Orbital-Angular-Momentum Multiplexed Continuous-Variable Entanglement from Four-Wave Mixing in Hot Atomic Vapor

Xiaozhou Pan, Sheng Yu, Yanfen Zhou, Kun Zhang, Kai Zhang, Shuchao Lv, Sijin Li, Wei Wang, and Jietai Jing

Phys. Rev. Lett. 123, 070506 – Published 16 August 2019

Abstract

Multiplexing is crucial for the data-carrying capacity of information communication systems. Orbital angular momentum (OAM) with a topological charge $ℓ$ ( $ℓ$ integer) provides a degree of freedom to realize multiplexing. In this Letter, we report an experimental implementation of OAM multiplexed continuous variables (CV) entanglement based on a four-wave mixing (FWM) process, in which 13 pairs of entangled Laguerre-Gauss (LG) modes, ${LG}_{ℓ, pr}$ and ${LG}_{- ℓ, conj}$ , are simultaneously and deterministically generated, where $ℓ$ ( $ℓ$ integer) is the topological charge corresponding to the OAM mode and pr (conj) indicates a probe (conjugate) beam. In the meanwhile, we experimentally show that there is no entanglement between the modes of ${LG}_{ℓ, pr}$ and ${LG}_{ℓ, conj}$ ( $ℓ \neq 0$ ). These results clearly confirm the conservation of OAM in the FWM process from the viewpoint of a CV system. In addition, we investigate the entanglement properties of three types of coherent superposition of OAM modes. In the end, we also study the effect of the pump beam radius on the number of OAM multiplexing. Such OAM multiplexed CV entanglement provides a new perspective and platform to study CV quantum information protocols.

Received 8 October 2018

DOI:https://doi.org/10.1103/PhysRevLett.123.070506

Physics Subject Headings (PhySH)

Angular momentum of light Entanglement production Optical quantum information processing Quantum entanglement

Four-wave mixing

Quantum Information, Science & Technology

Authors & Affiliations

Xiaozhou Pan¹, Sheng Yu¹, Yanfen Zhou¹, Kun Zhang¹, Kai Zhang¹, Shuchao Lv¹, Sijin Li¹, Wei Wang¹, and Jietai Jing^1,2,3,*

¹State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China
²Department of Physics, Zhejiang University, Hangzhou 310027, China
³Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China

^*Corresponding author. jtjing@phy.ecnu.edu.cn

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Vol. 123, Iss. 7 — 16 August 2019

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Images

Figure 1
Schematic experimental setup for generating and detecting the OAM multiplexed CV entanglement from a FWM process. (a) The FWM process happens in a Rb cell and the generated multiple pairs of OAM modes from it are detected by two BHDs. The obtained photocurrents are analyzed by two sets of SAs. Rb cell: hot ${}^{85}{Rb}$ vapor cell; $P$ : pump beam; pr: probe beam; conj: conjugate beam; $ℓ$ : topological charge; ${LO}_{- ℓ, pr}$ and ${LO}_{ℓ, conj}$ : local oscillator of pr and conjugate beams; ${BS}_{1}$ and ${BS}_{2}$ : $50 ∶ 50$ beam splitters; ${BHD}_{1}$ and ${BHD}_{2}$ : balanced homodyne detections; ${SA}_{1}$ and ${SA}_{2}$ : spectrum analyzers. (b) The involved energy level diagram of the double- $Λ$ scheme in the $D 1$ line of ${}^{85}{Rb}$ . The wavelength of the pump beam is about 794.9708 nm, corresponding to a frequency of 377.1102 THz. The pr beam frequency is redshifted by 3.04 GHz from the pump beam. (c) The resultant OAM spectrum from the FWM process, indicating the OAM conservation of such process. (d) A Dove prism is inserted into the optical path of ${LO}_{pr}$ so as to transfer the ${LO}_{- ℓ, pr}$ mode to the ${LO}_{ℓ, pr}$ mode when we test the entanglement between ${LG}_{- ℓ, pr}$ and ${LG}_{- ℓ, conj}$ modes.
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Figure 2
The entanglement test between ${LG}_{ℓ, pr}$ and ${LG}_{- ℓ, conj}$ modes vs $ℓ$ . Trace $A$ (red triangle) denotes the intensity gain of pr and trace $B$ (blue dot) is the symplectic eigenvalue $ν$ of the corresponding PT CM.
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Figure 3
The entanglement test between ${LG}_{- ℓ, pr}$ and ${LG}_{- ℓ, conj}$ modes vs $ℓ$ . Trace $A$ (red triangle) denotes the intensity gain of pr and trace $B$ (blue dot) is the symplectic eigenvalue $ν$ of the corresponding PT CM.
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Figure 4
The entanglement test for three types of coherent OAM superposition modes. (a) The entanglement test between $\sqrt{k} {LG}_{1, pr} + \sqrt{1 - k} {LG}_{5, pr}$ and $\sqrt{k} {LG}_{- 1, conj} + \sqrt{1 - k}$ ${LG}_{- 5, conj}$ modes vs $k$ . The second row are the computer-generated hologram in the case of $k = 0.5$ and the corresponding image of output fields. (b) The entanglement test between ${LG}_{ℓ, pr} + {LG}_{- ℓ, pr}$ and ${LG}_{- ℓ, conj} + {LG}_{ℓ, conj}$ modes vs $ℓ$ . The second row are the computer-generated hologram in the case of $ℓ = 3$ and the corresponding image of output fields. (c) The entanglement test between ${LG}_{1, pr} + e^{2 i θ} {LG}_{- 1, pr}$ and ${LG}_{- 1, conj} + e^{2 i θ} {LG}_{1, conj}$ modes vs phase $θ$ . The second row are the computer-generated hologram in the case of $θ = 45 °$ and the corresponding image of output fields. For all subfigures, trace $A$ (red triangle) denotes the intensity gain of pr and trace $B$ (blue dot) is the symplectic eigenvalue $ν$ of the corresponding PT CM.
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Figure 5
The entanglement test between ${LG}_{ℓ, pr}$ and ${LG}_{- ℓ, conj}$ modes vs $ℓ$ when the pump beam radius $w_{P}$ is set to (a) $255 μ m$ , (b) $355 μ m$ , (c) $450 μ m$ , and (d) $600 μ m$ , respectively. Trace $A$ (red triangle) denotes the intensity gain of pr and trace $B$ (blue dot) is the symplectic eigenvalue $ν$ of the corresponding PT CM. Their numbers of OAM multiplexing ( $N_{mux}$ ) are 7, 11, 13, and 15, respectively. The pump power is kept at 140 mW.
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