Duality and bistability in an optomechanical cavity coupled to a Rydberg superatom

Dong Yan, Zhi-Hai Wang, Chun-Nian Ren, Hang Gao, Yong Li, and Jin-Hui Wu

Phys. Rev. A 91, 023813 – Published 11 February 2015

Abstract

We study the steady-state behaviors of a typical optomechanical cavity coupled to cold Rydberg atoms with dipole-dipole interactions. The interacting atoms are described as one superatom of three collective states in a ladder configuration in the limit of a strong dipole blockade and a weak cavity field. We find that this hybrid system exhibits phenomena of conditional duality and nonlinear bistability in terms of mirror displacement, number of cavity photons, and Rydberg population, depending on the detuning of the cavity field, the strength of the optical driving field, and the number of cold atoms. It is of particular interest that the two branches of relevant curves may intersect to yield a nontrivial duality and bistability. Such correlated optical, mechanical, and atomic responses arise from the efficient feedback between atom-light and optomechanical interactions and have realistic applications, e.g., in realizing accurate optomechanical detection or attaining deterministic single photons.

Received 22 October 2014

DOI:https://doi.org/10.1103/PhysRevA.91.023813

Authors & Affiliations

Dong Yan^1,2,3, Zhi-Hai Wang⁴, Chun-Nian Ren⁵, Hang Gao², Yong Li^4,*, and Jin-Hui Wu^1,†

¹Center for Quantum Sciences, Northeast Normal University, Changchun 130117, People's Republic of China
²School of Mathematics and Statistics, Northeast Normal University, Changchun 130117, People's Republic of China
³School of Science, Changchun University, Changchun 130022, People's Republic of China
⁴Beijing Computational Science Research Center, Beijing 100084, People's Republic of China
⁵School of Information Science and Technology, Qingdao University of Science and Technology, Qingdao 266061, People's Republic of China

^*liyong@csrc.ac.cn
^†jhwu@nenu.edu.cn

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Vol. 91, Iss. 2 — February 2015

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Images

Figure 1
(a) Schematic diagram of a hybrid optomechanical cavity containing one SA composed of many interacting cold Rydberg atoms. A classical driving field of frequency $ω_{d}$ is used to excite a single-mode quantum cavity field of frequency $ω_{c}$ , which acts upon the SA together with a classical pumping field of frequency $ω_{p}$ . (b) Top: Each cold atom is driven to form a ladder-level configuration with $V_{vdW}$ representing the vdW potential of dipole-dipole interaction. Bottom: Schematic diagram of the SA levels in the weak cavity field limit with the coupling strength on the transition $|E^{(1)}〉 \leftrightarrow |G〉$ being enhanced by the factor $\sqrt{n_{s a}}$ as compared to that on the transition $|e〉 \leftrightarrow |g〉$ .
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Figure 2
Steady-state solutions of $〈x〉$ (a), $Δ_{c}$ (b), $〈ϱ_{r r}〉$ (c), and Im( $χ$ ) (d) versus $Δ_{0}$ , with $Δ_{p} = 0$ and $n_{s a} = 10^{4}$ . The black solid, blue dashed, and red dotted curves correspond to $β = 1.0 \times 10^{3}$ ${Hz}^{1 / 2}$ , $4.0 \times 10^{3}$ ${Hz}^{1 / 2}$ , and $8.0 \times 10^{3}$ ${Hz}^{1 / 2}$ , respectively. Other useful parameters are given at the beginning of Sec. 3.
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Figure 3
Steady-state solutions of $〈 x 〉$ (a), $Δ_{c}$ (b), $〈 ϱ_{r r} 〉$ (c), and $〈 n 〉$ (d) versus $Δ_{0}$ with the same parameters as in Fig. 2 except $β = 1.5 \times 10^{4}$ ${Hz}^{1 / 2}$ . The black, blue, and red curves are calculated for one Rydberg SA, many three-level atoms, and many two-level atoms, respectively. In all curves, the solid parts (black solid, blue solid-circle, and red solid-triangle) correspond to the stable solutions while the other (dotted, dashed, and dash-dotted) parts correspond to the unstable solutions.
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Figure 4
Rydberg population $〈 ϱ_{r r} 〉$ and mirror displacement $〈 x 〉$ versus the strength of the driving field $β$ (left panels) and the number of cold atoms $n_{s a}$ (right panels) with the same parameters as in Fig. 2 except $Δ_{0} = 0$ .
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Figure 5
Rydberg population $〈 ϱ_{r r} 〉$ and mirror displacement $〈 x 〉$ versus cavity detuning $Δ_{0}$ with the same parameters as in Fig. 2 except $n_{s a} = 2000$ , $β = 2.0 \times 10^{3}$ ${Hz}^{1 / 2}$ , and $Δ_{p} = + 10$ MHz (left panels) and $Δ_{p} = - 10$ MHz (right panels). The black solid, blue dashed, and red dotted curves in panels (c) and (d) refer to one Rydberg SA, many three-level atoms, and many two-level atoms, respectively.
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Figure 6
Rydberg population $〈 ϱ_{r r} 〉$ and mirror displacement $〈 x 〉$ versus cavity detuning $Δ_{0}$ with the same parameters for one Rydberg SA as in Fig. 5 except $β = 1.0 \times 10^{4}$ ${Hz}^{1 / 2}$ . The black, blue, and red curves are calculated for one Rydberg SA, many three-level atoms, and many two-level atoms, respectively. In all curves, the solid parts (black solid, blue solid-circle, and red solid-triangle) correspond to the stable solutions while the other parts (dotted, dashed, and dash-dotted) correspond to the unstable solutions.
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