Abstract

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.

© 2015 Optical Society of America

1. Introduction

Atomic coherence, which is generated by the interaction of an atom with coherent electromagnetic fields, has been studied in the field of atomic physics since coherent light sources were first developed. In particular, two-photon coherence phenomena due to the interaction of two coherent fields and a three-level atomic system, such as electromagnetically induced transparency (EIT) and electromagnetically induced absorption (EIA), are widely regarded as important [1–4]. Two-photon coherence phenomena are understood as a quantum interference effect between two quantum transitions. Recently, quantum interference effects have been intensively studied in artificial atomic systems such as superconducting circuits [5], quantum dots [6], metamaterials [7], optomechanics [8], and nitrogen vacancy centers in diamond [9], because the EIT observed in an artificial atomic system has been proved to be quantum interference.

However, multi-photon coherence effects involving more than two photons, such as three-photon electromagnetically induced absorption (TPEIA), four-wave mixing, and six-wave mixing [10–19], are also very interesting. Pandey reported significant results regarding the role of different types of multi-photon coherence, such as those in three-level Λ-type, four-level N-type, and five-level M-type systems [14]. Ben-Aroya and Eisenstein reported high-contrast TPEIA in an N-type configuration of a three-level Λ-type system interacting with three separate electromagnetic fields and proposed the application of TPEIA to a small atomic clock [15]. Many studies of multi-photon coherence have been performed in degenerate two-level, three-level Λ-type, and four-level N-type atomic systems [10–15]. Basically, those studies considered three-level Λ-type atomic systems.

Comparing ladder-type and Λ-type atomic systems, multi-photon coherence in a ladder-type atomic system has been the subject of relatively little investigation [16–20]. The spectral features of a ladder-type atomic system differ from those of a Λ-type atomic system because the decay channels of a ladder-type atomic system differ from those of a Λ-type atomic system. Understanding the multi-photon coherence phenomena in a ladder-type atomic system is meaningful because of interesting applications in quantum optics [21–23]. Recently, TPEIA in ladder-type atomic systems was experimentally demonstrated and theoretically decomposed into two-photon coherence and three-photon coherence (TPC) components [19]. Whereas the important characteristic of EIT is transmittance at a two-photon resonance, TPEIA due to TPC exhibits absorption at a three-photon resonance [14, 19]. The even- and odd-photon coherence contributed to the transmittance and absorption spectra, respectively. Although EIT and TPEIA in a ladder-type atomic system have been observed and described using a simple atomic model [19], no findings on the relationship between two- and three-photon coherence in ladder-type atomic systems have been reported.

In this paper, we examine the relationship between two- and three-photon coherence in terms of the transition route and coupling intensity in a 5S1/2–5P3/2–5D5/2 ladder-type system of 87Rb atoms. The spectral features of TPEIA in each transition between hyperfine states were investigated to confirm the relationship between two- and three-photon coherence. In addition, we measured the relative magnitudes of EIT and TPEIA as a function of the coupling field intensity to discuss the strength of TPC. To illuminate the experimental results for TPEIA and EIT, the relationship between two-photon coherence and TPC was numerically calculated using a Doppler-broadened ladder-type three-level atomic system.

2. Experimental setup

Figure 1(a) shows the three-level ladder-type atomic system interacting with a probe field (Ωp) and two coupling fields (ΩC1 and ΩC2) in the 5S1/2 –5P3/2 –5D5/2 transition of 87Rb. δp, δC1, and δC2 are the detuning frequencies from the resonances of the probe and the two coupling fields, respectively. The two-photon detuning is δp+δC1, and the three-photon detuning is δp+δC1δC2, where δC=δC1=δC2. The decay channels and transition probabilities depend on the hyperfine states of the ladder-type atomic system, which consists of a ground state (5S1/2), an intermediate state (5P3/2), and an excited state (5D5/2). The branching ratios of three-level ladder-type atomic systems determine the spectral features due to two-photon coherence.

 figure: Fig. 1

Fig. 1 (a) Energy level diagram for the 5S1/2–5P3/2–5D5/2 transitions of 87Rb (I = 3/2), (b) Experimental schematic; the probe field (Ωp) and two counter-propagating coupling fields (ΩC1 and ΩC2) in a pure Rb vapor cell (PD: photo-current detector, PBS: polarization beam splitter, QWP: quarter-wave plate, M: Mirror).

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Our experimental setup, shown in Fig. 1(b), is the same as that used for TPEIA in Doppler-broadened ladder-type atomic systems [19]. Two external cavity diode lasers (one for the Ωp field and the other for ΩC1, and ΩC2 fields) were independently operated at wavelengths of 780 nm and 775.8 nm, respectively. The linewidths of the two lasers were estimated to be less than 1 MHz. They were linearly polarized in the perpendicular direction, and the intensities of the probe and coupling lasers were 2.7 μW/mm2 and 6.5 mW/mm2, respectively. The probe and coupling fields counter-propagate through an 5cm-long pure Rb atom vapor cell, and the mirror-reflected coupling field roles as the ΩC2 field whose power was adjusted by rotating quarter-wave plate. All of three fields completely overlap. The temperature of vapor cell was not controlled in a room-temperature. The effect of the Earth’s magnetic field was minimized by having the vapor cell be housed in three-layers μ-metal chamber. Although the two coupling fields (ΩC1 and ΩC2) are counter-propagated like a standing-wave coupling field, TPC does not require spatial intensity modulation of the coupling fields. To measure the atomic coherence effects when the probe or coupling laser frequency is scanned, the probe field was measured using a photocurrent detector.

3. Experimental results and discussion

The ladder-type EIT and TPEIA of the 5S1/2–5P3/2–5D5/2 transition of 87Rb are the transmittance due to two-photon coherence and absorption due to TPC, respectively, as shown in Figs. 2(a) and 2(b). To investigate the relationship between the EIT and TPEIA in terms of the transition routes, we observed the EIT and TPEIA spectra using both methods, scanning the probe and coupling laser frequencies, respectively. In particular, we focused on the spectral features at the 5S1/2(F = 2)–5P3/2(F′ = 3)–5D5/2(F″ = 4) transition, considering a simple three-level ladder-type atomic system.

 figure: Fig. 2

Fig. 2 (a) EIT and TPEIA spectra as a function of the detuning frequency of the probe laser, where the frequency of the coupling laser is fixed at the 5P3/2(F′ = 3)–5D5/2(F″ = 4) transition. (b) EIT and TPEIA spectra as a function of the detuning frequency of the coupling laser, where the frequency of the probe laser is fixed at the 5S1/2(F = 2)–5P3/2(F′ = 3) transition.

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Figure 2(a) shows the narrow ladder-type EIT and TPEIA spectra with the Doppler background, where the probe laser frequency was scanned over ± 150 MHz at the resonance of the 5S1/2(F = 2)–5P3/2(F′ = 3) transition, and the coupling laser frequency was free running at the 5P3/2(F′ = 3)–5D5/2(F″ = 4) transition; the intensities of the probe and coupling lasers were 2.7 μW/mm2 and 6.5 mW/mm2, respectively. As shown by the black curve in Fig. 2(a), the ladder-type EIT spectrum of this transition has a double structure, with a narrow EIT transmittance due to two-photon coherence and a broad transmittance due to a saturation effect [24, 25]. Interestingly on the EIT spectrum, we could observe the clear two steep side-peaks at the boundary between the EIT and the broad transmittance. These two side-peaks arise from the wavelength mismatch between probe and coupling lasers due to the Doppler effect. To date, it has been observed in several ladder-type atomic systems with large difference of wavelength between probe and coupling lasers [26, 27]. It is a bit difficult to observe the two side-peaks in our system since the two wavelengths 780 nm and 775.8 nm are close. This means that our experimental setup is useful for coherent spectroscopy in a ladder-type atomic system. We obtained the TPEIA spectrum by adding ΩC2, as shown by the red curve in Fig. 2(a). The magnitude of the TPEIA is twice that of the EIT. We will discuss the relative magnitudes of the EIT and TPEIA as a function of the coupling field intensity in detail.

Figure 2(b) shows the narrow ladder-type EIT and TPEIA spectra without the Doppler background, where the coupling laser frequency was scanned around the 5P3/2(F′ = 3)–5D5/2(F″ = 4) transition, and the probe laser frequency was locked at the 5S1/2(F = 2)–5P3/2(F′ = 3) transition. As mentioned above, the double structure of the ladder-type EIT is clearly apparent. Although the EIT spectrum in Fig. 2(a) is similar to that in Fig. 2(b) except for the Doppler background, the TPEIA spectrum in Fig. 2(b) differs from that in Fig. 2(a). In particular, the TPEIA in the Doppler-broadened atomic medium included the velocity-selective effect needed to satisfy the three-photon resonance condition. Because the probe laser frequency is fixed at the 5S1/2(F = 2)–5P3/2(F′ = 3) transition, the only atom group with zero velocity contributed to the TPEIA spectrum. The spectrum obtained using coupling laser frequency scanning is useful for discussing the relationship between the EIT and TPEIA in detail in terms of the transition routes.

The well-known selection rule between hyperfine states, ΔF = 0, ± 1, determines the spontaneous decay paths. An atomic coherence, i.e., coupled atomic states with coherent fields, is significantly related to the decay rates between hyperfine states. Figure 3 shows the transition routes between hyperfine states and the TPEIA spectra according to the coupling laser detuning. For the 5S1/2(F = 2)–5P3/2(F′ = 2)–5D5/2(F″ = 1, 2, 3) transition, when the atoms are resonant with the coupling and probe lasers, the population of the 5S1/2(F = 2) state may be depleted by single and double resonance optical pumping. However, the 5S1/2(F = 2)–5P3/2(F′ = 3)–5D5/2(F″ = 4) transition may be modeled as a simple three-level system, even though there is a transition channel from the 5D5/2 state to the 6P3/2 state. As mentioned above, the ladder-type EIT and TPEIA are strongly apparent in this transition.

 figure: Fig. 3

Fig. 3 (a) Transition routes between hyperfine states obtained by scanning the detuning frequency of the probe laser. (b) absorption spectra of the probe laser in each section according to the coupling laser detuning for the 5S1/2(F = 2)–5P3/2–5D5/2 transition.

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Figure 3(b) shows the absorption spectra of the probe laser in each section according to the coupling laser detuning, where the probe laser frequency was scanned over the 5S1/2(F = 2)–5P3/2(F′ = 2, 3) transition. When the coupling laser frequency is resonant with the 5P3/2(F′ = 3)–5D5/2(F″ = 3 or 4) transition, we observed TPEIA signals at the 5S1/2(F = 2)–5P3/2(F′ = 2)–5D5/2(F″ = 3) and 5S1/2(F = 2)–5P3/2(F′ = 3)–5D5/2(F″ = 4) transitions (red and blue, respectively). However, in other two sections (green and black), TPEIA is not observed. In that cases, although the two-photon resonance of the 5S1/2(F = 2)–5P3/2(F′ = 2) + δp–5D5/2(F″ = 1, 2, 3) and 5S1/2(F = 2)–5P3/2(F′ = 3) + δp–5D5/2(F″ = 2, 3, 4) transitions is satisfied by the probe laser detuning δp, there is no three-photon resonance, as shown in Figs. 3(a) and 3(b) [19].

Regarding the magnitude of the two TPEIA peaks of F″ = 3 and 4, the TPEIA signal of F″ = 4 is significantly larger than that of F″ = 3 because of the different decay routes. To illustrate the dependence of the TPEIA on a transition, we consider the relationship between two-photon coherence and TPC. A ladder-type EIT due to two-photon coherence is dominant at the 5S1/2(F = 2)–5P3/2(F′ = 3)–5D5/2(F″ = 4) transition, whereas double resonance optical pumping (DROP) and two-photon absorption (TPA) effects are more dominant than EIT in the 5S1/2(F = 2)–5P3/2(F′ = 2)–5D5/2(F″ = 3) transition [28]. For a three-photon process to occur, two-photon coherence is necessary because of the interconnection between two-photon and three-photon processes [16].

Figure 4(a) shows the transition routes between hyperfine states obtained by scanning the coupling laser detuning, where the frequency of the probe laser was set to the 5S1/2(F = 2)–5P3/2(F′ = 2 or 3) transition. In the case of the scanning the frequency of the coupling, there is always three-photon resonance as well as two-photon resonance at the hyperfine states of 5D5/2 state, as shown in Fig. 4(a). When the probe laser is resonant with the 5S1/2(F = 2)–5P3/2(F′ = 2) transition, atoms in the 5S1/2(F = 2) ground state can be optically pumped into the other ground state, 5S1/2(F = 1). The 5S1/2(F = 2)–5P3/2(F′ = 2)–5D5/2 transition is an open ladder-type atomic system that includes decays into the other ground state, 5S1/2(F = 1). In an open ladder-type atomic system, whether DROP or TPA occurs is determined by the decay rates of the hyperfine states [24]. Figure 4(b) shows the absorption spectra of both EIT and TPEIA configurations as a function of the coupling laser frequency detuning, where the probe laser frequency is resonant with the 5S1/2(F = 2)–5P3/2(F′ = 2) transition. As shown in Fig. 4(b), although the transmittance signal in the EIT configuration of the 5S1/2(F = 2)–5P3/2(F′ = 2)–5D5/2(F″ = 3) transition is weak, the TPEIA peak was clearly observed. However, the very weak two-photon coherence signal of the 5D5/2(F″ = 2) state was transformed to weak TPEIA because of weak TPC.

 figure: Fig. 4

Fig. 4 (a) Transition routes between hyperfine states obtained by scanning the detuning frequency of the coupling laser. EIT and TPEIA spectra of the probe laser as a function of the coupling laser detuning for the frequency of the probe laser of the (b) 5S1/2(F = 2)–5P3/2(F′ = 2) and (c) 5S1/2(F = 2)–5P3/2(F′ = 3) transitions, respectively.

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When the frequency of the probe laser was fixed to the 5S1/2(F = 2)–5P3/2(F′ = 3) transition, we clearly observed the TPEIA peaks in the 5D5/2(F″ = 3 and 4) state in Fig. 4(c). In contrast to the TPEIA spectra of Fig. 3(b), the signal of this 5D5/2(F″ = 3) state changed from transmittance to absorption and the TPEIA spectra exhibit hyperfine structure. This reason is the velocity-selective effect needed to satisfy with the three-photon resonance condition according to the coupling laser detuning. Although the transmittance signal of the 5S1/2(F = 2)–5P3/2(F′ = 3)–5D5/2(F″ = 3) transition includes the DROP effect, two-photon coherence still occurs in this transition, and the two-photon coherence component contributed to the TPEIA signal. However, the signal in the 5S1/2(F = 2)–5P3/2(F′ = 3)–5D5/2(F″ = 2) transition is transmittance, because the DROP is the dominant effect for this transmittance signal. Comparing the ladder-type EIT and the TPEIA spectra in Figs. 4(b) and 4(c), TPEIA due to TPC was observed in the transition routes in which a dominant two-photon coherence effect appeared. Therefore, we could confirm that the condition for two-photon coherence is a good condition for TPC phenomena.

Atomic coherence depends significantly on the intensities of the interacting coherent fields. Two-photon coherence has been studied under conditions of a weak probe and a strong coupling laser [11–13]. The additional coupling field intensity needed for the three-photon process switches the phenomenon from EIT due to two-photon coherence to TPEIA due to TPC. We investigated the relationship between two-photon and three-photon coherence in terms of the spectral features according to the additional coupling intensity when the probe and coupling laser intensities were constant. Figure 5 shows the absorption spectra of the probe laser according to the additional coupling intensity, where the frequency of the probe laser was fixed at the 5S1/2(F = 2)–5P3/2(F′ = 3) transition, and that of the coupling laser was scanned over the 5P3/2(F′ = 3)–5D5/2 transition. The two lasers were linearly polarized in the perpendicular direction, and the intensities of the probe and coupling lasers were 2.7 μW/mm2 and 6.5 mW/mm2, respectively. For the 5D5/2(F″ = 4) hyperfine state, EIT was transformed to TPEIA as the additional coupling laser intensity increased. At an additional coupling laser intensity of about 1.5 mW/mm2, a crossover between EIT and TPEIA appears to occur. If the observed absorption spectrum is decomposed into one-photon, two-photon, and three-photon coherence components, the total spectrum is a linear combination of the three components [19]. This crossover signal can be understood as the sum of the two-photon and three-photon coherence components. Therefore, when the coherent channel for TPC is generated by the interaction with the additional coupling laser, TPC is added to the already generated and fixed two-photon coherence.

 figure: Fig. 5

Fig. 5 Absorption spectra of the probe laser according to the additional coupling intensity.

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Comparing the relative magnitudes of the EIT and TPEIA as a function of the coupling field intensity, we discuss the dependence of the coupling laser intensity on the relative magnitudes of two-photon and three-photon coherence. Figures 6(a) and 6(b) show the ladder-type EIT spectra according to the coupling field intensity (ΩC1) without ΩC2, and the TPEIA spectra according to both coupling field intensities (ΩC1 and ΩC2), respectively. As the intensity of ΩC1 increased, the narrow EIT component of the 5D5/2(F″ = 4) state increased significantly compared with the other transmittance peaks of the 5D5/2(F″ = 2 and 3) states, as shown in Fig. 6(a). When the intensities of both ΩC1 and ΩC2 increased simultaneously, the change in the TPEIA in Fig. 6(b) appears similar to that of the EIT. However, the magnitude of the TPEIA in the 5D5/2(F″ = 4) state was approximately twice that of the EIT.

 figure: Fig. 6

Fig. 6 (a) Ladder-type EIT spectra according to the coupling field intensity (ΩC1) without ΩC2, (b) TPEIA spectra according to both coupling field intensities (ΩC1 and ΩC2), and (c) normalized magnitude of EIT (blue squares) and TPEIA (red circles) for 5D5/2(F″ = 4).

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Figure 6(c) shows the relative magnitude of the EIT (blue squares) with that of normalized TPEIA (red circles) for 5D5/2(F″ = 4) and growing slopes of the magnitude with exponential fit. The measured spectrums were averaged 4 times and each measurement was repeated more than 5 times. The errors of the data points in Fig. 6(c) were estimated to be from 0.01 to 0.03 which could be negligible. When the coupling laser power was increased, the magnitudes of both the EIT and TPEIA increased exponentially. In the regime of not strong intensities of coupling, the magnitude of the EIT is approximately proportional to ΩC12, while the density matrix elements for TPEIA can be composed by terms which are proportional to ΩC14, ΩC12, ΩC22 and ΩC24. Thus, regarding the relative magnitudes of the EIT and TPEIA as a function of the coupling field intensity, the TPEIA due to TPC grows faster than that of the EIT due to two-photon coherence. Therefore, we confirmed that the TPC in the ladder-type atomic system increases more rapidly than the two-photon coherence because of the additional coupling field (ΩC2).

To understand the dynamics of the multi-photon coherence in ladder-type atomic systems, we employed a three-level atomic system considering TPC, as shown in Fig. 7(a). To consider the TPC of a ladder-type three-level atomic system, we assumed a modified three-level atomic system with two intermediate states (|2 and |2'). This model is the same as that of our previous work [19]. The decay rates (γ1 and γ2) of the intermediate and excited states are 6 MHz and 0.97 MHz, respectively. The branching ratios of the intermediate and excited states are denoted as b1 and b2, respectively. For the 5S1/2(F = 2)–5P3/2(F′ = 3)–5D5/2(F″ = 4) transition, the branching ratios are determined to b1 = 1 and b2 = 0.75, considering the decay channel of the 6P3/2 state.

 figure: Fig. 7

Fig. 7 (a) Three-level atomic model considering TPC, consisting of a ground state (|1), intermediate states (|2 and |2'), and an excited state (|3). (b) Numerically calculated EIT and TPEIA spectra in the ladder-type three-level atomic model.

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The numerical results of the density matrix were averaged over the Maxwell–Boltzmann velocity distribution in the Doppler-broadened ladder-type atomic system; Fig. 7(b) shows the resulting calculated EIT spectrum (Ωp = 0.4 MHz, ΩC1 = 10 MHz, and ΩC2 = 0 MHz) and TPEIA spectrum (Ωp = 0.4 MHz, ΩC1 = 10 MHz, and ΩC2 = 8 MHz), considering the reflected coupling field ΩC2. The calculated ladder-type EIT spectrum shows the double structure due to the EIT and a saturation effect. However, the spectral feature of TPEIA is narrow absorption with broad transmittance, which is in good agreement with the experimental result in Fig. 2(b). If the two-photon coherence terms in the density matrix elements are not considered, not only EIT but also TPEIA did not appear. Therefore, we confirmed that two-photon coherence is a precondition for TPEIA due to TPC.

We numerically investigated the transformation from EIT to TPEIA according to the additional coupling field ΩC2, which is similar to the experimental results shown in Fig. 5. When the coupling field ΩC1 was fixed at 10 MHz, and ΩC2 was increased from zero to 8 MHz, the calculated spectra changed from EIT due to two-photon coherence to TPEIA due to TPC, as shown in Fig. 8(a). In addition, Fig. 8(b) shows the calculated TPEIA spectra for various ΩC1 and ΩC2. In the experiment, ΩC2 was the coupling field ΩC1 reflected by a mirror after passing through a Rb cell. The intensity of ΩC2 decreased because of reflection by the cell windows and absorption of Rb atoms. When the ratio of ΩC2 to ΩC1 was set to 0.8, the calculated TPEIA spectra in terms of the Rabi frequency of the coupling fields are in good agreement with the experimental results in Fig. 6(b). Although the simple atomic model for considering TPC differs from the real atomic system with hyperfine structures and Zeeman sublevels, the observed spectra were shown to be in good agreement with the numerical calculations.

 figure: Fig. 8

Fig. 8 (a) Numerically calculated transformation of EIT to TPEIA spectra for various additional coupling fields ΩC2. (b) Numerically calculated TPEIA spectra for various ΩC1 and ΩC2, where the ratio of ΩC2 to ΩC1 is 0.8.

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4. Conclusion

We investigated the relationship between two-photon and three-photon coherence, examining ladder-type EIT and TPEIA spectra in terms of the transition routes between the hyperfine states and the coupling laser intensity for the 5S1/2–5P3/2-5D5/2 transition of 87Rb atoms. When we investigated the relationship between the EIT and TPEIA in terms of the transition routes, the TPEIA due to TPC was observed only in the transition routes that generated a dominant two-photon coherence effect. From the observed EIT and TPEIA spectra as a function of the probe or coupling laser frequency detuning, we confirmed that the condition for two-photon coherence was a good condition for TPC phenomena. When a coherent channel for TPC was generated by interaction with the additional coupling laser, the ladder-type EIT was transformed to TPEIA as the additional coupling laser intensity increased. This crossover spectrum between EIT and TPEIA was understood as a linear summation of the two-photon and three-photon coherence components. We also measured the relative magnitudes of the EIT and TPEIA as a function of the coupling field intensity; the increase of TPEIA due to TPC is faster than that of the EIT due to two-photon coherence. From this result, we could estimate the relationship between the two-photon and three-photon coherence and the coupling laser intensity. We believe that our results contribute to an understanding of the relationship between two-photon and three-photon coherence in ladder-type atomic systems.

Acknowledgment

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (NRF-2012R1A2A1A01006579).

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20. T. Hong, C. Cramer, W. Nagourney, and E. N. Fortson, “Optical clocks based on ultranarrow three-photon resonances in alkaline earth atoms,” Phys. Rev. Lett. 94(5), 050801 (2005). [CrossRef]   [PubMed]  

21. R. T. Willis, F. E. Becerra, L. A. Orozco, and S. L. Rolston, “Photon statistics and polarization correlations at telecommunications wavelengths from a warm atomic ensemble,” Opt. Express 19(15), 14632–14641 (2011). [CrossRef]   [PubMed]  

22. D.-S. Ding, Z.-Y. Zhou, B.-S. Shi, X.-B. Zou, and G.-C. Guo, “Generation of non-classical correlated photon pairs via a ladder-type atomic configuration: theory and experiment,” Opt. Express 20(10), 11433–11444 (2012). [CrossRef]   [PubMed]  

23. B. Srivathsan, G. K. Gulati, B. Chng, G. Maslennikov, D. Matsukevich, and C. Kurtsiefer, “Narrow band source of transform-limited photon pairs via four-wave mixing in a cold atomic ensemble,” Phys. Rev. Lett. 111(12), 123602 (2013). [CrossRef]   [PubMed]  

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

25. H.-R. Noh and H. S. 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(12), 11128–11137 (2011). [PubMed]  

26. A. K. Mohapatra, T. R. Jackson, and C. S. Adams, “Coherent optical detection of highly excited Rydberg states using electromagnetically induced transparency,” Phys. Rev. Lett. 98(11), 113003 (2007). [CrossRef]   [PubMed]  

27. K. Pandey, A. Wasan, and V. Natarajan, “Coherent control of magneto-optic rotation,” J. Phys. At. Mol. Opt. Phys. 41(22), 225503 (2008). [CrossRef]  

28. H. S. Moon and H.-R. Noh, “Resonant two-photon absorption and electromagnetically induced transparency in open ladder-type atomic system,” Opt. Express 21(6), 7447–7455 (2013). [CrossRef]   [PubMed]  

References

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  1. K. J. Boller, A. Imamolu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991).
    [Crossref] [PubMed]
  2. S. E. Harris, “Electromagnetically Induced Transparency,” Phys. Today 50(7), 36–42 (1997).
    [Crossref]
  3. M. Xiao, Y. Li, S. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74(5), 666–669 (1995).
    [Crossref] [PubMed]
  4. 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(4), 2996–3002 (1998).
    [Crossref]
  5. A. A. Abdumalikov, O. Astafiev, A. M. Zagoskin, Y. A. Pashkin, Y. Nakamura, and J. S. Tsai, “Electromagnetically induced transparency on a single artificial atom,” Phys. Rev. Lett. 104(19), 193601 (2010).
    [Crossref] [PubMed]
  6. W. W. Chow, H. C. Schneider, and M. C. Phillips, “Theory of quantum-coherence phenomena in semiconductor quantum dots,” Phys. Rev. A 68(5), 053802 (2003).
    [Crossref]
  7. Y. Sun, H. Jiang, Y. Yang, Y. Zhang, H. Chen, and S. Zhu, “Electromagnetically induced transparency in metamaterials: Influence of intrinsic loss and dynamic evolution,” Phys. Rev. B 83(19), 195140 (2011).
    [Crossref]
  8. A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472(7341), 69–73 (2011).
    [Crossref] [PubMed]
  9. K. Jensen, N. Leefer, A. Jarmola, Y. Dumeige, V. M. Acosta, P. Kehayias, B. Patton, and D. Budker, “Cavity-enhanced room-temperature magnetometry using absorption by nitrogen-vacancy centers in diamond,” Phys. Rev. Lett. 112(16), 160802 (2014).
    [Crossref] [PubMed]
  10. H. Kang, G. Hernandez, and Y. Zhu, “Slow-light six-wave mixing at low light intensities,” Phys. Rev. Lett. 93(7), 073601 (2004).
    [Crossref] [PubMed]
  11. I. Novikova, D. F. Phillips, A. S. Zibrov, R. L. Walsworth, A. V. Taichenachev, and V. I. Yudin, “Comparison of 87Rb N-resonances for D1 and D2 transitions,” Opt. Lett. 31(15), 2353–2355 (2006).
    [Crossref] [PubMed]
  12. Y. Zhang, A. W. Brown, and M. Xiao, “Opening four-wave mixing and six-wave mixing channels via dual electromagnetically induced transparency windows,” Phys. Rev. Lett. 99(12), 123603 (2007).
    [Crossref] [PubMed]
  13. S. A. Babin, D. V. Churkin, E. V. Podivilov, V. V. Potapov, and D. A. Shapiro, “Splitting of the peak of electromagnetically induced transparency by the higher-order spatial harmonics of the atomic coherence,” Phys. Rev. A 67(4), 043808 (2003).
    [Crossref]
  14. K. Pandey, “Role of different types of subsystems in a doubly driven Λ system in 87Rb,” Phys. Rev. A 87(4), 043838 (2013).
    [Crossref]
  15. I. Ben-Aroya and G. Eisenstein, “Observation of large contrast electromagnetically induced absorption resonance due to population transfer in a three-level Λ-system interacting with three separate electromagnetic fields,” Opt. Express 19(10), 9956–9961 (2011).
    [Crossref] [PubMed]
  16. H.-R. Noh and H. S. Moon, “Diagrammatic analysis of multiphoton processes in a ladder-type three-level atomic system,” Phys. Rev. A 84(5), 053827 (2011).
    [Crossref]
  17. U. Khadka, H. Zheng, and M. Xiao, “Four-wave-mixing between the upper excited states in a ladder-type atomic configuration,” Opt. Express 20(6), 6204–6214 (2012).
    [Crossref] [PubMed]
  18. C. Carr, M. Tanasittikosol, A. Sargsyan, D. Sarkisyan, C. S. Adams, and K. J. Weatherill, “Three-photon electromagnetically induced transparency using Rydberg states,” Opt. Lett. 37(18), 3858–3860 (2012).
    [Crossref] [PubMed]
  19. H. S. Moon and T. Jeong, “Three-photon electromagnetically induced absorption in a ladder-type atomic system,” Phys. Rev. A 89(3), 033822 (2014).
    [Crossref]
  20. T. Hong, C. Cramer, W. Nagourney, and E. N. Fortson, “Optical clocks based on ultranarrow three-photon resonances in alkaline earth atoms,” Phys. Rev. Lett. 94(5), 050801 (2005).
    [Crossref] [PubMed]
  21. R. T. Willis, F. E. Becerra, L. A. Orozco, and S. L. Rolston, “Photon statistics and polarization correlations at telecommunications wavelengths from a warm atomic ensemble,” Opt. Express 19(15), 14632–14641 (2011).
    [Crossref] [PubMed]
  22. D.-S. Ding, Z.-Y. Zhou, B.-S. Shi, X.-B. Zou, and G.-C. Guo, “Generation of non-classical correlated photon pairs via a ladder-type atomic configuration: theory and experiment,” Opt. Express 20(10), 11433–11444 (2012).
    [Crossref] [PubMed]
  23. B. Srivathsan, G. K. Gulati, B. Chng, G. Maslennikov, D. Matsukevich, and C. Kurtsiefer, “Narrow band source of transform-limited photon pairs via four-wave mixing in a cold atomic ensemble,” Phys. Rev. Lett. 111(12), 123602 (2013).
    [Crossref] [PubMed]
  24. H. S. Moon, L. Lee, and J. B. Kim, “Double resonance optical pumping effects in electromagnetically induced transparency,” Opt. Express 16(16), 12163–12170 (2008).
    [Crossref] [PubMed]
  25. H.-R. Noh and H. S. 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(12), 11128–11137 (2011).
    [PubMed]
  26. A. K. Mohapatra, T. R. Jackson, and C. S. Adams, “Coherent optical detection of highly excited Rydberg states using electromagnetically induced transparency,” Phys. Rev. Lett. 98(11), 113003 (2007).
    [Crossref] [PubMed]
  27. K. Pandey, A. Wasan, and V. Natarajan, “Coherent control of magneto-optic rotation,” J. Phys. At. Mol. Opt. Phys. 41(22), 225503 (2008).
    [Crossref]
  28. H. S. Moon and H.-R. Noh, “Resonant two-photon absorption and electromagnetically induced transparency in open ladder-type atomic system,” Opt. Express 21(6), 7447–7455 (2013).
    [Crossref] [PubMed]

2014 (2)

K. Jensen, N. Leefer, A. Jarmola, Y. Dumeige, V. M. Acosta, P. Kehayias, B. Patton, and D. Budker, “Cavity-enhanced room-temperature magnetometry using absorption by nitrogen-vacancy centers in diamond,” Phys. Rev. Lett. 112(16), 160802 (2014).
[Crossref] [PubMed]

H. S. Moon and T. Jeong, “Three-photon electromagnetically induced absorption in a ladder-type atomic system,” Phys. Rev. A 89(3), 033822 (2014).
[Crossref]

2013 (3)

B. Srivathsan, G. K. Gulati, B. Chng, G. Maslennikov, D. Matsukevich, and C. Kurtsiefer, “Narrow band source of transform-limited photon pairs via four-wave mixing in a cold atomic ensemble,” Phys. Rev. Lett. 111(12), 123602 (2013).
[Crossref] [PubMed]

H. S. Moon and H.-R. Noh, “Resonant two-photon absorption and electromagnetically induced transparency in open ladder-type atomic system,” Opt. Express 21(6), 7447–7455 (2013).
[Crossref] [PubMed]

K. Pandey, “Role of different types of subsystems in a doubly driven Λ system in 87Rb,” Phys. Rev. A 87(4), 043838 (2013).
[Crossref]

2012 (3)

2011 (6)

H.-R. Noh and H. S. 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(12), 11128–11137 (2011).
[PubMed]

R. T. Willis, F. E. Becerra, L. A. Orozco, and S. L. Rolston, “Photon statistics and polarization correlations at telecommunications wavelengths from a warm atomic ensemble,” Opt. Express 19(15), 14632–14641 (2011).
[Crossref] [PubMed]

I. Ben-Aroya and G. Eisenstein, “Observation of large contrast electromagnetically induced absorption resonance due to population transfer in a three-level Λ-system interacting with three separate electromagnetic fields,” Opt. Express 19(10), 9956–9961 (2011).
[Crossref] [PubMed]

H.-R. Noh and H. S. Moon, “Diagrammatic analysis of multiphoton processes in a ladder-type three-level atomic system,” Phys. Rev. A 84(5), 053827 (2011).
[Crossref]

Y. Sun, H. Jiang, Y. Yang, Y. Zhang, H. Chen, and S. Zhu, “Electromagnetically induced transparency in metamaterials: Influence of intrinsic loss and dynamic evolution,” Phys. Rev. B 83(19), 195140 (2011).
[Crossref]

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472(7341), 69–73 (2011).
[Crossref] [PubMed]

2010 (1)

A. A. Abdumalikov, O. Astafiev, A. M. Zagoskin, Y. A. Pashkin, Y. Nakamura, and J. S. Tsai, “Electromagnetically induced transparency on a single artificial atom,” Phys. Rev. Lett. 104(19), 193601 (2010).
[Crossref] [PubMed]

2008 (2)

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

K. Pandey, A. Wasan, and V. Natarajan, “Coherent control of magneto-optic rotation,” J. Phys. At. Mol. Opt. Phys. 41(22), 225503 (2008).
[Crossref]

2007 (2)

A. K. Mohapatra, T. R. Jackson, and C. S. Adams, “Coherent optical detection of highly excited Rydberg states using electromagnetically induced transparency,” Phys. Rev. Lett. 98(11), 113003 (2007).
[Crossref] [PubMed]

Y. Zhang, A. W. Brown, and M. Xiao, “Opening four-wave mixing and six-wave mixing channels via dual electromagnetically induced transparency windows,” Phys. Rev. Lett. 99(12), 123603 (2007).
[Crossref] [PubMed]

2006 (1)

2005 (1)

T. Hong, C. Cramer, W. Nagourney, and E. N. Fortson, “Optical clocks based on ultranarrow three-photon resonances in alkaline earth atoms,” Phys. Rev. Lett. 94(5), 050801 (2005).
[Crossref] [PubMed]

2004 (1)

H. Kang, G. Hernandez, and Y. Zhu, “Slow-light six-wave mixing at low light intensities,” Phys. Rev. Lett. 93(7), 073601 (2004).
[Crossref] [PubMed]

2003 (2)

S. A. Babin, D. V. Churkin, E. V. Podivilov, V. V. Potapov, and D. A. Shapiro, “Splitting of the peak of electromagnetically induced transparency by the higher-order spatial harmonics of the atomic coherence,” Phys. Rev. A 67(4), 043808 (2003).
[Crossref]

W. W. Chow, H. C. Schneider, and M. C. Phillips, “Theory of quantum-coherence phenomena in semiconductor quantum dots,” Phys. Rev. A 68(5), 053802 (2003).
[Crossref]

1998 (1)

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(4), 2996–3002 (1998).
[Crossref]

1997 (1)

S. E. Harris, “Electromagnetically Induced Transparency,” Phys. Today 50(7), 36–42 (1997).
[Crossref]

1995 (1)

M. Xiao, Y. Li, S. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74(5), 666–669 (1995).
[Crossref] [PubMed]

1991 (1)

K. J. Boller, A. Imamolu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991).
[Crossref] [PubMed]

Abdumalikov, A. A.

A. A. Abdumalikov, O. Astafiev, A. M. Zagoskin, Y. A. Pashkin, Y. Nakamura, and J. S. Tsai, “Electromagnetically induced transparency on a single artificial atom,” Phys. Rev. Lett. 104(19), 193601 (2010).
[Crossref] [PubMed]

Acosta, V. M.

K. Jensen, N. Leefer, A. Jarmola, Y. Dumeige, V. M. Acosta, P. Kehayias, B. Patton, and D. Budker, “Cavity-enhanced room-temperature magnetometry using absorption by nitrogen-vacancy centers in diamond,” Phys. Rev. Lett. 112(16), 160802 (2014).
[Crossref] [PubMed]

Adams, C. S.

C. Carr, M. Tanasittikosol, A. Sargsyan, D. Sarkisyan, C. S. Adams, and K. J. Weatherill, “Three-photon electromagnetically induced transparency using Rydberg states,” Opt. Lett. 37(18), 3858–3860 (2012).
[Crossref] [PubMed]

A. K. Mohapatra, T. R. Jackson, and C. S. Adams, “Coherent optical detection of highly excited Rydberg states using electromagnetically induced transparency,” Phys. Rev. Lett. 98(11), 113003 (2007).
[Crossref] [PubMed]

Akulshin, A. M.

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(4), 2996–3002 (1998).
[Crossref]

Astafiev, O.

A. A. Abdumalikov, O. Astafiev, A. M. Zagoskin, Y. A. Pashkin, Y. Nakamura, and J. S. Tsai, “Electromagnetically induced transparency on a single artificial atom,” Phys. Rev. Lett. 104(19), 193601 (2010).
[Crossref] [PubMed]

Babin, S. A.

S. A. Babin, D. V. Churkin, E. V. Podivilov, V. V. Potapov, and D. A. Shapiro, “Splitting of the peak of electromagnetically induced transparency by the higher-order spatial harmonics of the atomic coherence,” Phys. Rev. A 67(4), 043808 (2003).
[Crossref]

Barreiro, S.

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(4), 2996–3002 (1998).
[Crossref]

Becerra, F. E.

Ben-Aroya, I.

Boller, K. J.

K. J. Boller, A. Imamolu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991).
[Crossref] [PubMed]

Brown, A. W.

Y. Zhang, A. W. Brown, and M. Xiao, “Opening four-wave mixing and six-wave mixing channels via dual electromagnetically induced transparency windows,” Phys. Rev. Lett. 99(12), 123603 (2007).
[Crossref] [PubMed]

Budker, D.

K. Jensen, N. Leefer, A. Jarmola, Y. Dumeige, V. M. Acosta, P. Kehayias, B. Patton, and D. Budker, “Cavity-enhanced room-temperature magnetometry using absorption by nitrogen-vacancy centers in diamond,” Phys. Rev. Lett. 112(16), 160802 (2014).
[Crossref] [PubMed]

Carr, C.

Chan, J.

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472(7341), 69–73 (2011).
[Crossref] [PubMed]

Chang, D. E.

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472(7341), 69–73 (2011).
[Crossref] [PubMed]

Chen, H.

Y. Sun, H. Jiang, Y. Yang, Y. Zhang, H. Chen, and S. Zhu, “Electromagnetically induced transparency in metamaterials: Influence of intrinsic loss and dynamic evolution,” Phys. Rev. B 83(19), 195140 (2011).
[Crossref]

Chng, B.

B. Srivathsan, G. K. Gulati, B. Chng, G. Maslennikov, D. Matsukevich, and C. Kurtsiefer, “Narrow band source of transform-limited photon pairs via four-wave mixing in a cold atomic ensemble,” Phys. Rev. Lett. 111(12), 123602 (2013).
[Crossref] [PubMed]

Chow, W. W.

W. W. Chow, H. C. Schneider, and M. C. Phillips, “Theory of quantum-coherence phenomena in semiconductor quantum dots,” Phys. Rev. A 68(5), 053802 (2003).
[Crossref]

Churkin, D. V.

S. A. Babin, D. V. Churkin, E. V. Podivilov, V. V. Potapov, and D. A. Shapiro, “Splitting of the peak of electromagnetically induced transparency by the higher-order spatial harmonics of the atomic coherence,” Phys. Rev. A 67(4), 043808 (2003).
[Crossref]

Cramer, C.

T. Hong, C. Cramer, W. Nagourney, and E. N. Fortson, “Optical clocks based on ultranarrow three-photon resonances in alkaline earth atoms,” Phys. Rev. Lett. 94(5), 050801 (2005).
[Crossref] [PubMed]

Ding, D.-S.

Dumeige, Y.

K. Jensen, N. Leefer, A. Jarmola, Y. Dumeige, V. M. Acosta, P. Kehayias, B. Patton, and D. Budker, “Cavity-enhanced room-temperature magnetometry using absorption by nitrogen-vacancy centers in diamond,” Phys. Rev. Lett. 112(16), 160802 (2014).
[Crossref] [PubMed]

Eichenfield, M.

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472(7341), 69–73 (2011).
[Crossref] [PubMed]

Eisenstein, G.

Fortson, E. N.

T. Hong, C. Cramer, W. Nagourney, and E. N. Fortson, “Optical clocks based on ultranarrow three-photon resonances in alkaline earth atoms,” Phys. Rev. Lett. 94(5), 050801 (2005).
[Crossref] [PubMed]

Gea-Banacloche, J.

M. Xiao, Y. Li, S. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74(5), 666–669 (1995).
[Crossref] [PubMed]

Gulati, G. K.

B. Srivathsan, G. K. Gulati, B. Chng, G. Maslennikov, D. Matsukevich, and C. Kurtsiefer, “Narrow band source of transform-limited photon pairs via four-wave mixing in a cold atomic ensemble,” Phys. Rev. Lett. 111(12), 123602 (2013).
[Crossref] [PubMed]

Guo, G.-C.

Harris, S. E.

S. E. Harris, “Electromagnetically Induced Transparency,” Phys. Today 50(7), 36–42 (1997).
[Crossref]

K. J. Boller, A. Imamolu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991).
[Crossref] [PubMed]

Hernandez, G.

H. Kang, G. Hernandez, and Y. Zhu, “Slow-light six-wave mixing at low light intensities,” Phys. Rev. Lett. 93(7), 073601 (2004).
[Crossref] [PubMed]

Hill, J. T.

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472(7341), 69–73 (2011).
[Crossref] [PubMed]

Hong, T.

T. Hong, C. Cramer, W. Nagourney, and E. N. Fortson, “Optical clocks based on ultranarrow three-photon resonances in alkaline earth atoms,” Phys. Rev. Lett. 94(5), 050801 (2005).
[Crossref] [PubMed]

Imamolu, A.

K. J. Boller, A. Imamolu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991).
[Crossref] [PubMed]

Jackson, T. R.

A. K. Mohapatra, T. R. Jackson, and C. S. Adams, “Coherent optical detection of highly excited Rydberg states using electromagnetically induced transparency,” Phys. Rev. Lett. 98(11), 113003 (2007).
[Crossref] [PubMed]

Jarmola, A.

K. Jensen, N. Leefer, A. Jarmola, Y. Dumeige, V. M. Acosta, P. Kehayias, B. Patton, and D. Budker, “Cavity-enhanced room-temperature magnetometry using absorption by nitrogen-vacancy centers in diamond,” Phys. Rev. Lett. 112(16), 160802 (2014).
[Crossref] [PubMed]

Jensen, K.

K. Jensen, N. Leefer, A. Jarmola, Y. Dumeige, V. M. Acosta, P. Kehayias, B. Patton, and D. Budker, “Cavity-enhanced room-temperature magnetometry using absorption by nitrogen-vacancy centers in diamond,” Phys. Rev. Lett. 112(16), 160802 (2014).
[Crossref] [PubMed]

Jeong, T.

H. S. Moon and T. Jeong, “Three-photon electromagnetically induced absorption in a ladder-type atomic system,” Phys. Rev. A 89(3), 033822 (2014).
[Crossref]

Jiang, H.

Y. Sun, H. Jiang, Y. Yang, Y. Zhang, H. Chen, and S. Zhu, “Electromagnetically induced transparency in metamaterials: Influence of intrinsic loss and dynamic evolution,” Phys. Rev. B 83(19), 195140 (2011).
[Crossref]

Jin, S.

M. Xiao, Y. Li, S. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74(5), 666–669 (1995).
[Crossref] [PubMed]

Kang, H.

H. Kang, G. Hernandez, and Y. Zhu, “Slow-light six-wave mixing at low light intensities,” Phys. Rev. Lett. 93(7), 073601 (2004).
[Crossref] [PubMed]

Kehayias, P.

K. Jensen, N. Leefer, A. Jarmola, Y. Dumeige, V. M. Acosta, P. Kehayias, B. Patton, and D. Budker, “Cavity-enhanced room-temperature magnetometry using absorption by nitrogen-vacancy centers in diamond,” Phys. Rev. Lett. 112(16), 160802 (2014).
[Crossref] [PubMed]

Khadka, U.

Kim, J. B.

Kurtsiefer, C.

B. Srivathsan, G. K. Gulati, B. Chng, G. Maslennikov, D. Matsukevich, and C. Kurtsiefer, “Narrow band source of transform-limited photon pairs via four-wave mixing in a cold atomic ensemble,” Phys. Rev. Lett. 111(12), 123602 (2013).
[Crossref] [PubMed]

Lee, L.

Leefer, N.

K. Jensen, N. Leefer, A. Jarmola, Y. Dumeige, V. M. Acosta, P. Kehayias, B. Patton, and D. Budker, “Cavity-enhanced room-temperature magnetometry using absorption by nitrogen-vacancy centers in diamond,” Phys. Rev. Lett. 112(16), 160802 (2014).
[Crossref] [PubMed]

Lezama, A.

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(4), 2996–3002 (1998).
[Crossref]

Li, Y.

M. Xiao, Y. Li, S. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74(5), 666–669 (1995).
[Crossref] [PubMed]

Lin, Q.

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472(7341), 69–73 (2011).
[Crossref] [PubMed]

Maslennikov, G.

B. Srivathsan, G. K. Gulati, B. Chng, G. Maslennikov, D. Matsukevich, and C. Kurtsiefer, “Narrow band source of transform-limited photon pairs via four-wave mixing in a cold atomic ensemble,” Phys. Rev. Lett. 111(12), 123602 (2013).
[Crossref] [PubMed]

Matsukevich, D.

B. Srivathsan, G. K. Gulati, B. Chng, G. Maslennikov, D. Matsukevich, and C. Kurtsiefer, “Narrow band source of transform-limited photon pairs via four-wave mixing in a cold atomic ensemble,” Phys. Rev. Lett. 111(12), 123602 (2013).
[Crossref] [PubMed]

Mayer Alegre, T. P.

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472(7341), 69–73 (2011).
[Crossref] [PubMed]

Mohapatra, A. K.

A. K. Mohapatra, T. R. Jackson, and C. S. Adams, “Coherent optical detection of highly excited Rydberg states using electromagnetically induced transparency,” Phys. Rev. Lett. 98(11), 113003 (2007).
[Crossref] [PubMed]

Moon, H. S.

Nagourney, W.

T. Hong, C. Cramer, W. Nagourney, and E. N. Fortson, “Optical clocks based on ultranarrow three-photon resonances in alkaline earth atoms,” Phys. Rev. Lett. 94(5), 050801 (2005).
[Crossref] [PubMed]

Nakamura, Y.

A. A. Abdumalikov, O. Astafiev, A. M. Zagoskin, Y. A. Pashkin, Y. Nakamura, and J. S. Tsai, “Electromagnetically induced transparency on a single artificial atom,” Phys. Rev. Lett. 104(19), 193601 (2010).
[Crossref] [PubMed]

Natarajan, V.

K. Pandey, A. Wasan, and V. Natarajan, “Coherent control of magneto-optic rotation,” J. Phys. At. Mol. Opt. Phys. 41(22), 225503 (2008).
[Crossref]

Noh, H.-R.

Novikova, I.

Orozco, L. A.

Painter, O.

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472(7341), 69–73 (2011).
[Crossref] [PubMed]

Pandey, K.

K. Pandey, “Role of different types of subsystems in a doubly driven Λ system in 87Rb,” Phys. Rev. A 87(4), 043838 (2013).
[Crossref]

K. Pandey, A. Wasan, and V. Natarajan, “Coherent control of magneto-optic rotation,” J. Phys. At. Mol. Opt. Phys. 41(22), 225503 (2008).
[Crossref]

Pashkin, Y. A.

A. A. Abdumalikov, O. Astafiev, A. M. Zagoskin, Y. A. Pashkin, Y. Nakamura, and J. S. Tsai, “Electromagnetically induced transparency on a single artificial atom,” Phys. Rev. Lett. 104(19), 193601 (2010).
[Crossref] [PubMed]

Patton, B.

K. Jensen, N. Leefer, A. Jarmola, Y. Dumeige, V. M. Acosta, P. Kehayias, B. Patton, and D. Budker, “Cavity-enhanced room-temperature magnetometry using absorption by nitrogen-vacancy centers in diamond,” Phys. Rev. Lett. 112(16), 160802 (2014).
[Crossref] [PubMed]

Phillips, D. F.

Phillips, M. C.

W. W. Chow, H. C. Schneider, and M. C. Phillips, “Theory of quantum-coherence phenomena in semiconductor quantum dots,” Phys. Rev. A 68(5), 053802 (2003).
[Crossref]

Podivilov, E. V.

S. A. Babin, D. V. Churkin, E. V. Podivilov, V. V. Potapov, and D. A. Shapiro, “Splitting of the peak of electromagnetically induced transparency by the higher-order spatial harmonics of the atomic coherence,” Phys. Rev. A 67(4), 043808 (2003).
[Crossref]

Potapov, V. V.

S. A. Babin, D. V. Churkin, E. V. Podivilov, V. V. Potapov, and D. A. Shapiro, “Splitting of the peak of electromagnetically induced transparency by the higher-order spatial harmonics of the atomic coherence,” Phys. Rev. A 67(4), 043808 (2003).
[Crossref]

Rolston, S. L.

Safavi-Naeini, A. H.

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472(7341), 69–73 (2011).
[Crossref] [PubMed]

Sargsyan, A.

Sarkisyan, D.

Schneider, H. C.

W. W. Chow, H. C. Schneider, and M. C. Phillips, “Theory of quantum-coherence phenomena in semiconductor quantum dots,” Phys. Rev. A 68(5), 053802 (2003).
[Crossref]

Shapiro, D. A.

S. A. Babin, D. V. Churkin, E. V. Podivilov, V. V. Potapov, and D. A. Shapiro, “Splitting of the peak of electromagnetically induced transparency by the higher-order spatial harmonics of the atomic coherence,” Phys. Rev. A 67(4), 043808 (2003).
[Crossref]

Shi, B.-S.

Srivathsan, B.

B. Srivathsan, G. K. Gulati, B. Chng, G. Maslennikov, D. Matsukevich, and C. Kurtsiefer, “Narrow band source of transform-limited photon pairs via four-wave mixing in a cold atomic ensemble,” Phys. Rev. Lett. 111(12), 123602 (2013).
[Crossref] [PubMed]

Sun, Y.

Y. Sun, H. Jiang, Y. Yang, Y. Zhang, H. Chen, and S. Zhu, “Electromagnetically induced transparency in metamaterials: Influence of intrinsic loss and dynamic evolution,” Phys. Rev. B 83(19), 195140 (2011).
[Crossref]

Taichenachev, A. V.

Tanasittikosol, M.

Tsai, J. S.

A. A. Abdumalikov, O. Astafiev, A. M. Zagoskin, Y. A. Pashkin, Y. Nakamura, and J. S. Tsai, “Electromagnetically induced transparency on a single artificial atom,” Phys. Rev. Lett. 104(19), 193601 (2010).
[Crossref] [PubMed]

Walsworth, R. L.

Wasan, A.

K. Pandey, A. Wasan, and V. Natarajan, “Coherent control of magneto-optic rotation,” J. Phys. At. Mol. Opt. Phys. 41(22), 225503 (2008).
[Crossref]

Weatherill, K. J.

Willis, R. T.

Winger, M.

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472(7341), 69–73 (2011).
[Crossref] [PubMed]

Xiao, M.

U. Khadka, H. Zheng, and M. Xiao, “Four-wave-mixing between the upper excited states in a ladder-type atomic configuration,” Opt. Express 20(6), 6204–6214 (2012).
[Crossref] [PubMed]

Y. Zhang, A. W. Brown, and M. Xiao, “Opening four-wave mixing and six-wave mixing channels via dual electromagnetically induced transparency windows,” Phys. Rev. Lett. 99(12), 123603 (2007).
[Crossref] [PubMed]

M. Xiao, Y. Li, S. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74(5), 666–669 (1995).
[Crossref] [PubMed]

Yang, Y.

Y. Sun, H. Jiang, Y. Yang, Y. Zhang, H. Chen, and S. Zhu, “Electromagnetically induced transparency in metamaterials: Influence of intrinsic loss and dynamic evolution,” Phys. Rev. B 83(19), 195140 (2011).
[Crossref]

Yudin, V. I.

Zagoskin, A. M.

A. A. Abdumalikov, O. Astafiev, A. M. Zagoskin, Y. A. Pashkin, Y. Nakamura, and J. S. Tsai, “Electromagnetically induced transparency on a single artificial atom,” Phys. Rev. Lett. 104(19), 193601 (2010).
[Crossref] [PubMed]

Zhang, Y.

Y. Sun, H. Jiang, Y. Yang, Y. Zhang, H. Chen, and S. Zhu, “Electromagnetically induced transparency in metamaterials: Influence of intrinsic loss and dynamic evolution,” Phys. Rev. B 83(19), 195140 (2011).
[Crossref]

Y. Zhang, A. W. Brown, and M. Xiao, “Opening four-wave mixing and six-wave mixing channels via dual electromagnetically induced transparency windows,” Phys. Rev. Lett. 99(12), 123603 (2007).
[Crossref] [PubMed]

Zheng, H.

Zhou, Z.-Y.

Zhu, S.

Y. Sun, H. Jiang, Y. Yang, Y. Zhang, H. Chen, and S. Zhu, “Electromagnetically induced transparency in metamaterials: Influence of intrinsic loss and dynamic evolution,” Phys. Rev. B 83(19), 195140 (2011).
[Crossref]

Zhu, Y.

H. Kang, G. Hernandez, and Y. Zhu, “Slow-light six-wave mixing at low light intensities,” Phys. Rev. Lett. 93(7), 073601 (2004).
[Crossref] [PubMed]

Zibrov, A. S.

Zou, X.-B.

J. Phys. At. Mol. Opt. Phys. (1)

K. Pandey, A. Wasan, and V. Natarajan, “Coherent control of magneto-optic rotation,” J. Phys. At. Mol. Opt. Phys. 41(22), 225503 (2008).
[Crossref]

Nature (1)

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472(7341), 69–73 (2011).
[Crossref] [PubMed]

Opt. Express (7)

U. Khadka, H. Zheng, and M. Xiao, “Four-wave-mixing between the upper excited states in a ladder-type atomic configuration,” Opt. Express 20(6), 6204–6214 (2012).
[Crossref] [PubMed]

H. S. Moon and H.-R. Noh, “Resonant two-photon absorption and electromagnetically induced transparency in open ladder-type atomic system,” Opt. Express 21(6), 7447–7455 (2013).
[Crossref] [PubMed]

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

H.-R. Noh and H. S. 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(12), 11128–11137 (2011).
[PubMed]

I. Ben-Aroya and G. Eisenstein, “Observation of large contrast electromagnetically induced absorption resonance due to population transfer in a three-level Λ-system interacting with three separate electromagnetic fields,” Opt. Express 19(10), 9956–9961 (2011).
[Crossref] [PubMed]

R. T. Willis, F. E. Becerra, L. A. Orozco, and S. L. Rolston, “Photon statistics and polarization correlations at telecommunications wavelengths from a warm atomic ensemble,” Opt. Express 19(15), 14632–14641 (2011).
[Crossref] [PubMed]

D.-S. Ding, Z.-Y. Zhou, B.-S. Shi, X.-B. Zou, and G.-C. Guo, “Generation of non-classical correlated photon pairs via a ladder-type atomic configuration: theory and experiment,” Opt. Express 20(10), 11433–11444 (2012).
[Crossref] [PubMed]

Opt. Lett. (2)

Phys. Rev. A (6)

S. A. Babin, D. V. Churkin, E. V. Podivilov, V. V. Potapov, and D. A. Shapiro, “Splitting of the peak of electromagnetically induced transparency by the higher-order spatial harmonics of the atomic coherence,” Phys. Rev. A 67(4), 043808 (2003).
[Crossref]

K. Pandey, “Role of different types of subsystems in a doubly driven Λ system in 87Rb,” Phys. Rev. A 87(4), 043838 (2013).
[Crossref]

H. S. Moon and T. Jeong, “Three-photon electromagnetically induced absorption in a ladder-type atomic system,” Phys. Rev. A 89(3), 033822 (2014).
[Crossref]

W. W. Chow, H. C. Schneider, and M. C. Phillips, “Theory of quantum-coherence phenomena in semiconductor quantum dots,” Phys. Rev. A 68(5), 053802 (2003).
[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(4), 2996–3002 (1998).
[Crossref]

H.-R. Noh and H. S. Moon, “Diagrammatic analysis of multiphoton processes in a ladder-type three-level atomic system,” Phys. Rev. A 84(5), 053827 (2011).
[Crossref]

Phys. Rev. B (1)

Y. Sun, H. Jiang, Y. Yang, Y. Zhang, H. Chen, and S. Zhu, “Electromagnetically induced transparency in metamaterials: Influence of intrinsic loss and dynamic evolution,” Phys. Rev. B 83(19), 195140 (2011).
[Crossref]

Phys. Rev. Lett. (9)

K. Jensen, N. Leefer, A. Jarmola, Y. Dumeige, V. M. Acosta, P. Kehayias, B. Patton, and D. Budker, “Cavity-enhanced room-temperature magnetometry using absorption by nitrogen-vacancy centers in diamond,” Phys. Rev. Lett. 112(16), 160802 (2014).
[Crossref] [PubMed]

H. Kang, G. Hernandez, and Y. Zhu, “Slow-light six-wave mixing at low light intensities,” Phys. Rev. Lett. 93(7), 073601 (2004).
[Crossref] [PubMed]

A. A. Abdumalikov, O. Astafiev, A. M. Zagoskin, Y. A. Pashkin, Y. Nakamura, and J. S. Tsai, “Electromagnetically induced transparency on a single artificial atom,” Phys. Rev. Lett. 104(19), 193601 (2010).
[Crossref] [PubMed]

K. J. Boller, A. Imamolu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991).
[Crossref] [PubMed]

T. Hong, C. Cramer, W. Nagourney, and E. N. Fortson, “Optical clocks based on ultranarrow three-photon resonances in alkaline earth atoms,” Phys. Rev. Lett. 94(5), 050801 (2005).
[Crossref] [PubMed]

Y. Zhang, A. W. Brown, and M. Xiao, “Opening four-wave mixing and six-wave mixing channels via dual electromagnetically induced transparency windows,” Phys. Rev. Lett. 99(12), 123603 (2007).
[Crossref] [PubMed]

B. Srivathsan, G. K. Gulati, B. Chng, G. Maslennikov, D. Matsukevich, and C. Kurtsiefer, “Narrow band source of transform-limited photon pairs via four-wave mixing in a cold atomic ensemble,” Phys. Rev. Lett. 111(12), 123602 (2013).
[Crossref] [PubMed]

A. K. Mohapatra, T. R. Jackson, and C. S. Adams, “Coherent optical detection of highly excited Rydberg states using electromagnetically induced transparency,” Phys. Rev. Lett. 98(11), 113003 (2007).
[Crossref] [PubMed]

M. Xiao, Y. Li, S. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74(5), 666–669 (1995).
[Crossref] [PubMed]

Phys. Today (1)

S. E. Harris, “Electromagnetically Induced Transparency,” Phys. Today 50(7), 36–42 (1997).
[Crossref]

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Figures (8)

Fig. 1
Fig. 1 (a) Energy level diagram for the 5S1/2–5P3/2–5D5/2 transitions of 87Rb (I = 3/2), (b) Experimental schematic; the probe field (Ωp) and two counter-propagating coupling fields (ΩC1 and ΩC2) in a pure Rb vapor cell (PD: photo-current detector, PBS: polarization beam splitter, QWP: quarter-wave plate, M: Mirror).
Fig. 2
Fig. 2 (a) EIT and TPEIA spectra as a function of the detuning frequency of the probe laser, where the frequency of the coupling laser is fixed at the 5P3/2(F′ = 3)–5D5/2(F″ = 4) transition. (b) EIT and TPEIA spectra as a function of the detuning frequency of the coupling laser, where the frequency of the probe laser is fixed at the 5S1/2(F = 2)–5P3/2(F′ = 3) transition.
Fig. 3
Fig. 3 (a) Transition routes between hyperfine states obtained by scanning the detuning frequency of the probe laser. (b) absorption spectra of the probe laser in each section according to the coupling laser detuning for the 5S1/2(F = 2)–5P3/2–5D5/2 transition.
Fig. 4
Fig. 4 (a) Transition routes between hyperfine states obtained by scanning the detuning frequency of the coupling laser. EIT and TPEIA spectra of the probe laser as a function of the coupling laser detuning for the frequency of the probe laser of the (b) 5S1/2(F = 2)–5P3/2(F′ = 2) and (c) 5S1/2(F = 2)–5P3/2(F′ = 3) transitions, respectively.
Fig. 5
Fig. 5 Absorption spectra of the probe laser according to the additional coupling intensity.
Fig. 6
Fig. 6 (a) Ladder-type EIT spectra according to the coupling field intensity (ΩC1) without ΩC2, (b) TPEIA spectra according to both coupling field intensities (ΩC1 and ΩC2), and (c) normalized magnitude of EIT (blue squares) and TPEIA (red circles) for 5D5/2(F″ = 4).
Fig. 7
Fig. 7 (a) Three-level atomic model considering TPC, consisting of a ground state ( |1 ), intermediate states ( |2 and | 2' ), and an excited state ( |3 ). (b) Numerically calculated EIT and TPEIA spectra in the ladder-type three-level atomic model.
Fig. 8
Fig. 8 (a) Numerically calculated transformation of EIT to TPEIA spectra for various additional coupling fields ΩC2. (b) Numerically calculated TPEIA spectra for various ΩC1 and ΩC2, where the ratio of ΩC2 to ΩC1 is 0.8.

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