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Annalen der Physik

Ionization Phase‐Shifts Between Two Laser‐Dressed States of Potassium Atoms

Wankai Li, Yixuan Wang, Xing Li, Tao Yang, Dongdong Zhang, Dajun Ding

Published Aug 23, 2025• 2 citations
Publisher

Abstract

Abstract Resonance‐enhanced multiphoton ionization (REMPI) in potassium atom is investigated within the strong coupling regime using photoelectron momentum imaging techniques. The kinetic energy distribution of the ionized electrons reveals the eigenenergies of the dressed states, which exhibit Autler–Townes (AT) splitting. This splitting is proportional to the laser field strength. Partial wave analysis of the photoelectrons angular distributions (PAD) uncovers relative phase shifts between the dressed states, shedding light on attosecond ionization time delays. The observed phase shift between the two electron wave packets by the AT splitting arises from the combined effects of the Coulomb phase and the quantum defect phase.

DOI
10.1002/andp.202500091

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Abstract Resonance‐enhanced multiphoton ionization (REMPI) in potassium atom is investigated within the strong coupling regime using photoelectron momentum imaging techniques. The kinetic energy distribution of the ionized electrons reveals the eigenenergies of the dressed states, which exhibit Autler–Townes (AT) splitting. This splitting is proportional to the laser field strength. Partial wave analysis of the photoelectrons angular distributions (PAD) uncovers relative phase shifts between the dressed states, shedding light on attosecond ionization time delays. The observed phase shift between the two electron wave packets by the AT splitting arises from the combined effects of the Coulomb phase and the quantum defect phase.
A two-photon resonance in the sodium atom $3s\text{\ensuremath{-}}4s$ transition is investigated in the strong coupling regime with photoelectron momentum imaging techniques. The kinetic energies of the ionized electron map out the eigenenergies of the dressed states and emerge as the Autler-Townes (AT) splitting, which is proportional to the laser intensity due to the two-photon nature. The partial wave analysis of the angular distribution of the photoelectrons reveals the relative phase shift from dressed states which is related to the attosecond ionization time delays. The phase shift between the two electron wave packets produced from AT splitting are attributed to the combination of the Coulomb phase and the quantum defect phase.
We study the multiphoton ionization of potassium atoms in 800 nm and 400 nm femtosecond laser fields. In the 800 nm laser field, the potassium atom absorbs three photons and emits one electron via one photon resonance with the 4p intermediate state with the help of the ac-Stark shift. The resonance feature is clearly shown as an Autler–Townes (AT) splitting and is mapped out in the electron kinetic energy spectrum. In a 400 nm laser field, although one photon resonance is possible with the 5p state, no splitting is observed. The different transition amplitudes between 4s–4p and 4s–5p explain the observed results. Due to the AT effect, an unexpected peak in the photoelectron energy spectrum that violates the dipole transition rule is observed. A preliminary explanation involving the spin-orbit interaction in the p state is given to account for this component. The observed AT-splitting in the electron kinetic energy distribution can be used as an effective method to calibrate the intensity of a laser field.
We present a bound-continuum ionization model combined with numerical simulations to investigate the asymmetric features of Autler-Townes (AT) splitting in the ionization spectra of hydrogen atoms, induced by a spectrally phase-modulated ultrashort pulse. This model incorporates a resonance-enhanced two-photon ionization process, enabling transitions from the ground electronic state to the continuum state via the first excited electronic state through the absorption of two photons. By comparing our model predictions with exact numerical simulations based on time-dependent electronic wave-packet calculations, we demonstrate that the characteristics of the AT doublets, shaped by the spectral phase, emerge from the competing effects of selective population of dressed states and the transition amplitude to the continuum. In addition, through a perturbative analysis of the photoelectronic spectrum and the application of the Magnus expansion, we reveal a correlation between the number of AT fringes, resonant states, and pulse area, while drawing insights from bound states. This work enhances our understanding of how the spectral phase can be utilized to explore bound-state effects in ultrafast ionization dynamics.
We present the unambiguous determination of quantum phases in the multiphoton ionization (MPI) of potassium atoms by using a multichannel photoelectron interferometry scheme based on trichromatic pulse shaping. The colors of the laser field are chosen to produce three energetically separated photoelectron interferograms in the continuum. While the red pulse is two-photon resonant with the 3d3d3d state resulting in a (2+1)(2+1)(2+1) resonance-enhanced MPI (REMPI), a (1+2)(1+2)(1+2) REMPI occurs via the nonresonant intermediate 4p4p4p state with an initial green or blue pulse. We show that ionization via a nonresonant intermediate state lifts the degeneracy of photoelectron interferograms from pathways consisting of permutations of the colors. The analysis of the interferograms reveals a phase shift of $\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2$ depending on the sign of the detunings in the (1+2)(1+2)(1+2) REMPI pathways. In addition, we demonstrate that the photoionization time delay in the resonant (2+1)(2+1)(2+1) REMPI pathway gives rise to a linear spectral phase in the photoelectron spectra. Insights into the underlying MPI processes are gained through an analytic perturbative description and numerical simulations of a trichromatic driven three-level system coupled to the continuum.
The Autler-Townes effect due to near resonance transition between 4s-4p states in potassium atoms is mapped out in the photo-electron-momentum distribution and manifests itself as a splitting in the photo-electron kinetic energy spectra. The energy splitting fits well with the calculated Rabi frequency at low laser intensities and shows clear deviation at laser intensities above 1.5x10^11 W/cm^2. An effective Rabi frequency formulae including the ionization process explains the observed results. Our results reveal the possibility to tune the effective coupling strength with the cost of the number of level-populations.
We propose a scheme to control the shape of the Autler-Townes (AT) doublet in the photoelectron spectrum from atomic resonance-enhanced multiphoton ionization (REMPI). The scheme is based on the interference of two AT doublets created by ionization of the strongly driven atom from the ground and the resonantly excited state using tailored bichromatic femtosecond laser pulses. In this scheme, the quantum phase of the photoelectrons is crucial for the manipulation of the AT doublet. The laser polarization state and the relative optical phase between the two colors are used to manipulate the interference pattern. We develop an analytical model to describe the bichromatic REMPI process and provide a physical picture of the control mechanism. To validate the model, the results are compared to an ab initio calculation based on the solution of the two-dimensional time-dependent Schr\"odinger equation for the nonperturbative interaction of an atom with intense polarization-shaped bichromatic femtosecond-laser pulses. Our results indicate that the control mechanism is robust with respect to the laser intensity, facilitating its experimental observation.