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The Journal of Physical Chemistry Letters

Controlling Autler–Townes Splitting of the K 2 Molecule with Quantum Light

Zhaopeng Sun, Xiaoxiao Long, Yunquan Liu

Published May 29, 2026• 1 citation
Publisher

Abstract

Autler–Townes splitting (ATS) is a hallmark phenomenon of strong light–matter interaction, in which the resonant photoelectron energy spectrum splits into distinct peaks when driven by a strong electromagnetic field. We investigate the Autler–Townes Splitting (ATS) in K 2 molecules with quantum light. The triple splitting structures originating from three-photon ionization are analyzed under different types of driving fields, including bright squeezed vacuum (BSV), phase-squeezed coherent (PSC) light and amplitude-squeezed coherent (ASC) light by numerically solving the time-dependent Schrödinger equation. Compared with the results with the coherent-state (classical) light drive, we show that the ATS dynamics is sensitive with the squeezing parameter of quantum light, leading to modifications of the subband structures and splitting magnitudes. In particular, a BSV pulse exhibits a higher splitting efficiency than a classical pulse of the same mean intensity. This work has implications on ultrafast coherent control of molecular reactions with quantum light.

DOI
10.1021/acs.jpclett.6c01039

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Autler–Townes splitting (ATS) is a hallmark phenomenon of strong light–matter interaction, in which the resonant photoelectron energy spectrum splits into distinct peaks when driven by a strong electromagnetic field. We investigate the Autler–Townes Splitting (ATS) in K 2 molecules with quantum light. The triple splitting structures originating from three-photon ionization are analyzed under different types of driving fields, including bright squeezed vacuum (BSV), phase-squeezed coherent (PSC) light and amplitude-squeezed coherent (ASC) light by numerically solving the time-dependent Schrödinger equation. Compared with the results with the coherent-state (classical) light drive, we show that the ATS dynamics is sensitive with the squeezing parameter of quantum light, leading to modifications of the subband structures and splitting magnitudes. In particular, a BSV pulse exhibits a higher splitting efficiency than a classical pulse of the same mean intensity. This work has implications on ultrafast coherent control of molecular reactions with 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 theoretically investigate the Autler–Townes (AT) splitting in the photoelectron spectrum of four-level ladder K 2 molecule driven by a pump 1-pump 2-probe pulse via employing the time-dependent wave packet approach. The effects of the pump-1 laser intensity and wavelength on AT splitting are studied for the first time. The magnitude of AT splitting increases with increasing the pump-1 laser intensity. The triple splitting with asymmetric profile occurs due to the nonresonant excitation. The triple structure is transformed into a double structure (near-resonant region), and then becomes a peak (far-off resonant region) progressively as the pump-1 laser is detuned from the resonance wavelength, which can be explained in terms of the asymmetric excitation/population of dressed states. The splitting between adjacent peaks and the splitting between the two sideband peaks in the triplet do not change with the pump-1 pulse wavelength. The three peaks shift toward lower energy with the same shift 1/4* Δ 1 as the pump-1 wavelength changes in near-resonant region. The asymptotic behaviors of AT splitting with the pump-1 laser intensity are interesting in the threshold points of the near-resonant region and the far-off resonant region.
We theoretically investigate the Autler–Townes(AT)splitting in the photoelectron spectrum of four-level ladder K2molecule driven by a pump 1-pump 2-probe pulse via employing the time-dependent wave packet approach.The effects of the pump-1 laser intensity and wavelength on AT splitting are studied for the first time.The magnitude of AT splitting increases with increasing the pump-1 laser intensity.The triple splitting with asymmetric profile occurs due to the nonresonant excitation.The triple structure is transformed into a double structure(near-resonant region),and then becomes a peak(far-off resonant region)progressively as the pump-1 laser is detuned from the resonance wavelength,which can be explained in terms of the asymmetric excitation/population of dressed states.The splitting between adjacent peaks and the splitting between the two sideband peaks in the triplet do not change with the pump-1 pulse wavelength.The three peaks shift toward lower energy with the same shift 1/4*△1 as the pump-1 wavelength changes in near-resonant region.The asymptotic behaviors of AT splitting with the pump-1 laser intensity are interesting in the threshold points of the near-resonant region and the far-off resonant region.
We study the photoelectron spectra of hydrogen and helium ionized by intense ultrafast two-color XUV laser pulses by numerically solving the time-dependent Schrödinger equation.The photon energy of the pump pulse is tuned to the 1s-2p excitation energy, inducing Rabi oscillations between these bound states and forming an Autler-Townes (AT) doublet of dressed states.When ionized by a time-delayed ultrafast XUV pulse with duration shorter than the Rabi oscillation period, we find novel and drastically enhanced AT splittings in the photoionization spectrum.We identify their origin in terms of the temporal interference of two attosecond wave packets whose spectral distribution is controlled by the interplay between Rabi frequency and bandwidth of the probe pulse.These time-dependent features in the spectra can be much larger than the standard AT spacing induced by the pump pulse alone and can be controlled by the time delay and the duration of the probe pulse.
We theoretically investigate the Autler-Townes (AT) splitting in the photoelectron spectra of threelevel ladder K 2 molecule driven by a pump-probe pulse via employing the time-dependent wave packet approach. The effect of the pump/probe laser intensity and wavelength on AT splitting is detailed studied. The magnitude of AT splitting increases with increasing the pump laser intensity, but does not vary with probe intensity. The double splitting with asymmetric profiles arises due to the nonresonant excitation. The double structure is transformed into one peak progressively as the pump is detuned from the resonance wavelength, which can be explained in terms of the asymmetric excitation/population of dressed states. The splitting between AT doublet changes with pump wavelength, but does not change with probe wavelength. The double peaks shift to lower energy with the different shift with increasing pump wavelength, but with the same shift with probe wavelength.
Nonlinear optical processes, mediated by multiphoton interactions rather than single-photon response, are routinely exploited to enable a range of light-based functionalities in devices and applications. Nonlinear effects are enhanced through higher intensity fields, which is a limiting strategy owing to potential radiation damage. An alternative strategy relies on the fluctuation redistribution typical of quantum light, but experimental demonstrations at the most fundamental level have been limited. Here we report experimental nonlinear tunnelling ionization of isolated atoms, a pivotal nonlinear process that drives high-harmonic generation and forms the basis of attosecond science, boosted by quantum light -- bright squeezed vacuum (BSV). A BSV light with an average pulse energy of 300 nJ achieves an effective intensity equivalent to that of a coherent light with 7.1 {\textmu}J, demonstrating a more than 20-fold quantum boost in nonlinear effect from BSV light. This boost is revealed by matching the peaks of the photoelectron momentum spectra produced by the BSV and coherent light using angular streaking. Furthermore, we demonstrate control of the effective intensity of the BSV by tuning the correlation function at fixed average pulse energy, establishing a robust method to tailor nonlinear processes via quantum statistics rather than classical intensity scaling. These findings may facilitate the development of quantum-controlled strong-field dynamics using tailored quantum light sources.