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Multi-stability in cavity QED with spin–orbit coupled Bose–Einstein condensate

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Abstract

We investigate the steady-state multi-stability in a cavity system containing spin–orbit coupled Bose–Einstein condensate and driven by a strong pump laser. The applied magnetic field splits the Bose–Einstein condensate into pseudo-spin states, which then become momentum sensitive with two counter propagating Raman lasers directly interacting with ultra-cold atoms. After governing the steady-state dynamics for all associated subsystems, we show the emergence of multi-stable behavior of cavity photon number, which is unlike previous investigation on cavity-atom systems. However, this multi-stability can be tuned with associated system parameters. Furthermore, we illustrate the occurrence of mixed-stability behavior for atomic population of the pseudo-spin-\(\uparrow \) and spin-\(\downarrow \) states, which appear in so-called bi-unstable form. The collective behavior of these atomic number states interestingly possesses a population transitional phase (or population equilibrium intersection) among both of the spin states, which can be enhanced and controlled by spin–orbit coupling and Zeeman field effects. Additionally, we illustrate the emergence of another equilibrium intersection mediated by the increase in mechanical dissipation rate of the pseudo-spin states. These equilibrium intersections or population transitional phase could be caused by the non-trivial behavior of synthetic spin state mediated by cavity. Our findings are not only crucial for the subject of optical switching but also could provide a foundation for future studies on mechanical aspect of synthetic atomic states with cavity quantum electrodynamics.

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The computational data generated and analyzed to obtain the results during study are available from the corresponding author upon reasonable request.

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Acknowledgements

K.A.Y. acknowledges the support of Research Fund for International Young Scientists by NSFC under Grant No. KYZ04Y22050, Zhejiang Normal University research funding under Grant No. ZC304021914 and Zhejiang province postdoctoral research project under Grant Number ZC304021952. G.X.L. acknowledges the support of National Natural Science Foundation of China under Grant Nos. 11835011 and 12174346.

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  1. Department of Physics, Zhejiang Normal University, Jinhua, 321004, China

    Kashif Ammar Yasir, Yu Chengyong & Gao Xianlong

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  1. Kashif Ammar Yasir
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Correspondence to Kashif Ammar Yasir.

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Yasir, K.A., Chengyong, Y. & Xianlong, G. Multi-stability in cavity QED with spin–orbit coupled Bose–Einstein condensate. Nonlinear Dyn 111, 21177–21189 (2023). https://doi.org/10.1007/s11071-023-08964-z

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