Tunable magnon and optical bistability in a cavity optomagnomechanical system

MA Huifang; YAN Yingce; ZHOU Zhili; XIA Huarong; GAO Feng

doi:10.7498/aps.74.20250549

Abstract

This study establishes a theoretical framework for realizing and dynamically controlling magnon and optical bistability in a hybrid cavity optomagnomechanical system composed of microwave cavity mode, magnon mode, phonon mode, and optical cavity mode. The objective is to investigate the synergistic interplay among self-Kerr nonlinearity, magnetostrictive effect, and radiation pressure induced optomechanical coupling in generating and modulating bistable behavior. Furthermore, this work aims to reveal the transient quantum state transition dynamics between bistable states. The system Hamiltonian includes magnetic dipole interaction between the magnon mode and microwave cavity mode, magnomechanical interaction between the magnon mode and phonon mode, and optomechanical interaction between the phonon mode and optical cavity mode. In addition, the self-Kerr nonlinearity of the magnon mode is considered. Numerical analysis of the system dynamics is conducted using quantum Langevin equations that include dissipation and input noise terms. Steady-state analytical solutions for the average magnon number and optical photon number are derived, revealing a bistable characteristic with three possible solutions. Numerical simulations are performed using experimentally feasible parameters, including coupling strengths, frequency detunings, and dissipation rates. The results indicate that both magnon and optical bistabilities are tunable. Specifically, adjusting the microwave cavity–magnon coupling efficiency enables modulation of the energy transfer efficiency from microwave to magnon, thereby altering the hysteresis window and excitation threshold of the magnon bistability. Tuning the magnon-phonon interaction can influence the energy transfer from magnon to phonon. A larger magnon-pump detuning enhances nonlinear frequency shifts, alters energy transfer pathways, broadens the hysteresis loop, and increases the magnon population on the upper branch of the bistable curve. Higher magnon dissipation rate hinders the accumulation of nonlinear effect, narrowing the bistability window and shifting the threshold to higher pump powers. For optical bistability, stronger optomechanical interaction reduces the effective cavity loss and weakens the nonlinear response to the pump field, leading the amplitude of bistability to decrease and the hysteresis loop to narrow. The increase of the optical cavity–pump detuning suppresses energy transfer efficiency, necessitating higher pump power to achieve the same photon number, thereby enhancing the prominence of the bistability. Elevating the optical cavity dissipation rate requires stronger driving to compensate for photon losses, resulting in a narrower hysteresis loop and a rightward shift of the threshold. Sharp vertical jumps observed in the bistability curves correspond to instantaneous transitions at critical driving points, enabling switch-like behavior. Moreover, transient dynamics obtained by numerically solving the Langevin equations reveal the time evolution of magnon and photon numbers under nonequilibrium initial conditions. Within the bistability regime, the system exhibits quantum state transitions between low and high steady states. The transition rates are determined collectively by the system parameters. Therefore, this study provides a theoretical platform for the multi-parameter cooperative control of magnon and optical bistability. The tunability mechanism is governed by the joint action of coupling strength, detuning, and dissipation rate. The controllability of the bistability thresholds, hysteresis widths, and transient quantum state transition dynamics demonstrated in this work highlights the significant potential for applications such as tunable optical switches, quantum information processing devices, and fundamental studies of nonlinear quantum dynamics in hybrid systems.

Keywords:

Authors and contacts

1.
Department of Physics, Taiyuan Normal University, Jinzhong 030619, China
2.
Chinalco Intelligent Digital Dimension (Hangzhou) Engineering Design and Research Institute Co., Ltd., Hangzhou 310000, China
3.
School of Optoelectronic Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
4.
Key Laboratory of Time and Frequency Standards, National Time Service Center, Chinese Academy of Sciences, Xi’an 710600, China

Corresponding author: XIA Huarong, 2454673146@qq.com ; GAO Feng, summit_gao@ntsc.ac.cn

Funds: Project supported by the Natural Science Foundation of Chongqing, China (Grant No. CSTB2024NSCQ-MSX0746).

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References

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Cited By

图 1 腔光磁机系统的示意图　(a) 钇铁石榴石晶体中的磁振子模m通过磁偶极相互作用与微波腔模a耦合, 声子模b通过色散型磁致伸缩相互作用与磁振子模m耦合, 同时通过辐射压力与光学腔模c耦合; (b) 等效物理模型

Figure 1. Schematic diagram of the cavity opto-magnomechanical system: (a) The magnon mode m in the yttrium iron garnet crystal is coupled to the microwave cavity mode a via magnetic dipole interaction, the phonon mode b is coupled to the magnon mode m through dispersive magnetostrictive interactions and simultaneously coupled to the optical cavity mode c via radiation pressure; (b) the equivalent physical model.

DownLoad: Full-Size Img PowerPoint

图 2 稳态磁振子数$ {n_{\text{m}}} $随磁振子驱动场的归一化振幅$ {{{\varepsilon _{\text{d}}}} \mathord{\left/ {\vphantom {{{\varepsilon _{\text{d}}}} {{\kappa _m}}}} \right. } {{\kappa _m}}} $的变化图像　(a) 不同微波-磁振子耦合强度$ {g_a} $下, 蓝色曲线表现为更宽的双稳态窗口, 表明强微波-磁振子耦合能够增强能量转移效率; (b) 不同磁机械耦合强度$ {g_m} $下, 蓝色曲线所在的磁子数最低, 表明磁机械耦合增大导致磁振子能量向声子耗散增强, 固定光学腔驱动强度$ {\varepsilon _{\text{l}}} $ = 100 GHz

Figure 2. The variation of steady-state photon number $ {n_{\text{m}}} $ as a function of the normalized amplitude of the optical cavity driving field $ {{{\varepsilon _{\text{d}}}} \mathord{\left/ {\vphantom {{{\varepsilon _{\text{d}}}} {{\kappa _m}}}} \right. } {{\kappa _m}}} $: (a) Under different microwave-magnon coupling strength $ {g_a} $, the blue curve exhibits a wider bistable window, indicating that strong microwave-magnon coupling enhances energy transfer efficiency; (b) under different magnomechanical coupling strength $ {g_m} $, the blue curve corresponds to the lowest magnon number, suggesting that increased magnomechanical coupling leads to enhanced dissipation of magnon energy into phonons, assuming a fixed magnon driving strength of $ {\varepsilon _{\text{l}}} $ = 100 GHz.

DownLoad: Full-Size Img PowerPoint

图 3 稳态磁振子数$ {n_m} $随磁振子驱动场的归一化振幅$ {{{\varepsilon _{\text{d}}}} \mathord{\left/ {\vphantom {{{\varepsilon _{\text{d}}}} {{\kappa _m}}}} \right. } {{\kappa _m}}} $的变化图像　(a) 不同磁振子-泵浦失谐$ {\varDelta _m} $下, 蓝色曲线表现为更高的磁子数和更宽的双稳态窗口, 源于失谐增强非线性频移并改变能量转移路径; (b) 不同磁振子耗散率$ {\kappa _m} $下, 耗散率的增大使得双稳态回线宽度收窄且阈值右移, 表明更高的耗散抑制了非线性效应积累

Figure 3. The variation of steady-state photon number $ {n_m} $ as a function of the normalized amplitude of the optical cavity driving field $ {{{\varepsilon _{\text{d}}}} \mathord{\left/ {\vphantom {{{\varepsilon _{\text{d}}}} {{\kappa _m}}}} \right. } {{\kappa _m}}} $: (a) Under different magnon-pump detuning $ {\varDelta _m} $, the blue curve exhibits a higher magnon number and a wider bistable window, this is attributed to the enhanced nonlinear frequency shift caused by the detuning, which alters the energy transfer pathways; (b) under different magnon dissipation rate $ {\kappa _m} $, an increase in the decay rate results in a narrower bistable hysteresis loop and a rightward shift of the threshold, this indicates that higher decay rates suppress the accumulation of nonlinear effects.

DownLoad: Full-Size Img PowerPoint

图 4 稳态光子数$ {n_c} $随光学腔驱动场的归一化振幅$ {{{\varepsilon _{\text{l}}}} \mathord{\left/ {\vphantom {{{\varepsilon _{\text{l}}}} {{\kappa _m}}}} \right. } {{\kappa _m}}} $的变化图像　(a) 不同光机械耦合强度$ {g_c} $下, 蓝色曲线所在的双稳态幅度最小、回线最窄, 表明强耦合增大抑制双稳态; (b) 不同光学腔-泵浦失谐$ {\varDelta _c} $下, 蓝色曲线双稳态最显著, 表明较大的失谐抑制能量转移效率; (c) 不同光学腔耗散率$ {\kappa _c} $下, 耗散率的增大导致双稳态回线宽度变窄且阈值右移, 表明高损耗需更强泵浦补偿能量, 固定磁振子驱动强度$ {\varepsilon _{\text{d}}} = {10^4} $ GHz

Figure 4. The variation of steady-state photon number $ {n_c} $ as a function of the normalized amplitude of the optical cavity driving field $ {{{\varepsilon _{\text{l}}}} \mathord{\left/ {\vphantom {{{\varepsilon _{\text{l}}}} {{\kappa _m}}}} \right. } {{\kappa _m}}} $: (a) Under different optomechanical coupling strength $ {g_c} $, the blue curve exhibits the smallest bistable amplitude and narrowest hysteresis loop, indicating that stronger coupling enhances the suppression of bistability; (b) under different optical cavity-pump detuning $ {\varDelta _c} $, the blue curve exhibits the most pronounced bistability, demonstrating that larger detuning suppresses energy transfer efficiency; (c) under different optical cavity damping rate $ {\kappa _c} $, an increase in the decay rate leads to a narrower bistable hysteresis loop and a rightward shift of the threshold, this indicates that higher losses require stronger pumping to compensate for energy dissipation, assuming a fixed magnon driving strength of $ {\varepsilon _{\text{d}}} = {10^4} $ GHz.

DownLoad: Full-Size Img PowerPoint

图 5 (a) 磁振子数$ {n_m}\left( t \right) $随时间的演化曲线; (b) 光学腔光子数$ {n_c}\left( t \right) $随时间的演化曲线, 固定参数 $ {\kappa /{{{2\pi = 1{\text{ MHz}}}}}} $, 初始条件$ \left\langle {m\left( {0} \right)} \right\rangle = \left\langle {c\left( {0} \right)} \right\rangle = {0} $

Figure 5. (a) Temporal evolution of magnon population $ {n_m}\left( t \right) $; (b) temporal evolution of optical cavity photon population $ {n_c}\left( t \right) $, parameter is fixed at $ {\kappa /{{{2\pi = 1{\text{ MHz}}}}}} $ with initial condition $ \left\langle {m\left( {0} \right)} \right\rangle = \left\langle {c\left( {0} \right)} \right\rangle = {0} $.

DownLoad: Full-Size Img PowerPoint

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[2]	Gibbs H M, McCall S L, Venkatesan T N C 1976 Phys. Rev. Lett. 36 1135 Google Scholar
[3]	Chen Y Y, Li Y N, Wan R G 2018 J. Opt. Soc. Am. B 35 1240 Google Scholar
[4]	Kubytskyi V, Biehs S A, Ben-Abdallah P 2014 Phys. Rev. Lett. 113 074301 Google Scholar
[5]	Anton M A, Calderón O G, Melle S, Gonzalo I, Carreno F 2006 Opt. Commun. 268 146 Google Scholar
[6]	Chen S W, Zeng Y X, Li Z F, Mao Y, Dai X Y, Xiang Y J 2023 Nanophotonics 12 3613 Google Scholar
[7]	Sete E A, Eleuch H 2012 Phys. Rev. A 85 043824 Google Scholar
[8]	Wang Z P, Zhen S L, Yu B L 2015 Laser Phys. Lett. 12 046004 Google Scholar
[9]	Yan D, Wang Z H, Ren C N, Gao H, Li Y, Wu J H 2015 Phys. Rev. A 91 023813 Google Scholar
[10]	Wang Y P, Zhang G Q, Zhang D, Li T F, Hu C M, You J Q 2018 Phys. Rev. Lett. 120 057202 Google Scholar
[11]	Yang Z B, Jin H, Jin J W, Liu J Y, Liu H Y, Yang R C 2021 Phys. Rev. Research 3 023126 Google Scholar
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[14]	Shen R C, Li J, Fan Z Y, Wang Y P, You J Q 2022 Phys. Rev. Lett. 129 123601 Google Scholar
[15]	Wang Q, Verba R, Davídková K, Heinz B, Tian S X, Rao Y H, Guo M Y, Guo X Y, Dubs C, Pirro P, Chumak A V 2024 Nat. Commun. 15 7577 Google Scholar
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[36]	Wu Q, Hu Y H, Ma P C 2017 Int. J. Theor. Phys. 56 1635 Google Scholar
[37]	Barbhuiya S A, Bhattacherjee A B 2022 J. Appl. Phys. 132 123104 Google Scholar
[38]	Yeasmin S, Yadav S, Bhattacherjee A B, Banerjee S 2021 J. Mod. Opt. 68 975 Google Scholar
[39]	Kumar-Singh M, Mahajan S, Bhatt V, Yadav S, Jha P K, Bhattacherjee A B 2024 J. Appl. Phys. 136 214401 Google Scholar
[40]	Zhang G Q, Chen Z, Xiong W, Lam C H, You J Q 2021 Phys. Rev. B 104 064423 Google Scholar
[41]	Wu W J, Xu D, Qian J, Li J, Wang Y P, You J Q 2022 Chin. Phys. B 31 127503 Google Scholar
[42]	张高见, 王逸璞 2020 物理学报 69 047103 Google Scholar Zhang G J, Wang Y P 2020 Acta Phys. Sin. 69 047103 Google Scholar
[43]	Gröblacher S, Hammerer K, Vanner M R, Aspelmeyer M 2009 Nature 460 724 Google Scholar
[44]	Weis S, Rivière R, Deléglise S, Gavartin E, Arcizet O, Schliesser A, Kippenberg T J 2010 Science 330 1520 Google Scholar

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[20]	ZHU SHI-YAO. STUDY OF TWO-PHOTON OPTICAL BISTABILITY. Acta Physica Sinica, 1984, 33(1): 16-24. doi: 10.7498/aps.33.16

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