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Annalen der Physik

High‐Order Above‐Threshold Ionization by Thermal Light

Dejan B. Milošević, Wilhelm Becker

Published Mar 1, 2026• 3 citations
Publisher

Abstract

ABSTRACT Strong‐field ionization by thermal light is studied. Even though thermal light can be considered as completely classical stochastic light, it can also be treated as quantum light in the sense that it can be represented by a superposition of coherent states, similarly as has been done for the bright squeezed vacuum light, for example. Such a distribution over coherent states contains components with an intensity much higher than the average intensity of the thermal light. This increases the ionization probability by many orders of magnitude. For low intensities, in the multiphoton regime, the enhancement is by the factor of , with the multiphoton order of the process. This result is in agreement with an old experiment [ Phys. Rev. Lett . 32 (1974): 265] in which a similar enhancement factor appears if a multimode laser pulse is used instead of a single‐mode pulse. It is also shown that the plateau length in high‐order above‐threshold ionization by thermal light is extended by an order of magnitude in comparison with that of coherent laser light with the same average intensity.

DOI
10.1002/andp.202500620

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ABSTRACT Strong‐field ionization by thermal light is studied. Even though thermal light can be considered as completely classical stochastic light, it can also be treated as quantum light in the sense that it can be represented by a superposition of coherent states, similarly as has been done for the bright squeezed vacuum light, for example. Such a distribution over coherent states contains components with an intensity much higher than the average intensity of the thermal light. This increases the ionization probability by many orders of magnitude. For low intensities, in the multiphoton regime, the enhancement is by the factor of , with the multiphoton order of the process. This result is in agreement with an old experiment [ Phys. Rev. Lett . 32 (1974): 265] in which a similar enhancement factor appears if a multimode laser pulse is used instead of a single‐mode pulse. It is also shown that the plateau length in high‐order above‐threshold ionization by thermal light is extended by an order of magnitude in comparison with that of coherent laser light with the same average intensity.
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.
We study strong-field ionization by quantum lights with emphasis on high-order above-threshold ionization and the intensity-dependent enhancements in the photoelectron spectra. We find that the length of the plateau in the photoelectron energy spectrum generated by such quantum lights can be extended by an order of magnitude in comparison with that generated by the classical coherent laser light and that within this plateau resonantly enhanced groups of sharp peaks appear at energies which are integer multiple of the photon energy. We relate the observed intensity-dependent enhancements to the channel closing effect. Our results are particularly interesting in the context of the recent interplay and merging of quantum optics with strong-field physics and attoscience.
We investigate high-order above-threshold ionization (HATI) from intense quantum light-atom interaction, by numerically solving the fully quantum time-dependent Schr\"odinger equation based on quantum electrodynamics theory. Our simulations show that, in comparison with coherent-state (classical) light, the HATI spectra from intense quantum lights may have a higher cutoff energy and, moreover, for a given ponderomotive energy of the laser field, the cutoff energy is dependent on the laser wavelength and the ionization potential of the atom. The influence of quantum light on the HATI is revealed by examining the interplay between a quasiprobability distribution of the electric field of the quantum light and the Ammosov-Delone-Krainov ionization rate of the atom. Furthermore, analytical formulas of the cutoff energy of the HATI spectra for different quantum lights are derived.
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.
Quantum theory of high-order above-threshold ionization (HATI) of atoms, prepared in a coherent superposition of bound states, by a strong laser field is formulated. Numerical results are obtained using the solutions of the time-dependent Schr\"odinger equation and the improved strong-field approximation. As an example, coherent superposition of the excited 2s2s2s and 2p2p2p states of the He atom is used. Applying a two-level model, it is shown how the relative amplitude and phase of the states in this coherent superposition can be controlled with a weak resonant laser pulse. Numerical results presented for HATI by a strong nonresonant probe laser pulse confirm that the photoelectron spectra and the momentum distributions strongly depend on the relative phase of the states in the prepared coherent superposition. For the case of HATI by a strong resonant laser pulse, we modify our strong-field-approximation theory by applying the two-level model to describe the time evolution of the atomic bound state before the instant of ionization. Contrary to the HATI from a single state by a long laser pulse, the corresponding photoelectron spectra of HATI from the coherent superposition of states depend on the carrier-envelope phase of the resonant ionizing pulse. Therefore, the strong-field ionization from a coherent superposition of states by a resonant laser pulse can be used to determine the carrier-envelope phase for long pulses for which the standard methods such as stereo--above-threshold ionization technique fail. The results strongly depend on the relative amplitude and phase of states in the coherent superposition of states, which can be controlled with a weak resonant laser pulse.
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.