1. Introduction

Atomic coherence and interference in an optical medium interacting with lights have led to a counterintuitive phenomenon. One of the interesting atomic coherent phenomena is electromagnetically induced transparency (EIT) [1-5]. The EIT has attracted considerable attention in recent years and offer a variety of interesting and potentially important applications including light storage [6-8], quantum information [9,10], and precision magnetometers [11-12]. Most EITs have been studied in Λ, V, or ladder-type atomic systems based on a three-level atomic model [13].

The EIT is a phenomenon wherein a resonant probe laser is transmitted with weak absorption through a medium coupled by a coherent coupling laser. The λ-type EIT based on a three-level atomic system has been actively studied, as shown in Fig. 1(a). However, the λ- type EIT spectrum has an optical pumping effect by the coupling laser. When the atoms of the λ-type atomic system are resonant with the coupling laser, as in the case of ⁸⁷Rb atoms, most of the population in one ground state (F=2) may be optically pumped into another ground state (F=1) through an excited state (5P_3/2). Optical pumping affects the linear absorption spectral profile and the EIT spectrum. In the some cases, increasing the linear absorption through optical pumping surpasses even the EIT in the transmittance spectrum. The role of optical pumping using a coupling laser in the shaping of the EIT spectrum has already been discussed in an atomic vapor [14].

Comparing ladder-type EIT with λ-type, ladder-type EIT has been the subject of relatively little investigation and there are interesting differences in the experimental setup and the spectrum [15-18]. In the spectrum, there are hyperfine structures of an excited state in a ladder-type EIT spectrum. Further important difference from the λ-type EIT is that the linear absorption profile in the ladder-type EIT spectra is not distorted by the optical pumping. In the case of the ladder-type EIT, the population of the intermediate states (5P_3/2) is very low because of using the weak probe laser. So, there have been no reported findings on the optical pumping in a ladder-type EIT.

However, when the atoms are resonant with the fields of the two lasers, the probe laser (L₁) and the coupling laser (L₂), as shown in Fig. 1(b), there is optical pumping in the ladder-type atomic system due to the so-called double resonance optical pumping (DROP) phenomenon [19-21]. DROP, based on the interaction of molecules or atoms with two optical fields that are resonantly tuned to two transitions that share a common state, is the optical pumping phenomenon in the ladder-type atomic system. For the 5S_1/2-5P_3/2-5D_5/2 transition of ⁸⁷Rb atoms, as shown in Fig. 1(b), the population of one ground state (F=2) may be depleted because many atoms that have been excited into an excited state (5D_5/2) can be optically pumped into another ground state (F=1) through the intermediate states (5P_3/2) [20].

As is well known, EIT is a nonlinear phenomenon for atomic coherence, while optical pumping is a linear phenomenon for spontaneous decays. For the ladder-type EIT in the 5S_1/2- 5P_3/2-5D_5/2 transition of ⁸⁷Rb atoms, DROP undoubtedly affects the EIT spectrum. However, most previous results for the ladder-type EIT have neglected the DROP effect [15-18]. This is why the λ-type EIT is different from the spectrum change due to the optical pumping, but it difficult to analyze the difference of the spectra between EIT and DROP in the ladder-type EIT. The magnitude of the DROP is proportional to a two-photon transition probability and the frequency of the DROP is under the condition of the two-photon resonance similar to the EIT [20]. For this reason, the role of the DROP in the ladder-type EIT is more critical than that of optical pumping in the λ-type EIT.

In this paper, we identify the critical problem of optical pumping in the ladder-type EIT. The problem is that the DROP as a result of optical pumping may be dominant with the EIT due to the atomic coherence in the ladder-type system of alkali atoms, such as that shown in Fig. 1(b). We present a study of the influence of optical pumping on EIT in a 5S_1/2-5P_3/2-5D_5/2 ladder-type system with room temperature Rb atoms in a vapor cell.

 

Fig. 1 (a). Schemes of the λ-type atomic system in the 5S_1/2-5P_3/2 transition of ⁸⁷Rb atoms; (b) schemes of the ladder-type atomic system in the 5S_1/2-5P_3/2-5D_5/2 transition of ⁸⁷Rb atoms.

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2. Experimental setup

Figure 2(a) shows the experimental setup for a typical EIT in the 5S_1/2-5P_3/2-5D_5/2 ladder system of ⁸⁷Rb atoms [18]. The spontaneous decay rate of the 5P_3/2 level is approximately Γ_P = 6.0 MHz and the spontaneous decay rate of the 5D_5/2 level between the states of 5P_3/2 and 5D_5/2 is approximately Γ_D = 0.97 MHz. Two laser beams, the probe laser and coupling laser, counter-propagate through the Rb vapor cell. The wavelength of the probe laser is 780.2 nm and that of the coupling laser is 775.8 nm. Using a saturated absorption technique, we can monitor the frequency of the probe laser, which is scanned over the entire range of excited states in the 5P_3/2 transition of the Rb D₂ line. The coupling laser is free running around the 5D_5/2 transition.

Each laser’s power was controlled using a polarizing beam splitter (PBS) and a half-wave plate (HWP), and then the two laser beams were overlapped with a beam splitter (BS). Next, the beams were directed to pass through an aperture of 2 mm diameter and a 10 cm-long Rb vapor cell at room temperature. To minimize the effect of the Earth’s magnetic field, the Rb cell was wrapped three times with a μ-metal sheet. The probe laser was separated by the beam splitter and then detected using a Si photodiode (PD).

The ladder-type EIT spectrum of the 5S_1/2-5P_3/2-5D_5/2 transition of ⁸⁷Rb atoms has already been studied [18]. Figure 2(b) shows the typical ladder-type EIT spectrum that was a result of the previous study, where the probe intensity and coupling intensity were 0.5 mW/cm² and 7.5 mW/cm², respectively. We can observe the highly resolved hyperfine structures of the 5D_5/2 transitions in the transmittance spectrum of Fig. 2(b). At this time, the coupling intensity was reduced and the focusing lens used in previous studies was removed in order to obtain a narrow transmittance spectrum in the ladder-type atomic system [15-17].

 

Fig. 2. (a). Experimental setup to observe the ladder-type EIT spectrum (BS: beam splitter, AP: aperture, PD: photo diode, QWP: quarter-wave plate, and HWP: half-wave plate); (b) a typical ladder-type EIT spectrum of the 5S_1/2-5P_3/2-5D_5/2 transition.

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3. Experimental results and discussions

However, only recently we discovered that the transmittance signal can occur in not only the quantum destructive interference due to the atomic coherence, but also in the population change of the state that results from the optical pumping. When the probe laser is very weak and the coupling laser is strong, we can observe an interesting double structure transmittance spectrum in the 5S_1/2(F=2)-5P_3/2(F’=3)-5D_5/2(F”=4) cycling transition, as shown in Fig. 3. The double structure spectrum is composed of a narrow spectrum resulting from the EIT and a broad spectrum caused by the DROP, where the probe intensity and coupling intensity are 30 μW/cm² (profile-averaged Rabi frequency 0.1Γ_P) and 60 mW/cm² (profile-averaged Rabi frequency 1.6Γ_D), respectively. The polarizations of two lasers are perpendicular, linearly polarized lights. The spectral width of DROP is limited into the spontaneous decay rates (Γ_P and Γ_D) of the 5P_3/2 level and of the 5D_5/2 level and one of EIT is limited into the coherence dephasing rates (Γ_D/2) of the dipole forbidden transitions. In Fig. 3 the main broadening mechanism of DROP is due to the spontaneous decay and one of EIT is due to the phase noise between the probe laser and the coupling laser.

The EIT resulting from the atomic coherence is dominant in the cycling transition because the population of the 5S_1/2(F=2) ground state is not depleted by optical pumping due to the selection rule. However, we cannot observe a narrow EIT signal in the 5D_5/2(F”=2 and 3) transitions even though the peaks are sharp. In those transitions, the population of one ground state (F=2) may be depleted because the atoms that have been excited into an excited state (5D_5/2) can be optically pumped into another ground state (F=1) through intermediate states (5P_3/2). Thus, it can be understood that DROP surpasses EIT in those 5S_1/2(F=2)-5P_3/2(F’=3)- 5D_5/2(F”=2 and 3) transitions.

 

Fig. 3. Double structure transmittance spectrum in the 5S_1/2(F=2)-5P_3/2(F’=3)-5D_5/2(F”=4) cycling transition.

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Figure 4 is the transmittance spectra as a function of the intensity of the probe laser in the 5S_1/2(F=2)-5P_3/2(F’=3)-5D_5/2(F”=2,3,4) transitions of ⁸⁷Rb atoms, where the coupling intensity is 60 mW/cm². The polarizations of two lasers are perpendicular, linearly polarized lights. As the intensity of the probe laser is decreased, we can see the interesting phenomenon of the double structure transmittance spectrum in the cycling transition as shown in Fig. 4. In Fig. 4(c), we can clearly see the double structure spectrum with the narrow spectrum due to the EIT and the broad spectrum due to the DROP. In the cycling transition, when the intensity of the probe laser is weaker, the optical pumping effect is lower and the atomic coherence effect is relatively higher, because the population excited to the 5P_3/2(F’=3) intermediate state is decreased. However, as the intensity of the coupling laser is increased, the double structure spectrum becomes clearer. Because the intensity of the coupling laser is related to the atomic coherence, when the intensity of the coupling laser is stronger, the atomic coherence between the 5S_1/2(F=2) state and the 5D_5/2(F”=4) state is higher.

 

Fig. 4. The transmittance spectra according to the probe intensity in the 5S_1/2(F=2)- 5P_3/2(F’=1,2,3)-5D_5/2(F”=2,3,4) transition of ⁸⁷Rb atoms.

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Figure 5 is the transmittance spectra in the 189 MHz detuning of the coupling laser, where the probe intensity and coupling intensity are 0.25 mW/cm² and 50 mW/cm², respectively. The inset in Fig. 5 is the transmittance spectrum after being subtracted from the linear absorption. The spectrum in the cycling transition is dispersive-like. This is the typical spectrum of EIT in an atomic vapor under the condition of the frequency detuning of the coupling laser. This means that the narrow spectrum of the double structure spectrum is due to the EIT. In the other transitions, although the transmittance spectrum includes the atomic coherence effects, the features of the spectrum are maintained because the DROP is dominant. From these results, we can assert that the DROP critically affects the transmittance spectrum of the ladder-type EIT in alkali atoms with two ground states.

 

Fig. 5. The transmittance spectra in the 189 MHz detuning of the coupling laser.

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Although the energy levels of the Rb atoms used in our experiment have a much more complicated structure, a simple five-level ladder-type atomic system is useful in understanding the DROP effects of the ladder-type EIT, as shown in Fig. 6(a). The five-level ladder-type atomic system is based on the interaction of molecules or atoms with two optical fields that are resonantly tuned to two transitions that share a common state. The excited state |5〉 is coupled to the intermediate state |4〉 by a stronger coupling field with a Rabi frequency Ω_C and detuning Δ, while the intermediate state |4〉 is coupled to the ground state |2〉 by a weaker probe field with a Rabi frequency Ω_p and detuning δ. When the atoms are resonant with the fields of the two lasers, the population in |2〉 may be depleted because many atoms that have been excited into the excited state |5〉 can be optically pumped into another ground state |1〉 through the intermediate states (|3〉 or |4〉). γ_nm is the rate of spontaneous emission from state |n〉 to state |m〉, whereas γ₁₂ describes the decay rate of the coherences between these states.

We have tried to calculate numerically the density matrix equation in the five-level ladder-type atomic system. The time-dependent Schrodinger equation is written in the density matrix formalism as $\frac{\partial \hat{\mathit{\rho }}}{\partial \mathit{t}}=\frac{1}{\mathit{ih}}[{\mathit{H}}_{\mathit{t}},\hat{\rho }]$, where $\widehat{\rho }$ is the density matrix. The total Hamiltonian in the density matrix equation, H_t, is H(t) = H₀ + H_int + H_R, where H₀ and H_int are the unperturbed and the interaction Hamiltonians and H_R is the relaxation Hamiltonian described all relaxation processes. Figures 6(b) and 6(c) show the calculated transmittance spectra of the probe laser in the 5S_1/2(F=2)-5P_3/2(F’=3)-5D_5/2(F”=4) cycling transition for reasonable parameter values. When the coupling detuning Δ is 0, Fig. 6(b) shows a double structure transmittance spectrum composed of a narrow spectrum resulting from the EIT and a broad spectrum caused by the DROP, which is similar to the experimental spectrum (c) in Fig. 4, where Ω_p and Ω_C are 1.2 MHz (0.2 Γ_P) and 2.8 MHz (2.8 Γ_D), respectively. Also, when the coupling detuning Δ is 189 MHz, Fig. 6(c) shows the dispersive-like transmittance spectrum similar to the spectrum in the cycling transition of Fig. 5. Thus, it is confirmed that the calculated spectra agree with the experimental spectra.

 

Fig. 6. (a). Schemes of the ladder-type five-level atomic system; (b). the calculated transmittance spectrum of the probe laser in the on-resonance (Δ = 0); and (c). the calculated dispersive-like transmittance spectrum in the off-resonance (Δ = 189 MHz).

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4. Conclusion

In conclusion, we investigated that the ladder-type EIT spectrum included the DROP effects in the 5S_1/2-5P_3/2-5D_5/2 transition of ⁸⁷Rb atoms. The DROP is the optical pumping into another ground state through the intermediate states in the ladder-type atomic system. We dug up that the well-known ladder-type EIT spectrum included the DROP effect seriously. In the 5S_1/2(F=2)-5P_3/2(F’=3)-5D_5/2(F”=4) cycling transition, when the probe laser is very weak and the coupling laser is strong, we could observe the interesting double structure transmittance spectrum composed of the narrow spectrum due to the EIT and the broad spectrum resulting from the DROP. We simulated the transmittance spectrum of the probe laser in the simple five-level ladder-type atomic system, and the calculated spectra agree with the experimental results. We showed that most ladder-type EIT spectra included the DROP effects. The DROP may be dominant in the transmittance signal of the 5S_1/2(F=2)-5P_3/2(F’=3)-5D_5/2(F”=2 or 3) transition. In the case of the 5S_1/2(F=1)-5P_3/2(F’=0,1,2)-5D_5/2(F”=0,1,2,3) transition, we could not observe both the EIT and the DROP, because most atoms excited to 5P_3/2(F’=1,2) intermediate state spontaneously transferred into another 5S_1/2(F=2) ground state. The ladder-type EIT is not free from the optical pumping effect which is more serious in the ladder-type EIT than in the λ-type EIT. We believe that our results have helped attain an understanding of the coherent laser spectroscopy in the ladder-type atomic systems.