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Physical Review A

Transmittance signal in real ladder-type atoms

Heung‐Ryoul Noh, Han Seb Moon

Published Mar 19, 2012• 38 citations
Publisher

Abstract

We clarify an interpretation of transmittance signals in ladder-type atomic systems by discriminating the contributions of one-photon resonance, two-photon resonance, and a mixed term of both in the calculated spectra for these ladder-type multilevel atoms. When the two-photon-resonance effect is distinguished from an accurate spectrum calculated by modeling ladder-type electromagnetically-induced transparency for the $5{S}_{1/2}\ensuremath{-}5{P}_{3/2}\ensuremath{-}5{D}_{5/2}$ transitions of ${}^{87}$Rb atoms, we find that the transmittance signals for the $5{D}_{5/2}({F}^{\ensuremath{'}\ensuremath{'}}=2,3)$ states are mainly composed of the mixed term related not to pure-two-photon atomic coherence but to the optical-pumping effect whereas the transmittance signal for the $5{D}_{5/2}({F}^{\ensuremath{'}\ensuremath{'}}=4)$ state originates from both the pure-two-photon-resonance term and the mixed term.

DOI
10.1103/physreva.85.033817

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We clarify an interpretation of transmittance signals in ladder-type atomic systems by discriminating the contributions of one-photon resonance, two-photon resonance, and a mixed term of both in the calculated spectra for these ladder-type multilevel atoms. When the two-photon-resonance effect is distinguished from an accurate spectrum calculated by modeling ladder-type electromagnetically-induced transparency for the 5S1/2\ensuremath−5P3/2\ensuremath−5D5/25{S}_{1/2}\ensuremath{-}5{P}_{3/2}\ensuremath{-}5{D}_{5/2}5S1/2​\ensuremath−5P3/2​\ensuremath−5D5/2​ transitions of 87{}^{87}87Rb atoms, we find that the transmittance signals for the 5D5/2(F\ensuremath′\ensuremath′=2,3)5{D}_{5/2}({F}^{\ensuremath{'}\ensuremath{'}}=2,3)5D5/2​(F\ensuremath′\ensuremath′=2,3) states are mainly composed of the mixed term related not to pure-two-photon atomic coherence but to the optical-pumping effect whereas the transmittance signal for the 5D5/2(F\ensuremath′\ensuremath′=4)5{D}_{5/2}({F}^{\ensuremath{'}\ensuremath{'}}=4)5D5/2​(F\ensuremath′\ensuremath′=4) state originates from both the pure-two-photon-resonance term and the mixed term.
We have experimentally and theoretically studied resonant two-photon absorption (TPA) and electromagnetically induced transparency (EIT) in the open ladder-type atomic system of the 5S(1/2) (F = 1)-5P(3/2) (F' = 0, 1, 2)-5D(5/2) (F″ = 1, 2, 3) transitions in (87)Rb atoms. As the coupling laser intensity was increased, the resonant TPA was transformed to EIT for the 5S(1/2) (F = 1)-5P(3/2) (F' = 2)-5D(5/2) (F″ = 3) transition. The transformation of resonant TPA into EIT was numerically calculated for various coupling laser intensities, considering all the degenerate magnetic sublevels of the 5S(1/2)-5P(3/2)-5D(5/2) transition. From the numerical results, the crossover from TPA to EIT could be understood by the decomposition of the spectrum into an EIT component owing to the pure two-photon coherence and a TPA component caused by the mixed term.
We have experimentally and theoretically studied resonant two-photon absorption (TPA) and electromagnetically induced transparency (EIT) in the open ladder-type atomic system of the 5S(1/2) (F = 1)-5P(3/2) (F' = 0, 1, 2)-5D(5/2) (F″ = 1, 2, 3) transitions in (87)Rb atoms. As the coupling laser intensity was increased, the resonant TPA was transformed to EIT for the 5S(1/2) (F = 1)-5P(3/2) (F' = 2)-5D(5/2) (F″ = 3) transition. The transformation of resonant TPA into EIT was numerically calculated for various coupling laser intensities, considering all the degenerate magnetic sublevels of the 5S(1/2)-5P(3/2)-5D(5/2) transition. From the numerical results, the crossover from TPA to EIT could be understood by the decomposition of the spectrum into an EIT component owing to the pure two-photon coherence and a TPA component caused by the mixed term.
We report on three-photon electromagnetically induced absorption (TPEIA) due to three-photon coherence in ladder-type atomic systems for the 5S1/25{S}_{1/2}5S1/2​-5P3/25{P}_{3/2}5P3/2​-5D5/25{D}_{5/2}5D5/2​ transition in Rb atoms. When a counterpropagating coupling field was added to the typical ladder-type electromagnetically induced transparency (EIT) experiment, both EIT and two-photon absorption (TPA) switched to TPEIA. Considering three-photon coherence in a Doppler-broadened three-level ladder-type atomic system, the spectrum of the switch from EIT and TPA to TPEIA was numerically calculated and could be understood by decomposing the calculated spectrum into two-photon coherence and three-photon coherence components.
We present discrimination of the effect of one-photon and two-photon coherences in electromagnetically induced transparency for a three-level ladder-type atomic system. After the optical Bloch equations for a three-level atom, with either cycling or non-cycling transitions, were solved numerically, the solutions were averaged over the velocity distribution and finite transit time. Through this we were able to discriminate one-photon and two-photon coherence parts of the calculated spectra. We also found that the spectra showed peaks as the branching ratio of the intermediate (excited) state increased (decreased). The experimental results of previous reports [H. S. Moon, et al., Opt. Express 16, 12163 (2008); H. S. Moon and H. R. Noh, J. Phys. B 44, 055004 (2011)] could well be accounted for by this discrimination of one-photon and two-photon coherences in the transmittance signals for the simplified three-level atomic system.
We have investigated the optical pumping effects of single-resonance optical pumping (SROP) and double-resonance optical pumping (DROP) in the ladder-type electromagnetically induced transparency (EIT) of the 5S1/2–5P3/2–5D3/2 transition of 87Rb atoms. In the 5S1/2(F = 2)–5P3/2(F' = 3)–5D3/2(F'' = 2, 3) transition with the single-resonance cycling 5S1/2(F = 2)–5P3/2(F' = 3) transition, we observed the transmittance spectrum due to DROP and EIT. Based on our experimental results investigated according to the laser power (the probe and the coupling) and the coupling laser detuning, we revealed that DROP was significant for the transmittance spectrum. Particularly, in the 5S1/2(F = 2)–5P3/2(F' = 1, 2)–5D3/2(F'' = 1) transition without a cycling transition, we observed the two-photon absorption due to two-photon atomic coherence, when the probe laser power was weak and the coupling laser power was strong.
The polarization dependence of double-resonance optical pumping (DROP) in the ladder-type electromagnetically induced transparency (EIT) of the $5{S}_{1/2}\ensuremath{-}5{P}_{3/2}\ensuremath{-}5{D}_{5/2}$ transition of 87{}^{87}87Rb atoms is studied. The transmittance spectra in the $5{S}_{1/2}(F=2)\ensuremath{-}5{P}_{3/2}({F}^{\ensuremath{'}}=3)\ensuremath{-}5{D}_{5/2}({F}^{\ensuremath{'}\ensuremath{'}}=2,3,4)$ transition were observed as caused by EIT, DROP, and saturation effects in the various polarization combinations between the probe and coupling lasers. The features of the double-structure transmittance spectra in the $5{S}_{1/2}(F=2)\ensuremath{-}5{P}_{3/2}({F}^{\ensuremath{'}}=3)\ensuremath{-}5{D}_{5/2}({F}^{\ensuremath{'}\ensuremath{'}}=4)$ cycling transition were attributed to the difference in saturation effect according to the transition routes between the Zeeman sublevels and the EIT according to the two-photon transition probability.