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Physical Review Research

Intensity-dependent interferences in strong-field Rydberg-state excitation

xiaopeng Yi, Changtong Liang, Li Shuai Guo, W B Becker, Jing Chen

Published Jan 8, 2026• 1 citation
Publisher

Abstract

We conduct a systematic investigation of the oscillations of the Rydberg-state populations as a function of intensity arising from strong-field multiphoton excitation of Rydberg atoms. By numerically solving the time-dependent Schrödinger equation and by constructing a quantum model based on Freeman resonances, we elucidate the underlying physical mechanisms governing the intensity-dependent oscillatory behavior of the Rydberg-state population dynamics. Our analysis shows that these oscillations originate from the synergistic interplay of three distinct quantum-interference mechanisms: (1) interference between excitation pathways at the rising and falling edges of the laser pulse (long-time interference), (2) interference between different optical cycles within the same side of the laser pulse (short-time interference), and (3) interference within individual optical cycles (intracycle interference). Additionally, we find that ground-state depletion has varying degrees of influence on the oscillation patterns formed by the three interference mechanisms under different laser-intensity conditions.

DOI
10.1103/4d6p-55n1

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We conduct a systematic investigation of the oscillations of the Rydberg-state populations as a function of intensity arising from strong-field multiphoton excitation of Rydberg atoms. By numerically solving the time-dependent Schrödinger equation and by constructing a quantum model based on Freeman resonances, we elucidate the underlying physical mechanisms governing the intensity-dependent oscillatory behavior of the Rydberg-state population dynamics. Our analysis shows that these oscillations originate from the synergistic interplay of three distinct quantum-interference mechanisms: (1) interference between excitation pathways at the rising and falling edges of the laser pulse (long-time interference), (2) interference between different optical cycles within the same side of the laser pulse (short-time interference), and (3) interference within individual optical cycles (intracycle interference). Additionally, we find that ground-state depletion has varying degrees of influence on the oscillation patterns formed by the three interference mechanisms under different laser-intensity conditions.
The competition between multiphoton and tunneling mechanisms governs strong-field excitation of atoms, though the role of pulse duration in modulating this competition remains poorly understood. Here we report an intensity-dependent reversal in the excitation probabilities driven by 400-nm laser pulses in atomic hydrogen. At low intensity, the excitation rises with increasing pulse duration, but at higher intensity, the excitation drops as pulse duration increases. By resolving the excitation into individual Rydberg states, we find that the energy level with the principal quantum number n = 4 dominates and its modulation reflects an intricate interplay between parity-dependent intracycle interference and parity-independent intercycle interference. Using a tunneling-captured quantum model, we identify ground-state population depletion as the decisive factor controlling this behavior. Under moderate depletion, intracycle interference selectively enhances or suppresses specific peaks according to the parity of the final state; under excessive depletion, intercycle interference dominates, producing complex subpeak structures and stabilizing yields at higher intensities. Our results establish a unified picture of how quantum interference and population depletion jointly govern strong-field excitation dynamics.
The AC Stark shift of electronic levels is ubiquitous in the interaction of intense light fields with atoms and molecules. As the light intensity changes on the rising and falling edges of a femtosecond laser pulse, it shifts the Rydberg states in and out of multiphoton resonances with the ground state. The two resonant pathways for transient excitation arising at the leading and the trailing edges of the pulse generate Young's type interference, generally referred to as the St\"uckelberg oscillations. Here we report the observation of the St\"uckelberg oscillations in the intensity of the coherent free-induction decay following resonant multiphoton excitation. Moreover, combining the experimental results with accurate numerical simulations and a simple model, we use the St\"uckelberg oscillations to recover the population dynamics of strongly driven Rydberg states inside the laser pulse by all-optical measurements after the end of the pulse. We demonstrate the potential of this spectroscopy to characterize lifetimes of Rydberg states dressed by laser fields with strengths far exceeding the Coulomb field between the Rydberg electron and the core.
Abstract We demonstrate how strong-field multiphoton transitions between dynamically shifted atomic levels can be traced in the energy spectra of emitted photoelectrons. Applying an ultrafast and intense laser pulse, two-photon Rabi oscillations are induced between two bound states of an atom. A third photon from the same pulse directly ionizes the atom, thus the emitted photoelectrons coherently probe the underlying dynamics. As the instantaneous energy of photoelectrons follows the pulse intensity envelope, modulated by the ac Stark shifts, electrons emitted with the same energy but at different times—at the rising and falling edge of the pulse—will interfere leading to pronounced dynamic interference pattern in the spectra. We investigate this phenomenon both numerically and analytically by developing a minimal three-state model that incorporates two-photon coupling and dynamically shifted atomic levels. On the example of atomic lithium (2 s → → 4 s → continuum) we show how the individual ac Stark shifts and the two-photon Rabi frequency are reflected through the asymmetry, shifting and splitting of the interference structure of the computed photopeaks.
To study the physical mechanism of atomic Rydberg state excitation (RSE) in two-color laser fields, we solve the time-dependent Schrödinger equation (TDSE) to calculate the ionization and excitation of hydrogen atoms. The relationship between the excited state population and the excitation rate of hydrogen atoms and the intensity of the fundamental frequency (FW) field can be observed by adjusting the laser intensity of the second harmonic (SH) field. The results demonstrate that multiphoton resonance absorption aligns with the physical mechanism of atomic resonant state excitation in two-color laser fields.
Strong-field excitation provides new methods and means for coherent population of Rydberg states. In this study, we numerically solve the time-dependent Schrödinger equation to investigate the strong-field excitation and radiation dynamics under the cooperative interaction of terahertz (THz) and femtosecond strong laser pulses. In the radiation spectrum, the Rydberg states excited by the strong field are manifested as resonance peaks with energy below the ionization threshold. By using THz fields to control the electron motion on sub-optical cycles, we achieve modulation of Rydberg state population and high-order harmonic radiation under the influence of a strong laser field. We analyze the variation of the excited state population with THz intensity, frequency, and the angle between the infrared field polarization and the THz field. Our results show that, with the assistance of the THz field, population inversion occurs between the Rydberg states. This study provides a feasible scheme for THz amplification based on Rydberg atoms and holds significant implications for THz amplification, high-sensitivity detection, and quantum information processing.
Excitation and photoionization of Rydberg wave packets are described. Interference of bound-free transitions from many coherently populated Rydberg levels is shown to affect the dependence of the photoionization probability on the duration of interaction. Strong-field interference effects in such a system are described also. The most important of these is the field-induced interference stabilization of Rydberg atoms in a strong ionizing field. The intensity range in which this effect can exist is determined. The results derived are used for a qualitative model describing supercontinuum emission in the process of multiphoton ionization.