Anomalous Autler-Townes Splitting in Resonant Multiphoton Ionization Driven by Bright Squeezed Vacuum

Abstract: 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 $g^{(p+1)}$ limit to the $g^{(p)}$ 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.

• The paper demonstrates that bright squeezed vacuum driving leads to ATI-order dependent Autler-Townes splitting that scales as √(2p) with the ATI order.
• It employs a fully quantum electrodynamical framework to reveal photon-number-resolved Rabi dynamics and strong electron-field entanglement.
• The findings have practical implications for quantum control and state engineering in strong-field ionization and attosecond science.

Anomalous Autler-Townes Splitting in Resonant Multiphoton Ionization Driven by Bright Squeezed Vacuum

Introduction

The study explores resonant multiphoton ionization of atoms in strong laser fields, explicitly driven by bright squeezed vacuum (BSV) light, utilizing a fully quantum electrodynamical (QED) framework where both matter and field degrees of freedom are quantized. Traditional strong-field physics predominantly employs a semiclassical approximation: matter is quantum, but the driving field is classical. Here, the analysis is extended into the quantum regime, emphasizing the effects of strong photon-number fluctuations and resulting electron-field entanglement produced by BSV light, which are fundamentally absent in coherent-state (classical) driving.

Quantum Versus Semiclassical Paradigms

Coherent driving fields in the strong-coupling regime yield standard Rabi oscillations and Autler-Townes (AT) splitting, where the splitting is independent of the above-threshold ionization (ATI) order—reflecting a single effective Rabi frequency set by the field amplitude. In contrast, BSV fields have vanishing mean electric field but exhibit macroscopic photon flux and pronounced photon-number super-Poissonian statistics. When employed as drivers, BSV fields lead to multi-frequency Rabi dynamics due to their broad photon-number distribution, causing rapid collapse of coherent oscillations and generating significant light-matter entanglement. This breakdown of the semiclassical description mandates a joint quantum treatment.

Photoelectron Spectrum and Anomalous AT Splitting

Fully quantum simulations show that, under coherent driving, the AT splitting in the photoelectron spectrum is consistent across all ATI orders. For BSV driving, however, the AT splitting increases monotonically with ATI order, following a $\sqrt{2p}$ law (where $p$ is the ATI order), in direct contradiction to the semiclassical fixed splitting scenario. This distinction arises from two nontrivial effects:

• Photon-number-resolved Rabi splitting: Each Fock sector $n$ couples differently, yielding a range of Rabi frequencies rather than a single one.
• ATI-selective photon sampling: Higher-order ATI processes preferentially sample higher photon-number sectors in the BSV distribution.

Explicitly, for a $p$th-order ATI channel, the dominant AT splitting under BSV is:

$$\Delta\varepsilon_{\text{BSV}}^{(p)} \propto \sqrt{2p\bar n},$$

with $\bar n$ the mean photon number. This is in marked contrast to the coherent case:

$$\Delta\varepsilon_{\text{coh}} \propto \sqrt{\bar n},$$

yielding a splitting ratio scaling as $\sqrt{2p}$, in excellent agreement with extended Jaynes-Cummings modeling and full QED numerics (2606.07324).

Light-Matter Entanglement and Multiphoton Ionization Yields

The QED framework highlights that with strong BSV driving, significant electron-field entanglement develops during the interaction, as quantified via the von Neumann entropy. This entanglement is spectroscopically observable in joint electron-photon number coincidence distributions, where each ATI channel reveals a double-branch (split) structure wide in photon number.

Ionization yield analysis further reveals a crossover in the BSV enhancement factor as the field intensity rises and Rabi oscillations set in. At low intensities, where direct $(p+1)$-photon ionization dominates, yields scale with the $(p+1)$th-order field correlation function $p$0 of the BSV. As Rabi oscillations build up (intensity increases and the process becomes more resonant), the dominant scaling reduces to $p$1. Thus, the BSV enhancement is not static but dynamically evolves with the interaction, reflecting the underlying transition pathways.

Implications and Outlook

The results establish that strong-field strong-coupling regimes driven by nonclassical light cannot be captured within the semiclassical paradigm. The $p$2 scaling of AT splitting constitutes an unambiguous spectroscopic signature of field-induced electron-photon entanglement and giant photon-number fluctuations—observable with modern photoelectron spectroscopy.

Practically, these findings suggest new modalities for quantum control of atomic and molecular states via engineering of the quantum statistical properties of driving fields. BSV sources are now available with femtosecond time resolution, enabling experimental exploration of this regime. Theoretically, this work extends the interface between quantum optics and strong-field physics, underscoring the necessity of including quantum features of light even in the high-intensity limit. Extensions to multi-electron systems, high-harmonic generation, and macroscopic entanglement synthesis in solids are direct future directions—with ramifications for robust quantum state engineering and quantum information processing.

Conclusion

This work demonstrates, using ab initio quantum field theory simulations, that resonant multiphoton ionization driven by bright squeezed vacuum manifests fundamentally different strong-field phenomena from those induced by coherent light. The observed ATI-order dependent, anomalous AT splitting, and its characteristic scaling with the number of absorbed photons, exposes quantum light-matter correlation effects mediated by the statistical structure of the nonclassical driving field. These insights indicate previously unexplored quantum regimes and mechanisms for manipulating strong-field dynamics, with significant consequences for attosecond science, quantum metrology, and quantum technologies.