Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Line-shape study of two-color–three-photon ionization of Rb atoms

Ivo Cacelli, A. Fioretti, C. Gabbanini, Marina Mazzoni, Maurizio Persico

Published Aug 21, 2002• 0 citations
Publisher

Abstract

We report on the analysis of the line shapes in a two-color, three-photon ionization process of rubidium atoms in a magneto-optical trap. A cw and a pulsed laser are tuned almost at resonance with the ${5}^{2}{S}_{1/2}{\ensuremath{-}5}^{2}{P}_{3/2}$ and the ${5}^{2}{P}_{3/2}{\ensuremath{-}6}^{2}{D}_{5/2}$ transitions, respectively. The line shapes, recorded as functions of the pulsed laser wavelength, are strongly asymmetric with respect to the near resonance peak positions: in fact, they present long tails only on one side, according to the sign of the detuning of the cw laser. Moreover, the signal is overall stronger for negative than for positive detunings. Theoretical considerations based on the Autler-Townes scheme and computer simulations of the excitation-ionization dynamics show that the main source of asymmetry is the coupling of the two ionization pathways going through the ${6}^{2}{D}_{3/2}$ and ${6}^{2}{D}_{5/2}$ levels. In order to reproduce the experimental line shapes one must take into account the variability of the pulsed laser intensity and its finite coherence time.

DOI
10.1103/physreva.66.023408

Related papers

Few-photon single ionization of cold rubidium in the over-the-barrier regime

Huanyu Ma, Xincheng Wang, Linxuan Zhang +9 more

Photoionization of rubidium atoms cooled in a magneto-optical trap, characterized by the coexistence of the ground $5{S}_{1/2}$ and excited $5{P}_{3/2}$ states, is investigated experimentally and theoretically with the 400-nm femtosecond laser pulses at intensities of $I=(3\ifmmode\times\else\texttimes\fi{}{10}^{9})\text{--}(4.5\ifmmode\times\else\texttimes\fi{}{10}^{12})$ $\mathrm{W}/{\mathrm{cm}}^{2}$. The recoil-ion momentum distribution (RIMD) of ${\mathrm{Rb}}^{+}$ exhibits rich ringlike structures and their energies correspond to one-photon ionization of the $5{P}_{3/2}$ state and two-photon and three-photon ionizations of the $5{S}_{1/2}$ state, respectively. With increasing $I$, the dips near zero momentum (NZM) in the experimental RIMDs become shallow dramatically and their peaked ${\mathrm{Rb}}^{+}$ momenta ionized from the $5{P}_{3/2}$ state move obviously toward zero while the peaks from the $5{S}_{1/2}$ state do not shift. In addition, the ion-yield ratio of the $5{S}_{1/2}$ state to the $5{P}_{3/2}$ state varies from $I$ to ${I}^{1.5}$ as $I$ increases. These features indicate a transition from perturbative ionization to strongly perturbative ionization for the $5{P}_{3/2}$ state. Numerical simulations by solving the time-dependent Schr\"odinger equation (TDSE) can qualitatively explain the measurements of the RIMD, photoion angular distributions, and ion-yield ratio. However, some discrepancies still exist, especially for the NZM dip, which could stem from the electron-electron correlation that is neglected in the present TDSE simulations since we have adopted the single-active-electron approximation.

arXiv:2302.00124•Physical Review A•Mar 20, 2023•8 citations

Coherent control of multiphoton-ionization passage of excited-state rubidium atoms

Sangkyung Lee, Han-gyeol Lee, Jun-Woo Cho +3 more

We have investigated multiphoton-ionization passages of rubidium atoms initiated from the excited $5{P}_{3/2}$ energy state. For this we used coherent control schemes based on femtosecond laser pulse shaping applied to cold atoms spatially isolated in a magneto-optical trap. With programed laser pulses of spectral $\ensuremath{\pi}$-phase step, of which location was varied within the laser spectrum, the sequential two-photon-ionization passage along the $5{P}_{3/2}$-$5D$ continuum was probed in terms of trap-loss spectroscopy. The coherent control two-photon-ionization method unveiled not only the resonantly enhanced two-photon ionization but also the asymmetric nature of the ionization profile structure given as a function of the spectral phase step location. Experimental results show good agreement with the second-order perturbation calculation of the constituent possible ionization passages.

Physical Review A•Oct 31, 2012•5 citations

Line shape study of three-photon ionization through intermediate states of Rb atoms

A. Fioretti

We report a line shape study in a multiple level atomic system under the perturbation of a strong and pulsed laser field. The line shapes have been observed in the ion spectra during an experiment aimed to produce and detect translationally cold molecules in a rubidium magneto-optical trap and compared with the results of computer simulations of the atom-radiation dynamics.

AIP conference proceedings•Jan 1, 2001•0 citations

Three-photon laser excitation of mesoscopic ensembles of cold rubidium Rydberg atoms

Elena A. Yakshina, Denis B. Tretyakov, Vasily M. Entin +2 more

The spectra of three-photon laser excitation (according to the 5 S 1/2 → 5 P 3/2 → 6 S 1/2 → 37 P 3/2 scheme) of mesoscopic ensembles of cold Rb Rydberg atoms in a magneto-optical trap, using cw single-frequency lasers in each stage, have been investigated. The ensembles consisted of 1 to 5 atoms, and their presence was recorded by the selective field ionisation method with postselection according to the number of atoms. The dependence of the spectral shape on the excitation laser pulse duration has been studied. For 2-μs pulses, the minimum spectral width was found to be 1.3 MHz; it was determined by the laser linewidth and the spectral width of laser pulse. For pulses shorter than 0.5 μs, additional spectral broadening and occurrence of Rabi oscillations in the wings of three-photon resonances have been observed, a fact indicative of implementation of coherent three-photon laser excitation of Rydberg atoms. An analysis of the spectra within the four-level theoretical model based on optical Bloch equations showed good agreement between the experimental and theoretical results. The dependence of the shape of three-photon excitation spectrum on the number of recorded atoms was also studied. An increase in the average number of atoms leads to the occurrence of a dip in the single-atom excitation spectra; this dip is due to the specificity of the excitation and detection statistics of Rydberg atoms. The results obtained are important for applications of Rydberg atoms in quantum informatics.

Quantum Electronics•Oct 19, 2018•13 citations

Experimental and theoretical study of three-photon ionization of He( 1s2p3Po )

Matthieu Génévriez, Xavier Urbain, Mohand Brouri +3 more

A joint experimental and theoretical study of three-photon ionization of the $1s2p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}^{o}$(${M}_{L}=0,\ifmmode\pm\else\textpm\fi{}1$) states of helium is presented. The ion yield is recorded in the 690--730 nm wavelength range for different laser pulse energies, using an excited helium beam produced by photodetachment of helium negative ions. Two series of asymmetric peaks due to two-photon resonances with $1snp$ and $1snf$ Rydberg states are observed. In one series, the peaks have tails towards higher frequencies, while in the other series the tails change direction for higher Rydberg states. An effective Hamiltonian is built in the dressed state picture, and a numerical model simulating the traversal of the helium atom across the laser pulse is developed. The simulated and observed ion yields are in good qualitative agreement. The observed behavior is shown to result from the contributions of two different resonantly enhanced multiphoton ionization processes, depending on the magnetic quantum number ${M}_{L}$ of the initial state. The asymmetry reversal is explained by the strong $1s2p$--$1s3s$ dynamic Stark mixing for ${M}_{L}=0$.

Physical Review A•May 30, 2014•2 citations

Calculation of line shapes in double-resonance optical pumping

Heung‐Ryoul Noh, Han Seb Moon

A theoretical study on double-resonance optical pumping for the transitions $5{S}_{1/2}\text{\ensuremath{-}}5{P}_{3/2}\text{\ensuremath{-}}4{D}_{3/2,5/2}$ of $^{87}\text{R}\text{b}$ atoms is presented. The full-density-matrix equations in the presence the probe and the coupling laser beams for all relevant magnetic sublevels of the hyperfine levels were solved numerically, and the absorption of a probe beam was calculated as a function of the detuning of the coupling beam. The calculated results were compared with experimental data, and they showed an excellent agreement. The results were also compared with the approximate results calculated when the coherence between the ground and the highest excited levels was neglected. We found that the dominant operating mechanism for double-resonance signals was the optical pumping rather than the two-photon coherence, although the latter affected the signals significantly.

Physical Review A•Aug 14, 2009•29 citations
We report on the analysis of the line shapes in a two-color, three-photon ionization process of rubidium atoms in a magneto-optical trap. A cw and a pulsed laser are tuned almost at resonance with the 52S1/2\ensuremath−52P3/2{5}^{2}{S}_{1/2}{\ensuremath{-}5}^{2}{P}_{3/2}52S1/2​\ensuremath−52P3/2​ and the 52P3/2\ensuremath−62D5/2{5}^{2}{P}_{3/2}{\ensuremath{-}6}^{2}{D}_{5/2}52P3/2​\ensuremath−62D5/2​ transitions, respectively. The line shapes, recorded as functions of the pulsed laser wavelength, are strongly asymmetric with respect to the near resonance peak positions: in fact, they present long tails only on one side, according to the sign of the detuning of the cw laser. Moreover, the signal is overall stronger for negative than for positive detunings. Theoretical considerations based on the Autler-Townes scheme and computer simulations of the excitation-ionization dynamics show that the main source of asymmetry is the coupling of the two ionization pathways going through the 62D3/2{6}^{2}{D}_{3/2}62D3/2​ and 62D5/2{6}^{2}{D}_{5/2}62D5/2​ levels. In order to reproduce the experimental line shapes one must take into account the variability of the pulsed laser intensity and its finite coherence time.
Photoionization of rubidium atoms cooled in a magneto-optical trap, characterized by the coexistence of the ground 5S1/25{S}_{1/2}5S1/2​ and excited 5P3/25{P}_{3/2}5P3/2​ states, is investigated experimentally and theoretically with the 400-nm femtosecond laser pulses at intensities of $I=(3\ifmmode\times\else\texttimes\fi{}{10}^{9})\text{--}(4.5\ifmmode\times\else\texttimes\fi{}{10}^{12})$ W/cm2\mathrm{W}/{\mathrm{cm}}^{2}W/cm2. The recoil-ion momentum distribution (RIMD) of Rb+{\mathrm{Rb}}^{+}Rb+ exhibits rich ringlike structures and their energies correspond to one-photon ionization of the 5P3/25{P}_{3/2}5P3/2​ state and two-photon and three-photon ionizations of the 5S1/25{S}_{1/2}5S1/2​ state, respectively. With increasing III, the dips near zero momentum (NZM) in the experimental RIMDs become shallow dramatically and their peaked Rb+{\mathrm{Rb}}^{+}Rb+ momenta ionized from the 5P3/25{P}_{3/2}5P3/2​ state move obviously toward zero while the peaks from the 5S1/25{S}_{1/2}5S1/2​ state do not shift. In addition, the ion-yield ratio of the 5S1/25{S}_{1/2}5S1/2​ state to the 5P3/25{P}_{3/2}5P3/2​ state varies from III to I1.5{I}^{1.5}I1.5 as III increases. These features indicate a transition from perturbative ionization to strongly perturbative ionization for the 5P3/25{P}_{3/2}5P3/2​ state. Numerical simulations by solving the time-dependent Schr\"odinger equation (TDSE) can qualitatively explain the measurements of the RIMD, photoion angular distributions, and ion-yield ratio. However, some discrepancies still exist, especially for the NZM dip, which could stem from the electron-electron correlation that is neglected in the present TDSE simulations since we have adopted the single-active-electron approximation.
We have investigated multiphoton-ionization passages of rubidium atoms initiated from the excited 5P3/25{P}_{3/2}5P3/2​ energy state. For this we used coherent control schemes based on femtosecond laser pulse shaping applied to cold atoms spatially isolated in a magneto-optical trap. With programed laser pulses of spectral $\ensuremath{\pi}$-phase step, of which location was varied within the laser spectrum, the sequential two-photon-ionization passage along the 5P3/25{P}_{3/2}5P3/2​-5D5D5D continuum was probed in terms of trap-loss spectroscopy. The coherent control two-photon-ionization method unveiled not only the resonantly enhanced two-photon ionization but also the asymmetric nature of the ionization profile structure given as a function of the spectral phase step location. Experimental results show good agreement with the second-order perturbation calculation of the constituent possible ionization passages.
The spectra of three-photon laser excitation (according to the 5 S 1/2 → 5 P 3/2 → 6 S 1/2 → 37 P 3/2 scheme) of mesoscopic ensembles of cold Rb Rydberg atoms in a magneto-optical trap, using cw single-frequency lasers in each stage, have been investigated. The ensembles consisted of 1 to 5 atoms, and their presence was recorded by the selective field ionisation method with postselection according to the number of atoms. The dependence of the spectral shape on the excitation laser pulse duration has been studied. For 2-μs pulses, the minimum spectral width was found to be 1.3 MHz; it was determined by the laser linewidth and the spectral width of laser pulse. For pulses shorter than 0.5 μs, additional spectral broadening and occurrence of Rabi oscillations in the wings of three-photon resonances have been observed, a fact indicative of implementation of coherent three-photon laser excitation of Rydberg atoms. An analysis of the spectra within the four-level theoretical model based on optical Bloch equations showed good agreement between the experimental and theoretical results. The dependence of the shape of three-photon excitation spectrum on the number of recorded atoms was also studied. An increase in the average number of atoms leads to the occurrence of a dip in the single-atom excitation spectra; this dip is due to the specificity of the excitation and detection statistics of Rydberg atoms. The results obtained are important for applications of Rydberg atoms in quantum informatics.
A joint experimental and theoretical study of three-photon ionization of the 1s2p3Po1s2p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}^{o}1s2p3Po(${M}_{L}=0,\ifmmode\pm\else\textpm\fi{}1$) states of helium is presented. The ion yield is recorded in the 690--730 nm wavelength range for different laser pulse energies, using an excited helium beam produced by photodetachment of helium negative ions. Two series of asymmetric peaks due to two-photon resonances with 1snp1snp1snp and 1snf1snf1snf Rydberg states are observed. In one series, the peaks have tails towards higher frequencies, while in the other series the tails change direction for higher Rydberg states. An effective Hamiltonian is built in the dressed state picture, and a numerical model simulating the traversal of the helium atom across the laser pulse is developed. The simulated and observed ion yields are in good qualitative agreement. The observed behavior is shown to result from the contributions of two different resonantly enhanced multiphoton ionization processes, depending on the magnetic quantum number ML{M}_{L}ML​ of the initial state. The asymmetry reversal is explained by the strong 1s2p1s2p1s2p--1s3s1s3s1s3s dynamic Stark mixing for ML=0{M}_{L}=0ML​=0.
A theoretical study on double-resonance optical pumping for the transitions $5{S}_{1/2}\text{\ensuremath{-}}5{P}_{3/2}\text{\ensuremath{-}}4{D}_{3/2,5/2}$ of 87Rb^{87}\text{R}\text{b}87Rb atoms is presented. The full-density-matrix equations in the presence the probe and the coupling laser beams for all relevant magnetic sublevels of the hyperfine levels were solved numerically, and the absorption of a probe beam was calculated as a function of the detuning of the coupling beam. The calculated results were compared with experimental data, and they showed an excellent agreement. The results were also compared with the approximate results calculated when the coherence between the ground and the highest excited levels was neglected. We found that the dominant operating mechanism for double-resonance signals was the optical pumping rather than the two-photon coherence, although the latter affected the signals significantly.