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Optics Express

Discrimination of one-photon and two-photon coherence parts in electromagnetically induced transparency for a ladder-type three-level atomic system

Heung‐Ryoul Noh, Han Seb Moon

Published May 23, 2011• 40 citations
Publisher

Abstract

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.

DOI
10.1364/oe.19.011128

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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 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{}^{87}87Rb 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.
We present a diagrammatic method for complete characterization of multiphoton processes in three-level atomic systems. By considering the interaction routes of the coupling and probe photons for a ladder-type, three-level, noncycling (or cycling) atomic system, we are able to completely discriminate between the pure one-photon and the pure two-photon resonance effects, and the effect of their combination in electromagnetically induced transparency (EIT) using our diagrammatic method. We show that the proposed diagrammatic method is very useful for the analysis of multiphoton processes in ladder-type EIT.
We investigated the relationship between two- and three-photon coherence in terms of the transition routes and coupling field intensities in a Doppler-broadened ladder-type atomic system for the 5S1/2–5P3/2–5D5/2 transition in 87Rb atoms. Three-photon electromagnetically induced absorption (TPEIA) due to three-photon coherence was observed in the only transition route that exhibited a dominant two-photon coherence effect. We showed that two-photon coherence is a necessary condition for three-photon coherence phenomena. A comparison of the relative magnitudes of the electromagnetically induced transparency and TPEIA as a function of the coupling field intensity revealed that the increase of three-photon coherence was faster than that of two-photon coherence. Considering three-photon coherence in a Doppler-broadened ladder-type three-level atomic system, the relation between two- and three-photon coherence was numerically calculated.
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 investigated the relationship between two- and three-photon coherence in terms of the transition routes and coupling field intensities in a Doppler-broadened ladder-type atomic system for the 5S(1/2)-5P(3/2)-5D(5/2) transition in (87)Rb atoms. Three-photon electromagnetically induced absorption (TPEIA) due to three-photon coherence was observed in the only transition route that exhibited a dominant two-photon coherence effect. We showed that two-photon coherence is a necessary condition for three-photon coherence phenomena. A comparison of the relative magnitudes of the electromagnetically induced transparency and TPEIA as a function of the coupling field intensity revealed that the increase of three-photon coherence was faster than that of two-photon coherence. Considering three-photon coherence in a Doppler-broadened ladder-type three-level atomic system, the relation between two- and three-photon coherence was numerically calculated.
Ladder-type electromagnetically induced transparency (EIT) and two-photon absorption (TPA) under a low-light level of probe (0.2 μW/cm2(0.06Γ2)) and weak coupling power for a cesium atom at room temperature are investigated. Reduction of the fluorescence on the TPA in a three-level system via EIT interference is clearly observed and analyzed under the low probe Rabi frequency of about 0.30 MHz to avoid the affects from the vicinity of intermediate hyperfine states. The transparency ratio of EIT derived from the reduction of fluorescence is about 25%. Additionally, the EIT linewidth observed can be as narrow as 2.64 MHz, while the coupling Rabi frequency is around 2.66 MHz. By solving the steady-state optical Bloch equations, the numerical simulation spectra are in good agreement with EIT and TPA. According to our investigations, the Doppler velocity averaging effect over the thermal atoms reducing the linewidth of the EIT signal proves the advantage of observing the EIT in the room-temperature cell.