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

Optics Express, Vol. 19, Issue 12, pp. 11128-11137 (2011)

http://dx.doi.org/10.1364/OE.19.011128

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### 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.

© 2011 OSA

## 1. Introduction

1. S. E. Harris, “Electromagnetically induced transparency,” Phys. Today **50**, 36–42 (1997). [CrossRef]

2. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. **77**, 633–673 (2005). [CrossRef]

3. A. M. Akulshin, S. Barreiro, and A. Lezama, “Electromagnetically induced absorption and transparency due to resonant two-field excitation of quasidegenerate levels in Rb vapor,” Phys. Rev. A **57**, 2996–3002 (1998). [CrossRef]

4. E. Arimondo, “Coherent population trapping in laser spectroscopy,” Prog. Opt. **35**, 257–354 (1996). [CrossRef]

5. K. J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. **66**, 2593–2596 (1991). [CrossRef] [PubMed]

6. D. Budker and M. V. Romalis, “Optical magnetometry,” Nat. Phys. **3**, 227–234 (2007). [CrossRef]

7. M. D. Lukin, “Colloquium: Trapping and manipulating photon states in atomic ensembles,” Rev. Mod. Phys. **75**, 457–472 (2003). [CrossRef]

8. K. Hammerer, A. S. Søorensen, and E. S. Polzik, “Quantum interface between light and atomic ensembles,” Rev. Mod. Phys. **82**, 1041–1093 (2010). [CrossRef]

9. C. Y. Ye and A. S. Zibrov, “Width of the electromagnetically induced transparency resonance in atomic vapor,” Phys. Rev. A **65**, 023806 (2002). [CrossRef]

11. J. I. Kim, D. Haubrich, B. Kloter, and D. Meschede, “Strong effective saturation by optical pumping in three-level systems,” Phys. Rev. A **80**, 063801 (2009). [CrossRef]

12. R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Two-photon effects in continuous-wave electromagnetically-induced transparency,” Opt. Commun. **119**, 61–68 (1995). [CrossRef]

17. H. S. Moon, L. Lee, and J. B. Kim, “Coupling-intensity effects in ladder-type electromagnetically induced transparency of rubidium atoms,” J. Opt. Soc. Am. B **22**, 2529–2533 (2005). [CrossRef]

18. J. J. Clarke, W. A. van Wijngaarden, and H. Chen, “Electromagnetically induced transparency using a vapor cell and a laser-cooled sample of cesium atoms,” Phys. Rev. A **64**, 023818 (2001). [CrossRef]

19. B. Yang, Q. Liang, J. He, T. Zhang, and J. Wang, “Narrow-linewidth double-resonance optical pumping spectrum due to electromagnetically induced transparency in ladder-type inhomogeneously broadened media,” Phys. Rev. A **81**, 043803 (2010). [CrossRef]

20. N. Hayashi, A. Fujisawa, H. Kido, K. Takahashi, and M. Mitsunaga, “Interference between electromagnetically induced transparency and two-step excitation in three-level ladder systems,” J. Opt. Soc. Am. B **27**, 1645–1650 (2010). [CrossRef]

21. T. Y. Abi-Salloum, “Quantum interference between competing optical pathways in a three-level ladder system,” J. Mod. Opt. **57**, 1366–1376 (2010). [CrossRef]

*et al.*conducted an experimental and theoretical study on the interference between EIT and two-step excitation in three-level ladder systems [20

20. N. Hayashi, A. Fujisawa, H. Kido, K. Takahashi, and M. Mitsunaga, “Interference between electromagnetically induced transparency and two-step excitation in three-level ladder systems,” J. Opt. Soc. Am. B **27**, 1645–1650 (2010). [CrossRef]

## 2. Theory

*S*

_{1/2}−5

*P*

_{3/2}−5

*D*

_{5/2,3/2}of

^{87}Rb atoms. Figure 1(b) shows the EIT signals, this figure was previously published in [22

22. H. S. Moon, L. Lee, and J. B. Kim, “Double resonance optical pumping effects in electromagnetically induced transparency,” Opt. Express **16**, 12163–12170 (2008). [CrossRef] [PubMed]

23. H. S. Moon and H. R. Noh, “Optical pumping effects in ladder-type electromagnetically induced transparency of 5S_{1/2}−5P_{3/2}−5D_{3/2} transition of ^{87}Rb atoms,” J. Phys. B **44**, 055004 (2011). [CrossRef]

*P*

_{3/2}(

*F′*= 3) to 5

*D*

_{5/2}(

*F″*= 4), which is attributed to the EIT effect [22

22. H. S. Moon, L. Lee, and J. B. Kim, “Double resonance optical pumping effects in electromagnetically induced transparency,” Opt. Express **16**, 12163–12170 (2008). [CrossRef] [PubMed]

*P*

_{3/2}(

*F′*= 2) to 5

*D*

_{3/2}(

*F″*= 1), which was ascribed to a two-photon absorption signal [23

23. H. S. Moon and H. R. Noh, “Optical pumping effects in ladder-type electromagnetically induced transparency of 5S_{1/2}−5P_{3/2}−5D_{3/2} transition of ^{87}Rb atoms,” J. Phys. B **44**, 055004 (2011). [CrossRef]

22. H. S. Moon, L. Lee, and J. B. Kim, “Double resonance optical pumping effects in electromagnetically induced transparency,” Opt. Express **16**, 12163–12170 (2008). [CrossRef] [PubMed]

25. H. R. Noh and H. S. Moon, “Calculation of line shapes in double-resonance optical pumping,” Phys. Rev. A **80**, 022509 (2009). [CrossRef]

*P*

_{3/2}(

*F′*= 3)] to the ground state [5

*S*

_{1/2}(

*F*= 2)] is

*b*

_{1}= 1, whereas that of the excited state [5

*D*

_{5/2}(

*F″*= 4)] to the intermediate state [5

*P*

_{3/2}(

*F′*= 3)] is

*b*

_{2}= 0.74. Although we mentioned that transition 5

*S*

_{1/2}(

*F*= 2)–5

*P*

_{3/2}(

*F′*= 3)−5

*D*

_{5/2}(

*F″*= 4) was cycling, accurately speaking, the excited state has a decay channel to 6

*P*

_{3/2}. However, since the branching ratio is quite large and the transition strength is strong, the assumption of a cycling transition is still approximately correct. In the case of signal (B) in Fig. 1(b), the branching ratios are

*b*

_{1}≠ 1 and

*b*

_{2}≠ 1. The branching ratios for the signals (C) in Fig. 1(b) are

*b*

_{1}= 1 and

*b*

_{2}≠ 1. The difference between (A) and (C) lies in the magnitude of

*b*

_{2}. In the case of (C),

*b*

_{2}is much smaller than 0.74. In Fig. 1(b), we can say, roughly, that when

*b*

_{1}= 1 (

*b*≠ 1) we have transmittance (absorption) signals. The discussion for these observations will be given later.

*e*〉, |

*i*〉, and |

*g*〉, respectively. The resonant wavelength between the states |

*i*〉 and |

*g*〉, which is the probe line, is

*λ*

_{1}. In our calculation

*λ*

_{1}was chosen as 780.2 nm, which is the resonant wavelength for the 5

*S*

_{1/2}–5

*P*

_{3/2}transition line in Rb atoms. The probe laser frequency is scanned near this transition line. The coupling laser of the wavelength

*λ*

_{2}is fixed at the transition between

*|e*〉 and

*|i*〉. In our calculations

*λ*

_{2}was 775.8 nm, which is the resonant line for 5

*P*

_{3/2}−5

*D*

_{3/2,5/2}. The decay rates of the excited and the intermediate states are

*γ*

_{2}(= 2

*π*× 0.97 MHz) and

*γ*

_{1}(= 2

*π*× 6 MHz) [26

26. P. Siddons, C. S. Adams, C. Ge, and I. G. Hughes, “Absolute absorption on rubidium D lines: comparison between theory and experiment,” J. Phys. B **41**, 155004 (2008). [CrossRef]

*b*

_{2}and

*b*

_{1}, respectively. Therefore, when

*b*

_{1}=

*b*

_{2}= 1, the three-level system is cycling, whereas the system becomes open when either

*b*

_{1}≠ 1 or

*b*

_{2}≠ 1.

13. J. Gea-Banacloche, Y.-Q. Li, S.-Z. Jin, and M. Xiao, “Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: theory and experiment,” Phys. Rev. A **51**, 576–584 (1995). [CrossRef] [PubMed]

_{1}(Ω

_{2}) is the Rabi frequency of the probe (coupling) beam. In the optical Bloch equations,

*p*denotes the population of the state |

_{j}*j*〉 and

*ρ*is the coherence between the states |

_{j j′}*j*〉 and |

*j′*〉 with

*j, j′*=

*e,i,g*. The absorption coefficient of the probe beam is then given by

*δ*

_{p}(=

*ω*

_{1}−

*ω*

_{10}) and

*δ*

_{c}(=

*ω*

_{2}−

*ω*

_{20}) are the detunings of the probe and coupling lasers, respectively, where

*ω*

_{1(2)}= 2

*πc*/

*λ*

_{1(2)}and

*ω*

_{10(20)}are the resonant frequencies between the states |

*i*〉 and |

*g*〉 (|

*e*〉 and |

*i*〉).

*δ*

_{1(2)}is the effective detuning of the probe (pump) beam felt by an atom moving at velocity

*v*, and is given by

*δ*

_{1(2)}=

*δ*

_{p(c)}−

*k*

_{1(2)}

*v*. While we have

*k*

_{1}= 2

*π/λ*

_{1}for both schemes, we assume

*k*

_{2}= +(−)2

*π/λ*

_{2}for the copropagating (counterpropagating) scheme.

*t*in Eq. (5) is now given by

*α*

_{0}(

*δ*–

_{p}*k*

_{1}

*v*,

*δ*–

_{c}*k*

_{2}

*v*,

*t*), it must be averaged over the Maxwell-Boltzmann velocity distribution as follows [27]: where

*u*= (2

*k*

_{B}*T/M*)

^{1/2}is the most probable speed (

*T*= temperature of the vapor cell;

*M*= the mass of an atom). Finally, the signals must be averaged over the interaction time while the atoms are crossing the laser beam as follows:

*d*being the diameter of the laser beam [28

28. J. Sagle, R. K. Namiotka, and J. Huennekens, “Measurement and modelling of intensity dependent absorption and transit relaxation on the cesium D1 line,” J. Phys. B **29**, 2629–2643 (1996). [CrossRef]

*e*

^{−αl}where

*l*is the length of the cell, it is roughly proportional to Im

*ρ*. In what follows, we calculate and discuss the transmittance in terms of Im

_{ig}*ρ*. Using the rate equation approximation and solving the steady-state solutions of Eq. (4), Im

_{ig}*ρ*can be expressed in terms of populations (

_{ig}*p*and

_{i}*p*) and coherence (

_{g}*ρ*) as follows: Since the first term on the right-hand side of Eq. (6) consists of the populations of the intermediate and ground states, it represents the contribution of one-photon resonance in the spectrum. In contrast, the second term on the right-hand side of Eq. (6) is composed of the coherence between the excited and ground states. Thus, it refers to the contribution of the two-photon coherence effect. Therefore, we can discriminate the portion of one-photon and two-photon coherence parts in the transmittance signal.

_{eg}_{1},

_{1}(not shown) represent the background signal of the probe beam. The diagram for

_{1}[13

13. J. Gea-Banacloche, Y.-Q. Li, S.-Z. Jin, and M. Xiao, “Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: theory and experiment,” Phys. Rev. A **51**, 576–584 (1995). [CrossRef] [PubMed]

14. S. Wielandy and A. L. Gaeta, “Investigation of electromagnetically induced transparency in the strong probe regime,” Phys. Rev. A **58**, 2500–2505 (1998). [CrossRef]

_{2}are not shown. The next one for

_{2}are not shown. It should be noted that the interaction of five photons for the term

_{1}) and the other is the TPA term (∝

*n*≥ 5) is much smaller than the EIT term, we define all interactions except EIT (∝ Ω

_{1}) as TPA term roughly.

*ρ*on the right-hand side of Eq. (6) can be expressed in terms of the populations from the steady-state solutions of Eqs. (2)–(4). Thus, the second term on the right-hand side of Eq. (6) is given by: where Δ

_{eg}_{0}≡ 2(

*δ*

_{1}+

*δ*

_{2}) +

*iγ*

_{2}, Δ

_{1}≡ 2

*δ*

_{1}+

*iγ*

_{1}, and Δ

_{2}≡ 2

*δ*

_{2}+

*i*(

*γ*

_{1}+

*γ*

_{2}). Therefore, the EIT term, which is proportional to Ω

_{1}can be obtained by setting

*p*=

_{e}*p*= 0 and

_{i}*p*= 1 in Eq. (7). Thus we can obtain the explicit form of the contribution of the EIT effect in Eq. (6) as follows: We can see that the EIT term is independent of the branching ratios. The TPA contribution can be calculated by subtracting the EIT contribution from the two-photon coherence term in Eq. (6) or from Eq. (7). This EIT contribution will be discussed later by decomposing the two-photon coherence signal into the EIT part and TPA part in next section.

_{g}## 3. Calculated Results

*δ*, while

_{p}*δ*is fixed at 0, 250 MHz, 500 MHz, and 750 MHz, and where the lasers are set in a counterpropagating scheme. In Fig. 4, the Rabi frequencies were Ω

_{c}_{1}= 0.2

*γ*

_{1}and Ω

_{2}= 2.5

*γ*

_{2}, and the diameter of the laser beam was 1.5 mm. When the coupling laser is fixed at the resonance frequency, we could find a striking contribution from the two-photon coherence term in the signal. As the frequency of the coupling laser is detuned far from the resonance while at the same time the two-photon resonance condition is maintained, the one-photon resonance part is suppressed and becomes the same as that of the background signal. This is because the one-photon resonance part results from the single resonance between the ground and the intermediate states. In contrast, we found that the signal for the copropagating scheme was mainly composed of the one-photon resonance part, as shown in Fig. 4(b). It is quite reasonable that the effect of two-photon coherence is large for the counterpropagating scheme and small for the copropagating scheme. This is because the large effect of two-photon coherence for the counterpropagating scheme results from the fact that the sub-Doppler resonance condition can be satisfied for quite a broad range of velocity. The results in Fig. 4 verify that the discrimination of the one-photon and two-photon coherence parts in Eq. (6) is correct.

*b*

_{1}and

*b*

_{2}. Figure 5(a) [5(b)] shows the signals and their one-photon resonance part [two-photon coherence part] as a function of

*δ*where

_{p}*δ*= 0. The opposite case, the scanning of

_{c}*δ*, shows similar behavior to Fig. 5. The Rabi frequencies were Ω

_{c}_{1}= 0.2

*γ*

_{1}and Ω

_{2}= 2.5

*γ*

_{2}, and the diameter of the laser beam was 1.5 mm. In Fig. 5(a), when the transition line for the probe beam is cycling (

*b*

_{1}= 1), and as the branching ratio of the excited state (

*b*

_{2}) decreases (from left to the right at the lowest row), i.e., the leakage increases, the magnitude of the transmittance signal increases. At the same time, the relative contribution of the one-photon resonance effect does not change significantly. In contrast, as shown in the first panel of Fig. 5(a), with

*b*

_{2}= 1, as the branching ratio of the intermediate state into the ground state (

*b*

_{1}) decreases, the transmission peak changes into a transmission dip very quickly. In particular, the contribution of the one-photon resonance part shows abrupt variation.

*ṗ*+

_{e}*ṗ*+

_{i}*ṗ*= − (1 −

_{g}*b*

_{1})

*γ*

_{1}

*p*− (1 −

_{i}*b*

_{2})

*γ*

_{2}

*p*. Therefore, the decay rate of the leakage of the total population is given by As can be seen in Fig. 5, as the branching ratios decrease, i.e., the leakage increases, and the transmission increases. This is because the population of the ground state is decreased due to increased optical pumping. However, in order to understand the behavior of the signals as a function of on the branching ratios, it is necessary to know the behavior of the populations at

_{e}*δ*= ∞ and

_{p}*δ*= 0. Although the results with the scanned

_{p}*δ*are shown in Fig. 5, it is more convenient to explain the behavior of the spectrum by using a scanned

_{p}*δ*and a fixed

_{c}*δ*= 0 configuration. Assuming

_{p}*δ*= 0, let us consider the populations at

_{p}*δ*= ∞ and at the atomic transit time. As the detuning approaches

_{c}*δ*= 0,

_{c}*p*decreases, while

_{i}*p*increases due to the increased transition rate. Therefore, as can be seen in Eq. (9), the first term decreases and the second term increases. Thus, at

_{e}*b*

_{2}= 0 and

*b*

_{1}≠ 0, i.e., in the presence of leakage from the intermediate state, the leakage of the population at

*δ*= 0 is weaker than at

_{c}*δ*= ∞. Therefore, the population at

_{c}*δ*= 0 is greater than that at

_{c}*δ*= ∞. Accordingly, the absorption becomes larger, and the transmission becomes smaller. Thus, we observe the dip signals as shown in Fig. 5(a). In addition, at

_{c}*b*

_{2}≠ 0 and

*b*

_{1}= 0, we can do a similar analysis to before. Therefore, we can observe the peak signal. To sum up, the behavior of the one-photon resonance component of the spectra shown in Fig. 5(a) can be approximately explained in terms of the population leakage. The results in Fig. 5 show also that the branching ratio of the intermediate state (

*b*

_{1}) plays an important role in forming the shape of the signal.

*b*

_{1}=

*b*

_{2}= 1), we observe a transmittance signal, which is composed of transmittance (EIT) and an absorptive (TPA) signals. As the leakage of the population increases, the spectrum shows dip signals. As the leakage increases further, the dip signals also increase. Unlike the behavior of the one-photon resonance part, the two-photon component shows dip signals regardless of the branching ratio. Because the strength of the EIT is independent of branching ratio, it remains constant regardless of the branching ratios. In contrast, the dip signal in the TPA part increases more as the leakage increases (branching ratios decrease). This is because the two-photon absorption process is expedited as the decay into states other than the ground state increases. The width of the two-photon resonance signal looks comparable to that of the one-photon resonance signal. This is because of the slight difference in the wavelengths of the probe and the coupling lasers. When

*δ*= 0, two-photon resonance occurs at the frequency of

_{p}*v*. Therefore, considering the Maxwell-Boltzmann velocity distribution, we observe a broad two-photon resonance signal.

*b*

_{1}≃ 1. This corresponds to all signals except for (B) in Fig. 1(a). Therefore, we conclude that the peak signals in Fig. 1(a) are mostly composed of the one-photon resonance component. In contrast, in the case of signal (A), because of the strong transition strength, the two-photon coherence component exists as a relatively narrow signal on top of the broad one-photon resonance signal. As explained above, because the two-photon coherence signal is not so much narrower than the one-photon resonance signal, the two-photon resonance component contributed to the broad signal in signal (A) in Fig. 1(a) to a certain extent. If we are to discriminate the two-photon component accurately in signal (A) in Fig. 1(a), it is necessary to accurately calculate the signal by taking into account all the substates of the energy level. When the intermediate state has a decay rate (

*b*

_{1}≠ 1), we have a dip signal. This corresponds to signal (B) in Fig. 1(a). As can be seen in Fig. 5(a), both the one-photon and two-photon coherence components contribute to the overall dip signal.

## 4. Conclusions

*δ*= ∞ and

_{c}*δ*= 0. The total population at

_{c}*δ*= 0 is smaller than that at

_{c}*δ*= 0 when the excited (intermediate) state is not cycling. Therefore, the signal peaked as the branching ratio of the intermediate (excited) states increased (decreased). In order to more accurately explain these phenomena, a more elaborate calculation for real atoms is necessary. This calculation is currently being undertaken.

_{c}## Acknowledgments

## References and links

1. | S. E. Harris, “Electromagnetically induced transparency,” Phys. Today |

2. | M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. |

3. | A. M. Akulshin, S. Barreiro, and A. Lezama, “Electromagnetically induced absorption and transparency due to resonant two-field excitation of quasidegenerate levels in Rb vapor,” Phys. Rev. A |

4. | E. Arimondo, “Coherent population trapping in laser spectroscopy,” Prog. Opt. |

5. | K. J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. |

6. | D. Budker and M. V. Romalis, “Optical magnetometry,” Nat. Phys. |

7. | M. D. Lukin, “Colloquium: Trapping and manipulating photon states in atomic ensembles,” Rev. Mod. Phys. |

8. | K. Hammerer, A. S. Søorensen, and E. S. Polzik, “Quantum interface between light and atomic ensembles,” Rev. Mod. Phys. |

9. | C. Y. Ye and A. S. Zibrov, “Width of the electromagnetically induced transparency resonance in atomic vapor,” Phys. Rev. A |

10. | W. Jiang, Q.-F. Chen, Y.-S. Zhang, and G.-C. Guo, “Optical pumping-assisted electromagnetically induced transparency,” Phys. Rev. A |

11. | J. I. Kim, D. Haubrich, B. Kloter, and D. Meschede, “Strong effective saturation by optical pumping in three-level systems,” Phys. Rev. A |

12. | R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Two-photon effects in continuous-wave electromagnetically-induced transparency,” Opt. Commun. |

13. | J. Gea-Banacloche, Y.-Q. Li, S.-Z. Jin, and M. Xiao, “Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: theory and experiment,” Phys. Rev. A |

14. | S. Wielandy and A. L. Gaeta, “Investigation of electromagnetically induced transparency in the strong probe regime,” Phys. Rev. A |

15. | D. McGloin, M. H. Dunn, and D. J. Fulton, “Polarization effects in electromagnetically induced transparency,” Phys. Rev. A |

16. | S. D. Badger, I. G. Hughes, and C. S. Adams, “Hyperfine effects in electromagnetically induced transparency,” J. Phys. B |

17. | H. S. Moon, L. Lee, and J. B. Kim, “Coupling-intensity effects in ladder-type electromagnetically induced transparency of rubidium atoms,” J. Opt. Soc. Am. B |

18. | J. J. Clarke, W. A. van Wijngaarden, and H. Chen, “Electromagnetically induced transparency using a vapor cell and a laser-cooled sample of cesium atoms,” Phys. Rev. A |

19. | B. Yang, Q. Liang, J. He, T. Zhang, and J. Wang, “Narrow-linewidth double-resonance optical pumping spectrum due to electromagnetically induced transparency in ladder-type inhomogeneously broadened media,” Phys. Rev. A |

20. | N. Hayashi, A. Fujisawa, H. Kido, K. Takahashi, and M. Mitsunaga, “Interference between electromagnetically induced transparency and two-step excitation in three-level ladder systems,” J. Opt. Soc. Am. B |

21. | T. Y. Abi-Salloum, “Quantum interference between competing optical pathways in a three-level ladder system,” J. Mod. Opt. |

22. | H. S. Moon, L. Lee, and J. B. Kim, “Double resonance optical pumping effects in electromagnetically induced transparency,” Opt. Express |

23. | H. S. Moon and H. R. Noh, “Optical pumping effects in ladder-type electromagnetically induced transparency of 5S |

24. | H. S. Moon, L. Lee, and J. B. Kim, “Double resonance optical pumping of Rb atoms,” J. Opt. Soc. Am. B |

25. | H. R. Noh and H. S. Moon, “Calculation of line shapes in double-resonance optical pumping,” Phys. Rev. A |

26. | P. Siddons, C. S. Adams, C. Ge, and I. G. Hughes, “Absolute absorption on rubidium D lines: comparison between theory and experiment,” J. Phys. B |

27. | D. Meschede, |

28. | J. Sagle, R. K. Namiotka, and J. Huennekens, “Measurement and modelling of intensity dependent absorption and transit relaxation on the cesium D1 line,” J. Phys. B |

**OCIS Codes**

(020.1670) Atomic and molecular physics : Coherent optical effects

(020.3690) Atomic and molecular physics : Line shapes and shifts

(020.4180) Atomic and molecular physics : Multiphoton processes

(300.6210) Spectroscopy : Spectroscopy, atomic

**ToC Category:**

Atomic and Molecular Physics

**History**

Original Manuscript: April 11, 2011

Revised Manuscript: May 16, 2011

Manuscript Accepted: May 17, 2011

Published: May 23, 2011

**Citation**

Heung-Ryoul Noh and Han Seb Moon, "Discrimination of one-photon and two-photon coherence parts in electromagnetically induced transparency for a ladder-type three-level atomic system," Opt. Express **19**, 11128-11137 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-12-11128

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### References

- S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50, 36–42 (1997). [CrossRef]
- M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005). [CrossRef]
- A. M. Akulshin, S. Barreiro, and A. Lezama, “Electromagnetically induced absorption and transparency due to resonant two-field excitation of quasidegenerate levels in Rb vapor,” Phys. Rev. A 57, 2996–3002 (1998). [CrossRef]
- E. Arimondo, “Coherent population trapping in laser spectroscopy,” Prog. Opt. 35, 257–354 (1996). [CrossRef]
- K. J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991). [CrossRef] [PubMed]
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