Tunable partial polarization beam splitter and optomechanically induced Faraday effect

Xuan Mao, Guo-Qing Qin, Hong Yang, Zeguo Wang, Min Wang, Gui-Qin Li, Peng Xue, and Gui-Lu Long

Phys. Rev. A 105, 033526 – Published 29 March 2022

Abstract

The polarization beam splitter (PBS) is a crucial photonic element to separately extract transverse-electric and transverse-magnetic polarizations from propagating light fields. Here, we propose a concise, continuously tunable, and all-optical partial PBS in a vector optomechanical system which contains two orthogonal polarized cavity modes with degenerate frequency. The results show that one can manipulate the polarization states of different output fields by tuning the polarization angle of the pumping field and the system functions as a partial PBS when the pump laser polarizes vertically or horizontally. As a significant application of the tunable PBS, we propose a scheme of implementing quantum walks in resonator arrays without the aid of other auxiliary systems. Furthermore, we investigate the optomechanically induced Faraday effect in a vector optomechanical system which enables arbitrary tailoring of the input lights and the behaviors of polarization angles of the output fields in the undercoupling, critical coupling, and overcoupling regimes. Our findings prove the optomechanical system is a potential platform to manipulate the polarization states in multimode resonators and boost the process of applications related to polarization modulation.

Received 20 December 2021
Accepted 18 March 2022

DOI:https://doi.org/10.1103/PhysRevA.105.033526

Physics Subject Headings (PhySH)

Light-matter interaction Optomechanics

Optical microcavities

Atomic, Molecular & Optical

Authors & Affiliations

Xuan Mao^1,*, Guo-Qing Qin^1,*, Hong Yang¹, Zeguo Wang¹, Min Wang ², Gui-Qin Li^1,3, Peng Xue^4,†, and Gui-Lu Long ^{1,2,3,5,6,‡}

¹Department of Physics, State Key Laboratory of Low-Dimensional Quantum Physics, Tsinghua University, Beijing 100084, China
²Beijing Academy of Quantum Information Sciences, Beijing 100193, China
³Frontier Science Center for Quantum Information, Beijing 100084, China
⁴Beijing Computational Science Research Center, Beijing 100084, China
⁵Beijing National Research Center for Information Science and Technology, Beijing 100084, China
⁶School of Information, Tsinghua University, Beijing 100084, China

^*These authors contributed equally to this work.
^†gnep.eux@gmail.com
^‡gllong@tsinghua.edu.cn

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Vol. 105, Iss. 3 — March 2022

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Images

Figure 1
(a) Schematic of the vector optomechanical system. (b) Frequency spectrogram of the vector optomechanical system.
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Figure 2
Transmissions of different ports with different polarizations as a function of $θ / π$ and $δ / ω_{m}$ : (a) port 2 with vertical polarization, (b) port 2 with horizontal polarization, (c) port 4 with vertical polarization, and (d) port 4 with horizontal polarization. (e) and (f) illustrate the transmissions of ports 2 and 4 when $θ = 0$ . (g) and (h) illustrate the transmissions of ports 2 and 4 when $θ = π / 2$ . The parameters used in this system are $κ_{0 ↕} / 2 π = κ_{0 \leftrightarrow} / 2 π = κ_{0} / 2 π = 1$ MHz, $κ_{ex 1} / 2 π = 9$ MHz, $κ_{ex 2} / 2 π = 8$ MHz, $ω_{m} / 2 π = 90.47$ MHz, $Γ_{m} / 2 π = 22$ kHz, $G_{↕} / 2 π = 5.5 sin (θ)$ MHz, $G_{\leftrightarrow} / 2 π = 5.5 cos (θ)$ MHz, $c = 3 \times 10^{8}$ m/s, $λ = 1550$ nm, $P_{r} = 20 μ W$ , and $α = π / 4$ .
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Figure 3
The transmission of different ports with different polarizations as a function of $κ_{ex 2} / κ_{ex 20}$ and $δ / ω_{m}$ . (a)–(e) are in the case of $θ = 0$ and (f)–(j) are in the case of $θ = π / 2$ . (e) and (j) indicate the transmission rate of different ports with vertical or horizontal polarization when tuning the value of $κ_{ex 2}$ in the case of resonance $δ = ω_{m}$ . $κ_{ex 20} / 2 π = 8$ MHz and $κ_{ex 1} = κ_{ex 2} + κ_{0}$ . The other parameters are the same as that in Fig. 2.
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Figure 4
The total transmission rate as a function of $θ / π$ and $δ / ω_{m}$ : (a) port 2 $T_{2}$ and (b) port 4 $T_{4}$ . (c) The total transmission rate $T_{2}$ and $T_{4}$ as a function of $δ / ω_{m}$ with different values of $θ$ . The other parameters are the same as that in Fig. 2.
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Figure 5
(a) Schematic of implementation of QW in an optomechanical system. HWP: half-wavelength plate. (b) The probability distribution of the QW in resonator arrays with the walkers starting from $x = 0$ and the coin state chosen to be $(| H 〉 + | V 〉) / \sqrt{2}$ for the first six steps. (c) The standard deviation of the QW (blue solid line), the classical random walks (the red dashed line), and the QW in the resonator arrays (triangle markers) for the first 15 steps. The parameters are the same as that in Fig. 2.
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Figure 6
The angle between the polarization of the output field and the horizontal mode $β / π$ as a function of $θ / π$ and $Δ κ_{ex 2} / κ_{ex 20}$ : (a) port 2 and (c) port 4. (b) Schematic of the input and output field polarization angles in the vector optomechanical system. The angle $β / π$ of different ports as a function of $θ$ with different values of $Δ κ_{ex 2} / κ_{ex 20}$ : (d) 0.25, (e) 0, and (f) $- 0.25$ . $κ_{ex 20} / 2 π = 8$ MHz. The other parameters are the same as that in Fig. 2.
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