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Physical Review A

Transitions between Rydberg states in two-color corotating circularly polarized laser pulses

Yonas Gebre, Joel Venzke, Agnieszka Jaroń-Becker, Andreas Becker

Published Jan 5, 2021• 0 citations
Publisher

Abstract

We present a study of higher-order Raman ($\mathrm{\ensuremath{\Lambda}}, V$, and $S$) transitions between Rydberg states involving the absorption and emission of at least three photons in the interaction of two-color corotating circularly polarized laser pulses with the hydrogen atom. Our analysis is based on results of numerical solutions of the corresponding time-dependent Schr\"odinger equation. The results for the interaction with ($\ensuremath{\omega},2\ensuremath{\omega}$) fields show that the simultaneous interaction with both fields results in an excited state distribution over a broad range of magnetic quantum numbers. Indications of the impact of the $\mathrm{\ensuremath{\Lambda}}, V$, and $S$ transitions are found via the analysis of final distributions resulting from the preparation of the atom in specific Rydberg states. Furthermore, we show that similar mechanisms for the redistribution of population between Rydberg states are present in two-color fields with larger differences in the central frequencies, i.e., ($\ensuremath{\omega},3\ensuremath{\omega}$) and ($\ensuremath{\omega},4\ensuremath{\omega}$) fields.

DOI
10.1103/physreva.103.013101

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We present a study of higher-order Raman (\ensuremathΛ,V\mathrm{\ensuremath{\Lambda}}, V\ensuremathΛ,V, and SSS) transitions between Rydberg states involving the absorption and emission of at least three photons in the interaction of two-color corotating circularly polarized laser pulses with the hydrogen atom. Our analysis is based on results of numerical solutions of the corresponding time-dependent Schr"odinger equation. The results for the interaction with (\ensuremathω,2\ensuremathω\ensuremath{\omega},2\ensuremath{\omega}\ensuremathω,2\ensuremathω) fields show that the simultaneous interaction with both fields results in an excited state distribution over a broad range of magnetic quantum numbers. Indications of the impact of the \ensuremathΛ,V\mathrm{\ensuremath{\Lambda}}, V\ensuremathΛ,V, and SSS transitions are found via the analysis of final distributions resulting from the preparation of the atom in specific Rydberg states. Furthermore, we show that similar mechanisms for the redistribution of population between Rydberg states are present in two-color fields with larger differences in the central frequencies, i.e., (\ensuremathω,3\ensuremathω\ensuremath{\omega},3\ensuremath{\omega}\ensuremathω,3\ensuremathω) and (\ensuremathω,4\ensuremathω\ensuremath{\omega},4\ensuremath{\omega}\ensuremathω,4\ensuremathω) fields.
We study the excitation of the hydrogen atom by bichromatic circularly polarized laser pulses using numerical solutions of the time-dependent Schr\"odinger equation. The results are in agreement with the selection rules for multiphoton processes in such fields, namely, excited states are populated in which orbital angular momentum and magnetic quantum numbers are either both odd or both even, independent of the relative helicity, peak intensity, and pulse duration of the pulses. For co-rotating pulses the results show that excitation predominantly proceeds to states with magnetic quantum number of the same helicity as the laser pulses. Besides pathways via direct photon absorption from the ground state our results indicate that a transfer of population among the Rydberg states occurs via $\mathrm{\ensuremath{\Lambda}}$-type transitions. In the case of counter-rotating pulses the largest excitation probability is found for Rydberg states that differ in magnetic quantum number by $\mathrm{\ensuremath{\Delta}}m=\ifmmode\pm\else\textpm\fi{}3$. This pattern allows us to estimate how many photons from each of the two bichromatic fields have been absorbed. Finally, we confirm that a population in Rydberg states beyond a maximum orbital angular quantum number is unlikely.
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.
Rydberg states of atomic helium with principal quantum numbers ranging from n=20n=20n=20 to n=100n=100n=100 have been prepared by non-resonance-enhanced single-color two-photon excitation from the metastable 23S12\phantom{\rule{0.16em}{0ex}}{{}^{3}S}_{1}23S1​ state. Photoexcitation was carried out using linearly and circularly polarized pulsed laser radiation. In the case of excitation with circularly polarized radiation, Rydberg states with azimuthal quantum number $|{m}_{\ensuremath{\ell}}|=2$ were prepared in zero electric field and in homogeneous electric fields oriented parallel to the propagation axis of the laser radiation. In sufficiently strong electric fields, individual Rydberg--Stark states were resolved spectroscopically, highlighting the suitability of non-resonance-enhanced multiphoton excitation schemes for the preparation of long-lived high-$|{m}_{\ensuremath{\ell}}|$ hydrogenic Rydberg states for deceleration and trapping experiments. Applications of similar schemes for Doppler-free excitation of positronium atoms to Rydberg states are also discussed.
We have solved the time-dependent Schr\"odinger equation to analyze the time evolution of a hydrogen atom, initially in its ground 1s state, interacting with a one- or two-color linearly polarized laser pulse which is tuned close to a two-photon resonance with the 2s metastable state. The two-photon transition therefore does not involve an intermediate resonance state. Using a suitable combination of two laser pulses of different frequencies, population can be transferred from the 1s state to the 2s state via the continuum. In both the single-color and the two-color cases, a maximum amount of 17% of population can be found in the 2s state at the end of the pulse. We compare and interpret our results in terms of the time-independent Floquet eigenvalues. The system can also be modeled by an ``essential states'' two-level atom with decay. Both the Floquet and the time-dependent solutions are compared with the model predictions. The model allows systematic optimization studies for population transfer under a wide range of laser pulse parameters.
We calculate the two-color ionization profile of atomic hydrogen in the presence of both a weak tunable high-frequency laser field and a low-frequency laser field of moderate intensity. The high-frequency spectroscopic light is used to probe the structure of Rydberg states dressed by the low-frequency field. We construct the photoionization spectrum from the sum of the resonance contributions by calculating the transition dipole moments between the initial state and the dressed Rydberg states, analogous to the study of photoionization in the presence of a dc field carried out by Alvarez and Silverstone [Phys. Rev. Lett. 63, 1364 (1989)].
Our recent approximate analytical results on the evolution of the initial state and the excitation from this state of a band of high Rydberg states by an optical pulse [Phys. Rev. A 55, 2144 (1997)] are compared with more exact numerical results. The difference between the two approaches is that the approximations of representative atom-field couplings and equidistant spacing of high Rydberg states, applied in the analytical model, are removed in the numerical model. We find that the approximate analytical model is not able to reproduce all the results of the more exact numerical model, if the laser pulse is very short (i.e., much shorter that the Kepler period of the resonantly excited high Rydberg state) or very intense (i.e., when the Rabi period for the resonant transition is substantially shorter than the above Kepler period). This mainly concerns the redistribution of the population over different Rydberg states. The analytical model predicts a symmetric distribution centered around the resonantly excited Rydberg state, irrespective of the pulse duration and intensity, while the numerical model allows an asymmetric distribution with its maximum shifted towards lower Rydberg states. Despite the above-stated difference, the analytical model is able to give preliminary results for the total population of all the excited Rydberg states and the evolution of the initial state, imitating at least qualitatively the results of the numerical model in certain time and intensity scales.