1. Introduction

Rydberg atoms are excited atoms with one or more electrons that have very high principal quantum number and have been extensively studied over many decades [1]. Rydberg atoms display exaggerated collision properties and rich many-body behavior and became a attractive candidate for quantum logic gates [2,3] due to their enhanced interactions. An important process is the dipole blockade in the Rydberg excitation of atoms which due to the long-range dipole-dipole interaction shifting the Rydberg energy from its isolated atomic level. Rydberg atoms are usually produced by two or three photons excitation and detected by using the selective pulsed field ionization method [1] in room temperature atomic beam or laser cooled cold atoms [4,5]. This detection method has high efficiency but is destructive and atoms cannot be reused. For application of quantum information, a nondestructive detection of the Rydberg atoms is necessary [6]. Electromagnetically induced transparency (EIT) will be a good candidate for nondestructive detection, which is manifest as a decrease or absence of absorption of probe laser due to the quantum coherence effect when the probe laser is resonance with the atomic transition in three-level system. EIT has been widely studied in atomic vapor [7] and in laser cooled atoms [8] in Lamdba, Vee and ladder-type three-level systems. The quantum coherence is induced between two ground states for Lamdba-type system or between the ground and excited states for ladder-type system. Clarke group [9] observed the EIT signal of excited D states with a principal quantum number is up to n = 8 in ladder-type rubidium atomic system. Mohapatra group [6] demonstrated the coherent optical detection of highly excited Rydberg states using EIT in rubidium atomic cell. Raithel group [10] obtained Autler-Townes spectroscopy of the 5S_1/2-5P_3/2-44D ladder-type system in cold rubidium atoms. The ladder-type atomic system combines the attractive features of both ground dark states and Rydberg states. We can use this system to map the long range interaction of Rydberg state on to the ground state. Recently EIT involving Rydberg states has been observed in thermal rubidium atomic vapor cell and a strontium atomic beam [11]; Adams group [12] demonstrated a giant electro-optic effect based on polarizable dark states and obtained an electro-optic coefficient of 10⁻⁶ m/V², which is 6 orders of magnitude larger than the Kerr cell based on Nitrobenzene.

In this work, we obtain the high sensitivity spectroscopy of Rydberg atoms (n = 39-55) by using EIT in cesium atomic vapor cell at room temperature. A nondestructive probe of nD Rydberg level is observed and the EIT linewidth is measured to be about 5.6MHz which near the natural linewidth. The dependences of the EIT linewidth and magnitude on the coupling laser power are investigated in detail. The fine structures of Rydberg states (n = 39-55) are measured and the result is in good agreement with the quantum defect theory.

2. Experiments

Relevant atomic levels and the experimental setup are shown in Fig. 1 . We present a ladder three-level system with a ground state |1> (6S_1/2 F = 4), an excited state |2> (6P_3/2 F’ = 5) and |3> (Rydberg nD states) interacting with two laser fields, which is shown in Fig. 1 (a). The transition |1>→ |2 > is coupled with the weak probe field with wavelength of λ_p = 852.3 nm, and another transition |2>→ |3 > is coupled with the intense coupling field with wavelength of λ_c = 509 nm - 517 nm. The probe laser is produced by an external-cavity diode laser (Toptica DL100) with the laser linewidth of ~1MHz, the power of 50μW, and the waist of about 1.2mm (1/e² radius), which propagates through a room temperature cesium atom vapor cell with length of 60mm. The coupling laser, produced by a commercial frequency doubled tunable diode laser system (Toptica TA-SHG110) with the linewidth less than 2MHz, counter-propagates through the cell with a maximum power up to 100mW and a waist of 1.0mm (1/e² radius). The frequency of the coupling laser is calibrated by the wavelength meter (HF-Angstrom WSU-30). The absorption of the weak probe beam is measured by an avalanche photodiode (Hamamatsu Si APD, S3884).

 

Fig. 1 (a) Relevant levels scheme used for the experimental demonstration of a ladder-type EIT. Ω_p and Ω_c are Rabi frequencies of probe and coupling beam, γ₂ and γ₃ are delay rates of level |2> and |3>. (b) Schematic of the experimental setup, where SAS: saturated absorption spectroscopy; M: reflecting mirror; PBS: polarization prism; BS: beam splitter; ST: second EIT device used to lock the coupling laser; DM: dichroic mirror.

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The probe laser is scanned cross the transition of 6S_1/2 (F = 4) to 6P_3/2(F’ = 5). The coupling laser is locked to the transition of 6P_3/2(F’ = 5)→nD using EIT signal in second cell or scanned cross the transition from 6P_3/2(F’ = 5) to the nD Rydberg states (the nD-state hyperfine splitting is not resolved) and relevant transition frequency is taken from Ref [13]. In order to reduce the effect of the stray magnetic fields, cesium vapor cell is placed in the μ-metal shield material. The experimental schematic diagram is shown in Fig. 1(b).

3. Results and discussions

Figure 2 shows the typical saturated absorption spectroscopy (SAS) (a) and the 6S_1/2-6P_3/2-nD ladder-type three-level system EIT signal involved 40D_5/2 Rydberg atoms (b) with the probe laser is scanned through the transition of 6S_1/2 (F = 4) to 6P_3/2 and the intense coupling laser is locked to the transition of 6P_3/2(F’ = 5) to 40D_5/2 using the second cell. The power of probe and coupling laser are 50μW and 60mW, respectively and corresponding EIT linewidth is measured to be 16MHz.

 

Fig. 2 A saturated absorption spectroscopy of probe laser (a) and EIT signal of ladder three levels system of Rydberg atoms 40D_5/2 (b), the weak probe beam is scanned through the transition of 6S_1/2 (F = 4)→ 6P_3/2 and the coupling laser is locked to the transition of 6P_3/2 (F’ = 5)→40D_5/2 Rydberg state.

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We can obtain a theoretical prediction for the EIT line shape using an approximate expression for the susceptibility derived under the condition of a weak probe laser [14]

Where Ω_p,c, Δ_p,c, and ω_p,c are Rabi frequencies, detunings and resonance frequencies of the probe or coupling laser, respectively, and N(v) is the number density of cesium atoms with velocity v, c is speed of the light, γ_2,3 are the decay rates of the intermediate and upper states in the cascade system. Because the Rydberg states lifetime increase with the principal quantum number increasing and scaling as n ³, the lifetime of the 40D state is much longer than that of 6P state and measured to be about 39μs [16], the decay rate of 40D state γ₃ is much less than that of 6P state, so we can ignore γ₃ in Eq. (1). Keep the detuning of coupling laser is zero and integrate the imaginary part of Eq. (1) at room temperature and we can obtain the absorption coefficient through the vapor cell as a function of the probe detuning.

In order to study the effect of the power of coupling laser on the EIT spectra, we keep the probe laser power fixed to 50μW and change the coupling laser power with neutral attenuation plates and measure the EIT signals, the results are shown in Fig. 3 (a) for signal magnitude and (b) for linewidth as the function of coupling laser power. It is clear that the EIT magnitude increases as the coupling laser power increases at power less than 60mW. However when the laser power is more than 60mW, the EIT magnitude is no longer increased and tends to saturate and similar results have been found in reference [14]. In addition, the linewidth of EIT resonance is also increases as the laser power increases. When the coupling laser power is 5.2mW, the linewidth of 5.6MHz is obtained, which is close to the natural linewidth of the intermediate 6P state (5.2MHz). The reasons for the broadening linewidth are complicated; there are two main factors, one is the power broadening effect and the other is EIT effect and double resonance optical pumping (DROP) effect.

 

Fig. 3 40D EIT signal versus the power of the coupling laser with (a) for the signal magnitude and (b) for the linewidth.

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DROP is the optical pumping phenomenon in the ladder-type atomic system, which is based on the interaction of atoms with two optical fields that are resonant with two transitions that share a common state. Kim group [15] investigated the DROP effect in 5S_1/2-5P_3/2-5D_5/2 rubidium atomic ladder-type system, and they obtained the double structure spectrum with the narrow line for EIT and broad line for DROP. For the ladder-type system, the EIT signals can be observed in the counter-propagation regime of pump and probe lasers, while the DROP signals are observed in both the counter-propagation and co-propagation regime [14]. In order to investigate the DROP and EIT phenomena further, we make the pump and probe lasers co-propagation through the cesium vapor cell and measure the absorption of the probe laser. DROP signal is obtained and compared with the EIT signal. At the condition of the weak probe laser of 50μW, the DROP signal is much smaller than the EIT signal, as the population of the intermediate states is very low, so the DROP signal is very small or no DROP signal. EIT is a nonlinear effect for atomic coherence, there is a larger EIT signal although the power of probe laser is very small, and result is shown in Fig. 4 with the probe laser is locked to the transition of 6S_1/2(F = 4)→6P_3/2(F’ = 5) and the coupling laser is scanned cross the transition from 6P_3/2(F’ = 5) to 50D. The big and small peaks denote the coupling laser resonant with 6P_3/2(F’ = 5)→50D_5/2 and 6P_3/2(F’ = 5)→50D_3/2 transitions, respectively. However a larger DROP signal is obtained when we increase the power of the probe. On the other hand, DROP affects the EIT spectrum profile, the DROP signal linewidth is limited into the spontaneous decay rates of 6P and nD levels and that of the EIT is limited into the coherence dephasing rate of dipole forbidden transitions. For ladder-type EIT, we can obtain the signal with narrow linewidth by decreasing the probe laser power.

 

Fig. 4 DROP (a) and EIT (b) signals under the condition of the weak probe beam is locked to the transition of 6S_1/2 (F = 4)→ 6P_3/2 (F’ = 5) and the coupling laser is scanned through the transition of 6P_3/2 (F’ = 5)→50D Rydberg state.

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The fine structure splitting is an important parameter for Rydberg atoms and has been measured using two-photon absorption and a thermionic diode to detect the ionized Rydberg rubidium atoms [17]. The fine structure splitting of rubidium atoms was also obtained by laser excitation and field ionization of ultracold Rydberg atoms [18]. Here we obtain the cesium atomic nD states fine structure splittings by using the high sensitivity Rydberg atoms EIT spectroscopy at a room temperature vapor cell. We lock the probe laser to the transition of 6S_1/2(F = 4)→6P_3/2(F’ = 5) using polarization spectroscopy and tune the coupling laser frequency cross the 6P_3/2(F’ = 5)→40D transition in counter-propagating regime. We measure the probe absorption signal and obtain the fine structures of 40D. The corresponding excited wavenumber of coupling laser are 19596.2175 cm⁻¹ for 40D_3/2 and 19596.2556 cm⁻¹ for 40D_5/2, respectively, which is consistent with the theoretical value that is calculated using quantum defect theory. The EIT spectra give a measurement of 40D state fine structure splitting of 0.0381 cm⁻¹.

We change the wavelength of coupling laser for different nD states (n = 39-55) and further investigate the EIT resonance as well as fine structure. The fine structure splittings of the nD states are measured experimentally and Fig. 5 shown fine structure splittings as a function of principal quantum number n. We calculate the fine structure splittings of nD state according to the quantum defect theory and the result is shown in Fig. 5 with red solid line. It is clear that the experiment is in agreement with the quantum defect prediction.

 

Fig. 5 The measured Rydberg D state fine structure splittings as a function of the principal quantum number and the red solid line is the theoretical calculation by using the quantum defect theory, the quantum defect of cesium D state is 2.4699 [13].

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4. Conclusion

In conclusion, we have demonstrated EIT in ladder-type three levels system involved Rydberg states (n = 39-55) at the room temperature cesium cell, which providing a direct nondestructive probe of Rydberg energy levels. The dependences of the EIT linewidth and magnitude on coupling laser power are investigated and linewidth of 5.6MHz that is near to the natural linewidth is obtained. The fine structure splittings of nD states are also measured and the results are in agreement well with the quantum defect theory. Rydberg atom is very sensitive to external electric field and one important feature is the possibility to tune the interaction strength by electric field in Forster resonances process [5]. On the other hand, Rydberg atoms can lead to a giant electro-optic effect based on the polarizable dark states [12]. This effect will open up the prospect of single particle detection and single photon entanglement and so on.