Magnon-induced chaos in an optical $\mathcal{PT}$-symmetric resonator

Magnon-induced chaos in an optical $PT$ -symmetric resonator

Wen-Ling Xu, Xiao-Fei Liu, Yang Sun, Yong-Pan Gao, Tie-Jun Wang, and Chuan Wang

Phys. Rev. E 101, 012205 – Published 10 January 2020

Abstract

Optomagnonics supports optical modes with high-quality optical factors and strong photon-magnon interaction on the scale of micrometers. These novel features provide an effective way to modulate the electromagnetic field in optical microcavities. Here in this work, we studied the magnon-induced chaos in an optomagnonical cavity under the condition of parity-time symmetry, and the chaotic behaviors of electromagnetic field could be observed under ultralow thresholds. Even more, the existence optomagnetic interaction makes this chaotic phenomenon controllable through modulating the external field. This research will enrich the study of light matter interaction in the microcavity and provide a theoretical guidance for random number state generation and the realization of the chaotic encryption of information on chips.

Received 30 June 2019

DOI:https://doi.org/10.1103/PhysRevE.101.012205

Physics Subject Headings (PhySH)

Optomechanics Quantum optics

Atomic, Molecular & Optical

Authors & Affiliations

Wen-Ling Xu, Xiao-Fei Liu, Yang Sun, Yong-Pan Gao, Tie-Jun Wang ^*, and Chuan Wang

School of Science and the State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China

^*wangtiejun@bupt.edu.cn

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Vol. 101, Iss. 1 — January 2020

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Figure 1
Schematic diagram of an optomagnonical system. (a) WGM $PT$ -symmetric system including a YIG sphere $a_{1}$ coupled with an active cavity $a_{2}$ with coupling strength $J$ . Here $S_{in}$ and $S_{out}$ represent input and output, respectively. The frequency and amplitude of the driving field are $ω_{d}$ and $Ω_{d}$ ; $γ$ represents the decay rate of optical mode in $a_{1}$ and $κ$ represents the gain rate of cavity $a_{2}$ . (b) Optomagnonic cavity with homogeneous magnetization along the $z$ axis (an external magnetic field $H$ is added along the $z$ axis). The arrows represent the magnons with components in all directions. There is a localized optical mode with circular polarization in the $y - z$ plane. The dotted line indicates the homogeneous magnon mode couples to the optical mode with strength $G$ .
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Figure 2
Dependence of system dynamics on coupling strength $J$ . Panels (a), (d), and (g) are optical trajectories in phase space; panels (b), (e), and (h) are the evolution of optical intensity $I_{a}$ ; and panels (c), (f), and (i) are corresponding power spectrum $Ln S (ω)$ changed over $ω / Ω$ for different strength $J$ . [(a)–(c)] $J = 0.1 γ$ . [(d)–(f)] $J = 3 γ$ . [(g), (h), and (i)] $J = 8 γ$ . The decay rate of YIG is $γ = 1 MHz$ , the gain of active cavity is $κ = 0.4 γ$ , the coupling strength between magnon mode and optical mode is $G = 5 \times 10^{2} Hz$ , the precession frequency is $Ω = 5 MHz$ , the $x$ component of the macrospin $S$ is $S_{x} = 1 \times 10^{6}$ , the detuning is $Δ_{c} = Ω$ , and the driving amplitude is $Ω_{d} = 1 \times 10^{2} γ$ .
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Figure 3
Dependence of Lyapunov exponent on coupling strength $J$ . Lyapunov exponent in cavity $a_{1}$ varies with different $J / γ$ . The inset corresponds to the Lyapunov exponent for $J = 0.3 γ, J = 0.35 γ$ , and $J = 0.4 γ$ . Other system parameters are the same as in Fig. 2.
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Figure 4
Parameter $η$ defined as $S_{x} / S$ versus time $t$ with $J = 8 / γ$ . Here $S$ is the total spin with $S = \sqrt{{S_{x}^{2} + S_{y}^{2} + S_{z}^{2}}^{}}$ . Because of the fluctuation phenomenon, $η$ exhibits periodical change over time $t$ . Other system parameters are the same as in Fig. 2.
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Figure 5
Dependence of $PT$ -symmetric system dynamics on magnon. Panels (a), (d), and (g) are optical trajectories in the phase space; panels (b), (e), and (h) are the evolution of optical intensity $I_{a}$ ; panels (c), (f), and (i) are corresponding power spectrum $Ln S (ω)$ changed over $ω / Ω$ for different $S_{x}$ . (a) $S_{x} = 1 \times 10^{3}$ . (b) $S_{x} = 1 \times 10^{5}$ . (c) $S_{x} = 1 \times 10^{6}$ . The coupling strength $J = 2 γ$ between the two cavities is fixed, and other system parameters are the same as in Fig. 2.
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Figure 6
Dependence of Lyapunov exponent on driving amplitude $Ω_{d}$ . The red line indicates the effect of the driving amplitude on the Lyapunov exponent in the passive-passive system. When $Ω_{d} = 6 \times 10^{2} γ$ , Lyapunov exponent is positive and chaos will appear. The blue line indicates the effect of the driving amplitude on Lyapunov exponent in the $PT$ -symmetric system. When $Ω_{d} = 0.5 γ$ , Lyapunov exponent is positive. System parameters are $κ = - 0.4 γ, J = 3 γ$ and other parameters are the same as in Fig. 2.
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Physical Review E

covering statistical, nonlinear, biological, and soft matter physics

Magnon-induced chaos in an optical $PT$ -symmetric resonator

Wen-Ling Xu, Xiao-Fei Liu, Yang Sun, Yong-Pan Gao, Tie-Jun Wang, and Chuan Wang

Phys. Rev. E 101, 012205 – Published 10 January 2020

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Physical Review E

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Magnon-induced chaos in an optical PT-symmetric resonator

Wen-Ling Xu, Xiao-Fei Liu, Yang Sun, Yong-Pan Gao, Tie-Jun Wang, and Chuan Wang

Phys. Rev. E 101, 012205 – Published 10 January 2020

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Magnon-induced chaos in an optical $PT$ -symmetric resonator