published Mar 18, 2025• 17 citations
Publisher

Abstract

Strong field physics and quantum optics, two prosperous fields in modern science, have recently been connected with each other. Here, we study the quantum effect of bright squeezed vacuum light and thermal light on above-threshold ionization. With quantum strong-field approximation theory, we reveal a decoherence phenomenon caused by the statistics of photons, in which above-threshold ionization could be degenerated into a classical-like picture under the effect of quantum light. This represents a direct transition from the wavelike nature to the particlelike behavior of photoelectrons. We also reveal the ionization enhancement effect of the bunched light in photoionization from the perspective of autocorrelation function g ( n ) . The number distributions of electrons ionized by different quantum light fields are studied, and it is shown that the photon number distribution can be mapped onto the photoelectron number distribution. This finding enables the production of bunched electrons with strong-field ionization with quantum light.

DOI
10.1103/physrevresearch.7.l012072

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Strong field physics and quantum optics, two prosperous fields in modern science, have recently been connected with each other. Here, we study the quantum effect of bright squeezed vacuum light and thermal light on above-threshold ionization. With quantum strong-field approximation theory, we reveal a decoherence phenomenon caused by the statistics of photons, in which above-threshold ionization could be degenerated into a classical-like picture under the effect of quantum light. This represents a direct transition from the wavelike nature to the particlelike behavior of photoelectrons. We also reveal the ionization enhancement effect of the bunched light in photoionization from the perspective of autocorrelation function g ( n ) . The number distributions of electrons ionized by different quantum light fields are studied, and it is shown that the photon number distribution can be mapped onto the photoelectron number distribution. This finding enables the production of bunched electrons with strong-field ionization with quantum light.
Squeezed coherent quantum light is described by the complex squeeze parameter ζ = s e i ϑ and the coherent-state displacement parameter β = | β | e i ϕ β . Our study of strong-field ionization [D. Habibović and D. B. Milošević, ], which focused on bright squeezed vacuum quantum light with β = 0 and s ≫ 1 , is extended to ionization by squeezed coherent light. It is shown that the amplitudes s and | β | strongly influence the ionization process, whereas phases ϑ and ϕ β play a less significant role. The present work provides a unified treatment of coherent, squeezed vacuum, and squeezed coherent light within a single theoretical framework. The quantum nature of the driving field is incorporated by averaging the strong-field ionization probability over the Husimi-Kano phase-space distribution. Using neon as a representative target, we analyze how the parameters characterizing squeezed coherent light modify photoelectron spectra and intensity-dependent enhancements. We show that nonclassical photon statistics can lead to a pronounced steepening of the rescattering plateau and, at low mean intensities, to an effective suppression of the nominal high-energy cutoff. These effects originate from the reduced weight of high-intensity field components inherent to squeezed states and have no analog in strong-field ionization driven by a coherent light. Our results highlight the potential for quantum-statistical control of strong-field ionization and provide a foundation for exploring laser-matter interactions driven by quantum light.
Bright squeezed vacuum (BSV) light has a vanishing mean optical electric field yet can strongly enhance strong-field nonlinear responses beyond the conventional semiclassical paradigm. Here we examine this scenario in the light-matter strong-coupling regime by investigating resonant multiphoton ionization of atoms driven by BSV, using a fully quantum treatment of both the electron and the field. Our results show that the photoelectron energy spectrum exhibits an anomalous Autler-Townes splitting whose magnitude grows with the Above-threshold-ionization (ATI) order, rather than remaining essentially ATI-order independent as in the case of coherent driving. This behavior reflects a general scaling with the number of absorbed photons and originates from the broad photon-number fluctuations of the driving field together with the resulting electron-field entanglement. We further show that the BSV-induced enhancement of ionization yields evolves with intensity, crossing over from the g(p+1)g^{(p+1)}g(p+1) limit to the g(p)g^{(p)}g(p) limit as Rabi oscillations become established. These results identify a quantum regime of strong-field ionization governed by the interplay of photon statistics, nonlinear transitions, strong coupling, and nonseparable light-matter dynamics.
We demonstrate that quantum light statistics can be used to control strong-field ionization at the tunneling step. Using a bichromatic linearly polarized field composed of a strong coherent driver and a weak bright squeezed vacuum (BSV), we show through simulation that photoelectron momentum distributions (PMDs) exhibit asymmetries that exceed those obtained with classical fields of comparable intensity by orders of magnitude. This enhancement is uniquely linked to the nonclassical statistics of the BSV field. A semiclassical analysis based on the strong-field approximation (SFA) reveals that the effect originates from fluctuations in the instantaneous field amplitude, which strongly modify the tunneling ionization probability while leaving the electron's continuum dynamics essentially unchanged. This selective control enables reconstruction of ionization pathways and provides a robust route to extract sub-cycle dynamics from strong-field observables.
Strong-field ionization is the cornerstone of attosecond physics, which has been extensively studied under coherent-state driving. Recently, the interface between attosecond physics and quantum optics has emerged as a new frontier. Yet, owing to experimental limitations, the role of the quantum nature of light in atomic strong-field ionization has remained unexplored. Here, we demonstrate strong-field ionization of xenon atoms driven by bright squeezed vacuum (BSV) with average pulse energy up to 10 \textmu J. We show that, as a nonclassical state with zero mean field and strong intensity fluctuations, BSV selectively enhances the spider-like holographic structures in the photoelectron momentum distributions. Using a quantum-light-corrected quantum-trajectory Monte Carlo (q-QTMC) model, we attribute this effect to the intrinsic coherence of trajectory pairs emitted within the same subcycle field fluctuation. These dynamically correlated paths exhibit enhanced phase stability and remain robust against dephasing, whereas asynchronous paths are filtered out by field noise. Our results reveal a quantum-fluctuation-induced mechanism for coherence protection in strong-field processes, positioning BSV as an effective coherence filter and establishing a new regime of quantum-enabled noise-resilient ultrafast dynamics.
Above-threshold ionization (ATI) is a strong-field-driven process where electrons absorb more photons than required for ionization. While ATI dynamics and outputs are well-understood when driven by classical, perfectly coherent light, the recent development of nonclassical light sources for strong-field phenomena has spurred interest in their effect on the involved electron dynamics. In this work, we present a microscopic quantum optical theory describing ATI under the influence of strong squeezed light. We observe that squeezed light significantly enhances the coupling between light and matter, making their mutual backaction more important than under classical driving. This backaction profoundly impacts the electronic ionization times, as well as the nonclassical properties of the joint electron-light state. This results in pronounced entanglement features, both immediately after ionization and at later times. These entanglement features are reflected in the properties of the quantum optical state of the driving field, revealing notable non-Gaussian features that depend on both the amount of squeezing and the number of ionization events occurring during the interaction.
Strong-field ionization provides a fundamental route for probing nonlinear electron dynamics on ultrafast timescales, but it has been explored almost exclusively with classical coherent driving fields. Intense quantum light sources, particularly bright squeezed vacuum (BSV), now make it possible to ask how macroscopic photon-number fluctuations affect nonperturbative electron emission. Here, we address this question by performing shot-resolved BSV-photoelectron coincidence measurements in strong-field ionization of xenon atoms, with simultaneous access to the single-shot driving pulse intensity and the energy- and momentum-resolved photoelectron response. By calibrating the intensity-dependent ionization probability with a pulse-integrated Ammosov-Delone-Krainov response, we reconstruct the single-pulse ionization-yield distribution and quantify its fluctuations in electron momentum space. We find that intensity-conditioned BSV-driven spectra recover coherent-field-like cutoff scaling, while the reconstructed yield fluctuations increase toward higher electron energies and momenta, showing that high-energy electrons preferentially sample rare high-intensity BSV shots. Beyond ensemble-averaged spectra or photoelectron-number statistics, this approach resolves the momentum- and energy-dependent transfer of quantum-light fluctuations into atomic ionization yields. These results establish yield fluctuations as observables for strong-field quantum optics and benchmarks for theories beyond the classical-field approximation.