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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 12 — Jun. 6, 2011
  • pp: 11128–11137
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Discrimination of one-photon and two-photon coherence parts in electromagnetically induced transparency for a ladder-type three-level atomic system

Heung-Ryoul Noh and Han Seb Moon  »View Author Affiliations


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

Atomic coherence plays an important role in various spectroscopies including electromagnetically induced transparency (EIT) [1

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

, 2

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

], electromagnetically induced absorption (EIA) [3

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]

], and coherent population trapping (CPT) [4

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

]. Of these, EIT in particular has drawn considerable interest since the discovery of this phenomenon [5

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

] owing to its various potential applications such as precision magnetometers [6

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

], slow light and light storage [7

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

], and quantum information [8

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]

]. Although a basic underlying mechanism in EIT is known to be a two-photon atomic coherence resulting from a coherent interaction of the coupling and probe lasers with atoms, the optical pumping, in other words, the effect of one-photon resonance also affects the lineshapes in EIT significantly. The effect of optical pumping on the EIT lineshape was investigated in several papers, especially for the Λ-type atomic system [9

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

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]

].

2. Theory

Figure 1(a) shows the energy level diagram for the transitions 5S 1/2−5P 3/2−5D 5/2,3/2 of 87Rb 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

23. H. S. Moon and H. R. Noh, “Optical pumping effects in ladder-type electromagnetically induced transparency of 5S1/2−5P3/2−5D3/2 transition of 87Rb atoms,” J. Phys. B 44, 055004 (2011). [CrossRef]

], and many places. In Fig. 1(b), we observe three kinds of signals: signal (A) shows the double structure observed in the case of a transition from 5P 3/2(F′ = 3) to 5D 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]

]. The signal (B) is absorptive for the transition from 5P 3/2(F′ = 2) to 5D 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 5S1/2−5P3/2−5D3/2 transition of 87Rb atoms,” J. Phys. B 44, 055004 (2011). [CrossRef]

]. The final one (C) is the peak for the other four signals. These transmittance signals were attributed to the effect of a double resonance optical pumping (DROP) [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]

25

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

]. In this paper, we accurately interpret the observed signals by means of discrimination of one-photon and two-photon coherences.

Fig. 1 (a) Energy level diagram for the transitions 5S 1/2−5P 3/2−5D 5/2,3/2 of 87Rb atoms. The frequencies are expressed in units of MHz. (b) The observed EIT signals.

As can be seen in Fig. 1(b), there exists a variety of signals in the spectra. This variety mainly results from the branching ratio of the excited or intermediate levels. In the case of signal (A) in Fig. 1(b), the branching ratio of the intermediate state [5P 3/2(F′ = 3)] to the ground state [5S 1/2(F = 2)] is b 1 = 1, whereas that of the excited state [5D 5/2(F″ = 4)] to the intermediate state [5P 3/2(F′ = 3)] is b 2 = 0.74. Although we mentioned that transition 5S 1/2(F = 2)–5P 3/2(F′ = 3)−5D 5/2(F″ = 4) was cycling, accurately speaking, the excited state has a decay channel to 6P 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.

In order to study the effect of the branching ratios on the EIT spectra, we employed a simplified three-level ladder-type system, as shown in Fig. 2. In Fig. 2, the excited, intermediate, and ground states are denoted by |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 5S 1/2–5P 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 5P 3/2−5D 3/2,5/2. The decay rates of the excited and the intermediate states are γ 2(= 2π × 0.97 MHz) and γ 1(= 2π × 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]

], respectively. The branching ratios of the excited and intermediate states are defined to be 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.

Fig. 2 Energy level diagram of the simple three-level ladder-type atomic system.

Using the usual density matrix equation, the optical Bloch equations for each density matrix element can be derived (e.g. Eq. (1) in Ref. [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]

]). From the optical Bloch equations, the equations for the populations are
p˙e=γ2pe+i2Ω2(ρeiρie),p˙i=γ1pi+b2γ2pei2Ω2(ρeiρie)+i2Ω1(ρigρgi),p˙g=b1γ1pii2Ω1(ρigρgi),
(1)
and the equations for the coherences can be written as follows:
ρ˙ei=(γ1+γ22+iδ2)ρei+i2Ω2(pepi)+i2Ω1ρeg,
(2)
ρ˙eg=(γ22+i(δ1+δ2))ρeg+i2Ω1ρeii2Ω2ρig,
(3)
ρ˙ig=(γ12+iδ1)ρig+i2Ω1(pipg)i2Ω2ρeg,
(4)
where Ω12) is the Rabi frequency of the probe (coupling) beam. In the optical Bloch equations, pj denotes the population of the state |j〉 and ρj j′ is the coherence between the states |j〉 and |j′〉 with j, j′ = e,i,g. The absorption coefficient of the probe beam is then given by
α0=Nat3λ122πγ1Ω1Imρig.
(5)
δ p(= ω 1ω 10) and δ c(= ω 2ω 20) are the detunings of the probe and coupling lasers, respectively, where ω 1(2) = 2πc/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 = 2π/λ 1 for both schemes, we assume k 2 = +(−)2π/λ 2 for the copropagating (counterpropagating) scheme.

Since the absorption coefficient at a given time t in Eq. (5) is now given by α 0(δpk 1 v, δck 2 v,t), it must be averaged over the Maxwell-Boltzmann velocity distribution as follows [27

27. D. Meschede, Optics, Light and Lasers (Wiley-VCH, 2007).

]:
α1(t)=dve(v/u)2πuα0(δpk1v,δck2v,t),
where u = (2kB 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: α=(1/tav)0tavα1(t)dt, where tav=(=(π/2)d/u) is the average transit time with 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]

].

Since the transmittance is given approximately by e αl where l is the length of the cell, it is roughly proportional to Imρig. In what follows, we calculate and discuss the transmittance in terms of Imρig. Using the rate equation approximation and solving the steady-state solutions of Eq. (4), Imρig can be expressed in terms of populations (pi and pg) and coherence (ρeg) as follows:
Imρig=γ1Ω14δ12+γ12(pipg)+Im[Ω22δ1+iγ1ρeg].
(6)
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.

Fig. 3 Diagrams of interaction pathways for (a) one-photon and (b) two-photon coherences.

3. Calculated Results

We study the validity of the discrimination between the two contributions in Eq. (6) by averaging the solutions of the optical Bloch equations over the various velocities and atomic transit times. Figure 4(a) shows the spectra as a function of δp, while δc 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 Ω1 = 0.2γ 1 and Ω2 = 2.5γ 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.

Fig. 4 (a) Transmittance signals at various detunings of the coupling laser for a counter-propagating scheme. (b) Transmittance signals for a copropagating scheme.

In order to study the phenomena shown in Fig. 1(b) in ladder-type three-level atoms, we calculated the imaginary part of the coherence between the intermediate and the ground states by varying the values of 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 δp where δc = 0. The opposite case, the scanning of δc, shows similar behavior to Fig. 5. The Rabi frequencies were Ω1 = 0.2γ 1 and Ω2 = 2.5γ 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.

Fig. 5 Branching ratio dependence of the signals: (a) Total and one-photon resonance part, (b) Two-photon coherence part, and (c) Further discrimination of the two-photon coherence part.

From Eq. (1), we have the following equation for the populations: e + i + g = − (1 − b 1)γ 1 pi − (1 − b 2)γ 2 pe. Therefore, the decay rate of the leakage of the total population is given by
(1b1)γ1pi+(1b2)γ2pe.
(9)
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 δp = ∞ and δp = 0. Although the results with the scanned δp are shown in Fig. 5, it is more convenient to explain the behavior of the spectrum by using a scanned δc and a fixed δp = 0 configuration. Assuming δp = 0, let us consider the populations at δc = ∞ and at the atomic transit time. As the detuning approaches δc = 0, pi decreases, while pe 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 b 2 = 0 and b 1 ≠ 0, i.e., in the presence of leakage from the intermediate state, the leakage of the population at δc = 0 is weaker than at δc = ∞. Therefore, the population at δc = 0 is greater than that at δc = ∞. 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 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.

The two-photon coherence contribution of the total spectrum is presented in Fig. 5(b). Further discrimination of the two-photon coherence part using EIT and TPA is presented in Fig. 5(c). When the system is cycling (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 δp = 0, two-photon resonance occurs at the frequency of δc=2π(λ11λ21)v for atoms moving at a velocity of v. Therefore, considering the Maxwell-Boltzmann velocity distribution, we observe a broad two-photon resonance signal.

As can be seen in Fig. 5(a), the two-photon absorption contribution is much weaker than the contribution of the one-photon resonance signal when the intermediate state is almost cycling, i.e. 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

In this paper we described a theoretical study of EIT spectra for ladder-type three-level atoms. The signals are decomposed into two-parts: one is the one-photon resonance part and the other is the two-photon coherence part. We showed that the two-photon coherence part exhibited absorption and increased as the leakage to other states increased. For fixed values of the branching ratios, as the coupling laser intensity was increased, the EIT effect surpassed by the two-photon absorption effect in the two-photon resonance part of the signals. In contrast to the two-photon coherence part, the one-photon resonance part is dependent on the branching ratios. As the branching ratio of the intermediate (excited) state increased (decreased), the signals were transformed to peaks from dips. This interesting phenomenon can be understood by comparing the leakage of the populations at δc = ∞ and δc = 0. The total population at δc = 0 is smaller than that at δc = 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.

Acknowledgments

This work was supported by the Korea Research Foundation Grant funded by the Korean Government( KRF-2008-313-C00355 and 2009-0073051). Also, this work was supported by the Korea Science and Engineering Foundation(KOSEF) grant funded by the Korea government(MOST) (No. R01-2007-000-11636-0).

References and links

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]

10.

W. Jiang, Q.-F. Chen, Y.-S. Zhang, and G.-C. Guo, “Optical pumping-assisted electromagnetically induced transparency,” Phys. Rev. A 73, 053804 (2006). [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]

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]

15.

D. McGloin, M. H. Dunn, and D. J. Fulton, “Polarization effects in electromagnetically induced transparency,” Phys. Rev. A 62, 053802 (2000). [CrossRef]

16.

S. D. Badger, I. G. Hughes, and C. S. Adams, “Hyperfine effects in electromagnetically induced transparency,” J. Phys. B 34, L749–L756 (2001). [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]

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 5S1/2−5P3/2−5D3/2 transition of 87Rb atoms,” J. Phys. B 44, 055004 (2011). [CrossRef]

24.

H. S. Moon, L. Lee, and J. B. Kim, “Double resonance optical pumping of Rb atoms,” J. Opt. Soc. Am. B 24, 2157–2164 (2007). [CrossRef]

25.

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

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]

27.

D. Meschede, Optics, Light and Lasers (Wiley-VCH, 2007).

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]

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

  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]
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