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Physical Review A

Characterization of the two-photon transition phase in the buildup process of Rabi oscillations

Xu Zhang, Yijie Liao, Yongkun Chen, Miao Yu, Kunlong Liu, Peixiang Lu, Yueming Zhou

Published Mar 1, 2024• 10 citations
Publisher

Abstract

We achieve the complete characterization of the transition phase in the resonant two-photon ionization (TPI) of hydrogen at the high laser intensity where Rabi oscillation occurs. Different from previous studies which focused on the transition phase of resonant TPI in the perturbation region, in our work, we reveal the effect of Rabi oscillations on the transition phase in the high-intensity region. With bichromatic extreme-ultraviolet light, the transition phases of the $S$ and $D$ partial waves are decoded. By solving the time-dependent Schrodinger equation, we show that the transition phase depends on not only the pulse duration but also the laser intensity. This dependence is traced back to the modification of the atomic state structure, rather than the competition between resonant and nonresonant ionization paths at the lower laser intensity. Our work provides a way to manipulate the two-photon transition phase through laser intensity.

DOI
10.1103/physreva.109.033101

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We achieve the complete characterization of the transition phase in the resonant two-photon ionization (TPI) of hydrogen at the high laser intensity where Rabi oscillation occurs. Different from previous studies which focused on the transition phase of resonant TPI in the perturbation region, in our work, we reveal the effect of Rabi oscillations on the transition phase in the high-intensity region. With bichromatic extreme-ultraviolet light, the transition phases of the SSS and DDD partial waves are decoded. By solving the time-dependent Schrodinger equation, we show that the transition phase depends on not only the pulse duration but also the laser intensity. This dependence is traced back to the modification of the atomic state structure, rather than the competition between resonant and nonresonant ionization paths at the lower laser intensity. Our work provides a way to manipulate the two-photon transition phase through laser intensity.
We present an interferometric method for studying the Rabi dynamics in atoms by employing an $\ensuremath{\omega}\text{\ensuremath{-}}2\ensuremath{\omega}$ extreme ultraviolet pulse pair generated from the seeded free-electron laser. By solving the time-dependent Schr\"odinger equation (TDSE) for hydrogen atoms, we study the photoelectron spectrum that emerges when the $\ensuremath{\omega}$ pulse triggers Rabi oscillations between the ground state and the first excited state. The interference between the one-photon and two-photon ionization pathways in the photoelectron signal gives access to the phase difference between the one- and two-photon transition amplitudes. Compared to the cases without Rabi oscillations, an additional $\ensuremath{\pi}$ phase jump is observed in the energy domain. Based on perturbation theory, we demonstrate that this phase jump directly reflects the ultrafast buildup of Rabi oscillations in the time domain. The present $\ensuremath{\omega}\text{\ensuremath{-}}2\ensuremath{\omega}$ scheme can be generalized and applied to other more complex atoms or molecules provided that the populations of bound states can be efficiently and coherently modulated using the free-electron laser.
By numerically solving the three-dimensional time-dependent Schr\"odinger equation, two-photon ionization of hydrogen is investigated at the near-resonant frequencies of the $1s\text{\ensuremath{-}}2p$ transition. Due to the Rabi oscillations between the 1s1s1s and 2p2p2p states, the photoelectron energy spectra exhibit the Autler-Townes (AT) doublets and we focus on the energy spacing and the asymmetry of the doublets. Our results show that the laser frequency for the minimum energy spacing of AT doublets locates at the resonant frequency of the ac-stark-shifted states, while the symmetry of the AT doublets is affected both by the ac-stark shift and the nonresonant ionization pathway. Developing the minimal three-state model including all of the nonresonant (nonessential) states, the effects of the ac-stark shift and the nonresonant ionization pathway on the AT doublets due to the nonresonant states are identified. Furthermore, due to the nonresonant ionization pathway, the photoelectron angular distributions are distinctly different for the lower- and higher-energy peaks in the AT doublets and these angular distributions sensitively depend on the laser intensity and pulse duration. These results are well reproduced by our minimal three-state model.
We analyze theoretically the high intensity photoionization dynamics of a system with two atomic states resonantly coupled by coherent extreme ultraviolet laser radiation that also gives rise to the ionization. The ground state occupation of such a system is shown to exhibit damped Rabi oscillations. The corresponding ionization, which is responsible for the damping, scales almost linearly with the field intensity when the pulse length exceeds the Rabi period. For shorter pulses a quadratic scaling is found. The Rabi frequency is shifted compared to its value for an isolated two-level system. The shift increases with excitation intensity and can acquire a high percentage of the unrenormalized frequency at high intensities. Analytical results obtained within a simplified solvable model demonstrate that the damping and the shift both result from the coupling of the discrete states to the ionization continuum and are therefore closely related. Numerical simulations for a two-electron system reveal at high intensities the importance of off-resonant ionization channels.
When an atom is driven by a laser field with a photon energy that is nearly resonant with an atomic transition, it can undergo periodic population transfers between the ground and excited state, known as Rabi oscillations [1], [2]. The aim of this work is to study photoionization from atoms for parameters accessible to a free-electron laser (FEL) [3]. Using time dependent perturbation theory to model photoionization from a Rabi oscillating atom, we have shown that in addition to the expected pathway of ionization from the excited state, non-resonant two-photon ionization will have a comparable amplitude at intensities on the order of 1013W/cm2[3].
The influence of ultrashort low-frequency laser pulses of different intensities and pulse lengths on the dynamics of a resonantly driven atomic system is investigated theoretically. We demonstrate the periodical dependence of the total ionization rate on the appearance time of a strong few-cycle laser pulse. By depleting the excited state, the intense short pulse not only resets the Rabi oscillations, but also introduces a time shift that is proportional to the pulse length. This time shift can be employed to determine the ultrashort pulse length. In the case of ultrashort pulses with lower intensities, we observe side-bands in the two-photon ionization spectrum, whose intensities vary periodically with the appearance time of the pulse. This can be utilized to measure the period of Rabi oscillations. We have developed an S-matrix theory of two-colour ionization which can explain some of the observations of our numerical calculations. Furthermore, we have studied the high harmonic generation spectra as well as the attosecond pulses generated from the high harmonics. We show that the Rabi oscillation can be used to alter the ionization rate within laser sub-cycles and therefore select different quantum trajectories in the high harmonics generation.
We theoretically investigate strong-field ionization of hydrogen atoms by orthogonally polarized two-color (OTC) laser pulses consisting of a fundamental field that is resonant with the 1s - 2p transition and its second harmonic. Numerical simulations are performed by solving the two-dimensional time-dependent Schrödinger equation and recording the photoelectron momentum distribution. In this strong-field resonant ionization, the atom undergoes many Rabi cycles and the electron can be emitted within a completed Rabi-cycle leading to the splitting of the localized momentum distribution. Here, the splitting is attributed to dynamic Rabi-splitting as a result of the dynamic Stark effect. The employed OTC scheme is shown to be efficient for controlling the dynamic Rabi-splitting through the control of quantum-path interferences involved in one-photon and two-photon absorption processes. The control scheme is accomplished by varying the relative ratio intensity and optical phase between the two pulses, and its footprint is mapped in the momentum distribution. This is shown to lead to an asymmetric distribution and suppression of the ionization process. The obtained results suggest the OTC scheme as a tool for coherent control of dynamic Rabi-oscillations via the controlled quantum-path interferences, thus opening new directions towards designing quantum states via the control OTC scheme.