Synchronization and temporal nonreciprocity of optical microresonators via spontaneous symmetry breaking

Da Xu; Zi-Zhao Han; Yu-Kun Lu; Qihuang Gong; Cheng-Wei Qiu; Gang Chen; Yun-Feng Xiao

doi:doi:10.1117/1.AP.1.4.046002

Advanced Photonics, 2019, 1 (4): 046002, Published Online: Aug. 23, 2019

Synchronization and temporal nonreciprocity of optical microresonators via spontaneous symmetry breaking Download： 696次

Da Xu ¹Zi-Zhao Han ¹Yu-Kun Lu ¹Qihuang Gong ^1,2,3,4Cheng-Wei Qiu ⁵Gang Chen ^3,6,**Yun-Feng Xiao ^1,2,3,4,*

Author Affiliations

¹ Peking University, State Key Laboratory for Artificial Microstructures and Mesoscopic Physics, School of Physics, Beijing, China

² Nano-optoelectronics Frontier Center of the Ministry of Education, Collaborative Innovation Center of Quantum Matter, Beijing, China

³ Shanxi University, Collaborative Innovation Center of Extreme Optics, Taiyuan, China

⁴ Beijing Academy of Quantum Information Sciences, Beijing, China

⁵ National University of Singapore, Department of Electrical and Computer Engineering, Singapore, Singapore

⁶ Shanxi University, Institute of Laser Spectroscopy, State Key Laboratory of Quantum Optics and Quantum Optics Devices, Taiyuan, China

Figures & Tables

Fig. 1. Schematic diagram of the system. (a) Two detuned and self-sustained optical microcavities with different resonant frequencies, $ω_{10}$ and $ω_{20}$ , which are directly coupled at strength $g$ . (b)–(d) Frequency spectra of the coupled cavities, showing three different long-term states: unsynchronized, limit cycle (LC), and synchronized (Sync.). Light blue represents the noise backgrounds from which the first- and second-order synchronizations are distinguished.

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Fig. 2. Long-term evolutions of the two cavity modes under different coupling strengths. Three different categories are shown: (a) the unsynchronized ( $\tilde{g} = 0.3$ ), (b) limit cycle ( $\tilde{g} = 0.398$ ), and (c) synchronized states ( $\tilde{g} = 0.4$ ). (a1)–(c1) Phase difference; (a2)–(c2) transient frequencies; (a3)–(c3) trajectory encircling types (black cross as the axis); and (a4)–(c4) dynamical potential near the synchrony point. In all figures, the given detuning $\tilde{Δ} = 0.3$ and Kerr factor $\tilde{δ} = 0.1$ .

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Fig. 3. Parameter dependence of the synchronization. (a), (b) Maximum of the frequency differences, $\max | ω_{1} - ω_{2} |$ , versus the coupling strength $\tilde{g}$ , with ( $\tilde{Δ} = 0.2$ , $\tilde{δ} = 0.1$ ) in (a) and ( $\tilde{Δ} = 0.3$ , $\tilde{δ} = 0.1$ ) in (b); inset shows the derivative. (c) Phase diagram in the $(\tilde{Δ}, \tilde{g})$ plane with the Kerr factor $\tilde{δ} = 0.1$ . The inaccessible (gray), limit cycle (dark blue), and synchronized (light blue) regimes are marked. The red cross stands for the triple phase point $({\tilde{Δ}}_{T}, {\tilde{g}}_{T})$ . (d) The triple phase point $({\tilde{Δ}}_{T}, {\tilde{g}}_{T})$ depending on the Kerr factor $\tilde{δ}$ .

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Fig. 4. Hysteresis behavior in frequency difference. (a), (b) Frequency differences $| ω_{1} - ω_{2} |$ versus the evolution time $τ$ in the first- and second-order transition regimes. Insets: the real-time evolution of the coupling strength $\tilde{g} (τ)$ . (c), (d) Maxima of the frequency differences, $\max | ω_{1} - ω_{2} |$ versus $\tilde{g} (τ)$ . For each plot, the Kerr factor $\tilde{δ} = 0.1$ ; the detuning $\tilde{Δ} = 0.2$ in (a) and (c), and $\tilde{Δ} = 0.3$ in (b) and (d).

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Da Xu, Zi-Zhao Han, Yu-Kun Lu, Qihuang Gong, Cheng-Wei Qiu, Gang Chen, Yun-Feng Xiao. Synchronization and temporal nonreciprocity of optical microresonators via spontaneous symmetry breaking[J]. Advanced Photonics, 2019, 1(4): 046002.

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