Electromagnetically induced transparency with controlled van der Waals interaction

Huaizhi Wu, Meng-Meng Bian, Li-Tuo Shen, Rong-Xin Chen, Zhen-Biao Yang, and Shi-Biao Zheng

Phys. Rev. A 90, 045801 – Published 9 October 2014

Abstract

We study the electromagnetically induced transparency (EIT) effect with two individually addressed four-level Rydberg atoms subjected to the interatomic van der Waals interaction. We derive an effectively atomic Raman transition model where two ladders of the usual Rydberg EIT setting terminating at the same upper Rydberg level of long radiative lifetime are turned into a Rydberg EIT $λ$ setup via two-photon transitions, leaving the middle levels of each ladder largely detuned from the coupling and probe laser beams. It can hence overcome the limits of applications for EIT with atoms of the ladder-type level configuration involving a strongly decaying intermediate state by inducing coherence between two ground states. By probing one of the atoms, we observe four doublets of absorption induced by the Autler-Townes splitting and the van der Waals interaction. In particular, we find that the location of the EIT center remains unchanged compared to the interatomic-interaction-free case, which demonstrates that the interference among the multiple transition channels is basically destructive. The EIT with controlled Rydberg-Rydberg interaction among a few atoms provides a versatile tool for engineering the propagation dynamics of light.

Received 19 April 2014

DOI:https://doi.org/10.1103/PhysRevA.90.045801

Authors & Affiliations

Huaizhi Wu, Meng-Meng Bian, Li-Tuo Shen, Rong-Xin Chen, Zhen-Biao Yang, and Shi-Biao Zheng

Department of Physics, Fuzhou University, Fuzhou 350108, People's Republic of China

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Vol. 90, Iss. 4 — October 2014

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Figure 1
(a) Sketch of setup. (b) Atomic level structure and laser addressing scheme. The level structure consists of the Zeeman substates of the two hyperfine ground states $F = 1, 2$ of $5 s_{1 / 2}$ , the excited state $F^{'} = 2$ of $5 p_{1 / 2}$ , and $F^{''} = 3$ of the high-lying Rydberg state $n d_{3 / 2}$ . A $π$ -polarized laser beam red detuned to the $| F = 2, m_{F} = 2 〉 \to | F^{'} = 2, m_{F^{'}} = 2 〉$ transition and a $σ^{+}$ -polarized laser beam blue detuned to the $| F^{'} = 2, m_{F^{'}} = 2 〉 \to | F^{''} = 3, m_{F^{''}} = 3 〉$ transition together act as the coupling channel, while the probe scan is implemented by two $σ^{+}$ -polarized laser beams blue detuned to the $| F = 1, m_{F} = 1 〉 \to | F^{'} = 2, m_{F^{'}} = 2 〉$ transition and red detuned to the $| F^{'} = 2, m_{F^{'}} = 2 〉 \to | F^{''} = 3, m_{F^{''}} = 3 〉$ transition, respectively. The inset shows the reduced effective model where the two ladders of the usual Rydberg EIT setting terminating at the same upper Rydberg level are turned into the usual EIT $λ$ setup after eliminating the intermediate level $| e 〉$ for the large detuning regime. (c) Rydberg spectra without interatomic interaction for increasing probe Rabi frequencies $Ω_{p_{1}, p_{2}}$ . The resonance peaks are displaced due to the Stark shifts induced by the coupling and probe laser beams. The parameters are $Δ_{p_{2}} / 2 π = 50$ MHz, $Ω_{p_{2}} = Ω_{p_{1}}$ , $Δ_{c_{1}, c_{2}} / 2 π = 1$ GHz, $Ω_{c_{1}, c_{2}} / 2 π = 20$ MHz, and $(γ_{e c}, γ_{e p}, γ_{r}) / 2 π = (3, 3, 0.1)$ MHz.
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Figure 2
(a) Two-atom transition scheme involving the vdW interaction. The collective Rydberg excited state is shifted according to the attractive potential $V (R)$ . (b) Atomic transition channels induced by the vdW interaction and the AT splitting, not to scale (see the text).
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Figure 3
(a) Rydberg population versus probe laser detuning and the vdW interaction with $Ω_{p_{1}, p_{2}} / 2 π = 1$ MHz and $Δ_{p_{2}} / 2 π = 50$ MHz; other parameters are the same as in Fig. 1 and we have assumed that the two atoms uniformly interact with the coupling laser beams. As predicted in Fig. 2, eight resonant peaks (corresponding to the eight dipole-allowed atomic transition channels) can be resolved in the Rydberg spectra as the vdW interaction strength increases. A detailed calculation by considering two interacting Rydberg atoms with one of them being probed fits well with the numerical results (black dashed line). (b)-(e) Line cut of the Rydberg spectra along $V (R) / 2 π = 0.2$ , 0.5, 1, and 1.5 MHz in (a). The EIT center and the absorption peaks are indicated.
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Figure 4
Rydberg spectra for distinct spontaneous emission rates $γ_{r} / 2 π = 0.01$ , $0.05$ , and $0.1$ MHz corresponding to different Rydberg levels. The interatomic interaction strengths are (a) $V (R) / 2 π = 1.1$ MHz and (b) $V (R) / 2 π = 4$ MHz. Other parameters are the same as in Fig. 3.
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