- Access by Xinjiang University
Multistability and self-trapping in cavity-magnonic dimer
Phys. Rev. A 114, 033716 – Published 14 September, 2026
DOI: https://doi.org/10.1103/hg3n-vmhr
Abstract
We show that a driven-dissipative cavity-magnonic dimer supports multistability with coexisting symmetric and symmetry-broken steady states. The interplay between magnon Kerr nonlinearity and photon tunneling induces magnon self-trapping, leading to a persistent population imbalance between the two resonators. In the vicinity of saddle-node bifurcations, the system exhibits critical slowing down, with relaxation times far exceeding the intrinsic dissipation scale and critical exponents close to the universal saddle-node value . Beyond the semiclassical dynamics, we probe fluctuation signatures through the quantum fidelity and mutual information between the two magnon modes. We find that both the infidelity and the mutual information increase sharply near the phase boundaries, providing signatures of the multistable and symmetry-broken phases. Our results establish cavity magnonic dimers as a versatile platform for exploring nonlinear nonequilibrium physics in hybrid quantum systems.
Physics Subject Headings (PhySH)
Article Text
References (91)
- A. Polkovnikov, K. Sengupta, A. Silva, and M. Vengalattore, Colloquium: Nonequilibrium dynamics of closed interacting quantum systems, Rev. Mod. Phys. 83, 863 (2011).
- E. M. Kessler, G. Giedke, A. Imamoglu, S. F. Yelin, M. D. Lukin, and J. I. Cirac, Dissipative phase transition in a central spin system, Phys. Rev. A 86, 012116 (2012).
- I. Carusotto and C. Ciuti, Quantum fluids of light, Rev. Mod. Phys. 85, 299 (2013).
- F. Minganti, A. Biella, N. Bartolo, and C. Ciuti, Spectral theory of Liouvillians for dissipative phase transitions, Phys. Rev. A 98, 042118 (2018).
- Z.-L. Xiang, S. Ashhab, J. Q. You, and F. Nori, Hybrid quantum circuits: Superconducting circuits interacting with other quantum systems, Rev. Mod. Phys. 85, 623 (2013).
- G. Kurizki, P. Bertet, Y. Kubo, K. Mølmer, D. Petrosyan, P. Rabl, and J. Schmiedmayer, Quantum technologies with hybrid systems, Proc. Natl. Acad. Sci. USA 112, 3866 (2015).
- G. Beaulieu, F. Minganti, S. Frasca, V. Savona, S. Felicetti, R. Di Candia, and P. Scarlino, Observation of first- and second-order dissipative phase transitions in a two-photon driven Kerr resonator, Nat. Commun. 16, 1954 (2025).
- A. Angerer, S. Putz, D. O. Krimer, T. Astner, M. Zens, R. Glattauer, K. Streltsov, W. J. Munro, K. Nemoto, S. Rotter, et al., Ultralong relaxation times in bistable hybrid quantum systems, Sci. Adv. 3, e1701626 (2017).
- P. Brookes, G. Tancredi, A. D. Patterson, J. Rahamim, M. Esposito, T. K. Mavrogordatos, P. J. Leek, E. Ginossar, and M. H. Szymanska, Critical slowing down in circuit quantum electrodynamics, Sci. Adv. 7, eabe9492 (2021).
- P. Drummond and D. Walls, Quantum theory of optical bistability. I. Nonlinear polarisability model, J. Phys. A: Math. Gen. 13, 725 (1980).
- G. Rempe, R. J. Thompson, R. J. Brecha, W. D. Lee, and H. J. Kimble, Optical bistability and photon statistics in cavity quantum electrodynamics, Phys. Rev. Lett. 67, 1727 (1991).
- H. J. Carmichael, Breakdown of photon blockade: A dissipative quantum phase transition in zero dimensions, Phys. Rev. X 5, 031028 (2015).
- M. Fitzpatrick, N. M. Sundaresan, A. C. Li, J. Koch, and A. A. Houck, Observation of a dissipative phase transition in a one-dimensional circuit QED lattice, Phys. Rev. X 7, 011016 (2017).
- W. Casteels, F. Storme, A. Le Boité, and C. Ciuti, Power laws in the dynamic hysteresis of quantum nonlinear photonic resonators, Phys. Rev. A 93, 033824 (2016).
- N. Bartolo, F. Minganti, W. Casteels, and C. Ciuti, Exact steady state of a Kerr resonator with one- and two-photon driving and dissipation: Controllable Wigner-function multimodality and dissipative phase transitions, Phys. Rev. A 94, 033841 (2016).
- W. Casteels, R. Fazio, and C. Ciuti, Critical dynamical properties of a first-order dissipative phase transition, Phys. Rev. A 95, 012128 (2017).
- S. R. Rodriguez, W. Casteels, F. Storme, N. Carlon Zambon, I. Sagnes, L. Le Gratiet, E. Galopin, A. Lemaître, A. Amo, C. Ciuti, and J. Bloch, Probing a dissipative phase transition via dynamical optical hysteresis, Phys. Rev. Lett. 118, 247402 (2017).
- Q.-M. Chen, M. Fischer, Y. Nojiri, M. Renger, E. Xie, M. Partanen, S. Pogorzalek, K. G. Fedorov, A. Marx, F. Deppe, et al., Quantum behavior of the Duffing oscillator at the dissipative phase transition, Nat. Commun. 14, 2896 (2023).
- M. Marcuzzi, E. Levi, S. Diehl, J. P. Garrahan, and I. Lesanovsky, Universal nonequilibrium properties of dissipative Rydberg gases, Phys. Rev. Lett. 113, 210401 (2014).
- N. R. de Melo, C. G. Wade, N. Šibalić, J. M. Kondo, C. S. Adams, and K. J. Weatherill, Intrinsic optical bistability in a strongly driven Rydberg ensemble, Phys. Rev. A 93, 063863 (2016).
- R. Ghobadi, A. R. Bahrampour, and C. Simon, Quantum optomechanics in the bistable regime, Phys. Rev. A 84, 033846 (2011).
- F. Bibak, U. Delić, M. Aspelmeyer, and B. Dakić, Dissipative phase transitions in optomechanical systems, Phys. Rev. A 107, 053505 (2023).
- B. Cao, K. W. Mahmud, and M. Hafezi, Two coupled nonlinear cavities in a driven-dissipative environment, Phys. Rev. A 94, 063805 (2016).
- W. Casteels and C. Ciuti, Quantum entanglement in the spatial-symmetry-breaking phase transition of a driven-dissipative Bose-Hubbard dimer, Phys. Rev. A 95, 013812 (2017).
- W. Casteels and M. Wouters, Optically bistable driven-dissipative Bose-Hubbard dimer: Gutzwiller approaches and entanglement, Phys. Rev. A 95, 043833 (2017).
- B. Garbin, A. Giraldo, K. J. H. Peters, N. G. R. Broderick, A. Spakman, F. Raineri, A. Levenson, S. R. K. Rodriguez, B. Krauskopf, and A. M. Yacomotti, Spontaneous symmetry breaking in a coherently driven nanophotonic Bose-Hubbard dimer, Phys. Rev. Lett. 128, 053901 (2022).
- Y. Xu, F.-X. Sun, W. Zhang, Q. He, and H. Pu, Phase transition and multistability in Dicke dimer, Phys. Rev. Lett. 133, 233604 (2024).
- M. Albiez, R. Gati, J. Fölling, S. Hunsmann, M. Cristiani, and M. K. Oberthaler, Direct observation of tunneling and nonlinear self-trapping in a single bosonic Josephson junction, Phys. Rev. Lett. 95, 010402 (2005).
- S. Levy, E. Lahoud, I. Shomroni, and J. Steinhauer, The a.c. and d.c. Josephson effects in a Bose–Einstein condensate, Nature (London) 449, 579 (2007).
- T. Zibold, E. Nicklas, C. Gross, and M. K. Oberthaler, Classical bifurcation at the transition from Rabi to Josephson dynamics, Phys. Rev. Lett. 105, 204101 (2010).
- K. G. Lagoudakis, B. Pietka, M. Wouters, R. André, and B. Deveaud-Plédran, Coherent oscillations in an exciton-polariton Josephson junction, Phys. Rev. Lett. 105, 120403 (2010).
- S. Schmidt, D. Gerace, A. A. Houck, G. Blatter, and H. E. Türeci, Nonequilibrium delocalization-localization transition of photons in circuit quantum electrodynamics, Phys. Rev. B 82, 100507(R) (2010).
- M. Abbarchi, A. Amo, V. Sala, D. Solnyshkov, H. Flayac, L. Ferrier, I. Sagnes, E. Galopin, A. Lemaître, G. Malpuech, et al., Macroscopic quantum self-trapping and Josephson oscillations of exciton polaritons, Nat. Phys. 9, 275 (2013).
- G. Vivek, D. Mondal, and S. Sinha, Nonequilibrium dynamics of the Jaynes-Cummings dimer, Phys. Rev. E 108, 054116 (2023).
- T. Ray and M. Kulkarni, Ergodic and chaotic properties in a Tavis-Cummings dimer: Quantum and classical limit, Phys. Rev. A 110, 032220 (2024).
- G. Vivek, D. Mondal, S. Chakraborty, and S. Sinha, Self-trapping phenomenon, multistability and chaos in open anisotropic Dicke dimer, Phys. Rev. Lett. 134, 113404 (2025).
- D. Lachance-Quirion, Y. Tabuchi, A. Gloppe, K. Usami, and Y. Nakamura, Hybrid quantum systems based on magnonics, Appl. Phys. Express 12, 070101 (2019).
- B. Z. Rameshti, S. V. Kusminskiy, J. A. Haigh, K. Usami, D. Lachance-Quirion, Y. Nakamura, C.-M. Hu, H. X. Tang, G. E. Bauer, and Y. M. Blanter, Cavity magnonics, Phys. Rep. 979, 1 (2022).
- H. Yuan, Y. Cao, A. Kamra, R. A. Duine, and P. Yan, Quantum magnonics: When magnon spintronics meets quantum information science, Phys. Rep. 965, 1 (2022).
- M. Goryachev, W. G. Farr, D. L. Creedon, Y. Fan, M. Kostylev, and M. E. Tobar, High-cooperativity cavity QED with magnons at microwave frequencies, Phys. Rev. Appl. 2, 054002 (2014).
- D. Zhang, X.-M. Wang, T.-F. Li, X.-Q. Luo, W. Wu, F. Nori, and J. You, Cavity quantum electrodynamics with ferromagnetic magnons in a small yttrium-iron-garnet sphere, npj Quantum Inf. 1, 15014 (2015).
- L. V. Abdurakhimov, Y. M. Bunkov, and D. Konstantinov, Normal-mode splitting in the coupled system of hybridized nuclear magnons and microwave photons, Phys. Rev. Lett. 114, 226402 (2015).
- B. Zare Rameshti, Y. Cao, and G. E. Bauer, Magnetic spheres in microwave cavities, Phys. Rev. B 91, 214430 (2015).
- X. Zhang, C.-L. Zou, L. Jiang, and H. X. Tang, Strongly coupled magnons and cavity microwave photons, Phys. Rev. Lett. 113, 156401 (2014).
- Y. Tabuchi, S. Ishino, T. Ishikawa, R. Yamazaki, K. Usami, and Y. Nakamura, Hybridizing ferromagnetic magnons and microwave photons in the quantum limit, Phys. Rev. Lett. 113, 083603 (2014).
- L. Bai, M. Harder, Y. P. Chen, X. Fan, J. Q. Xiao, and C.-M. Hu, Spin pumping in electrodynamically coupled magnon-photon systems, Phys. Rev. Lett. 114, 227201 (2015).
- A. Osada, R. Hisatomi, A. Noguchi, Y. Tabuchi, R. Yamazaki, K. Usami, M. Sadgrove, R. Yalla, M. Nomura, and Y. Nakamura, Cavity optomagnonics with spin-orbit coupled photons, Phys. Rev. Lett. 116, 223601 (2016).
- N. Zhu, X. Zhang, X. Han, C.-L. Zou, C. Zhong, C.-H. Wang, L. Jiang, and H. X. Tang, Waveguide cavity optomagnonics for microwave-to-optics conversion, Optica 7, 1291 (2020).
- V. A. S. V. Bittencourt, I. Liberal, and S. Viola Kusminskiy, Optomagnonics in dispersive media: Magnon-photon coupling enhancement at the epsilon-near-zero frequency, Phys. Rev. Lett. 128, 183603 (2022).
- X. Zhang, C.-L. Zou, L. Jiang, and H. X. Tang, Cavity magnomechanics, Sci. Adv. 2, e1501286 (2016).
- C. A. Potts, E. Varga, V. A. S. V. Bittencourt, S. V. Kusminskiy, and J. P. Davis, Dynamical backaction magnomechanics, Phys. Rev. X 11, 031053 (2021).
- R.-C. Shen, J. Li, Z.-Y. Fan, Y.-P. Wang, and J. Q. You, Mechanical bistability in Kerr-modified cavity magnomechanics, Phys. Rev. Lett. 129, 123601 (2022).
- G.-T. Xu, Z. Shen, M. Zhang, Y. Wang, S. Wan, Y. Yang, T. Zhang, L. Bi, F.-W. Sun, G.-C. Guo, et al., Kerr-induced synchronization of a broadband magnon-phonon hybrid frequency comb, Phys. Rev. Lett. 135, 203604 (2025).
- Y. Tabuchi, S. Ishino, A. Noguchi, T. Ishikawa, R. Yamazaki, K. Usami, and Y. Nakamura, Coherent coupling between a ferromagnetic magnon and a superconducting qubit, Science 349, 405 (2015).
- R. Morris, A. Van Loo, S. Kosen, and A. Karenowska, Strong coupling of magnons in a YIG sphere to photons in a planar superconducting resonator in the quantum limit, Sci. Rep. 7, 11511 (2017).
- S. P. Wolski, D. Lachance-Quirion, Y. Tabuchi, S. Kono, A. Noguchi, K. Usami, and Y. Nakamura, Dissipation-based quantum sensing of magnons with a superconducting qubit, Phys. Rev. Lett. 125, 117701 (2020).
- B. Wang, Z.-X. Liu, C. Kong, H. Xiong, and Y. Wu, Magnon-induced transparency and amplification in -symmetric cavity-magnon system, Opt. Express 26, 20248 (2018).
- X. Zhang, C.-L. Zou, N. Zhu, F. Marquardt, L. Jiang, and H. X. Tang, Magnon dark modes and gradient memory, Nat. Commun. 6, 8914 (2015).
- R. Hisatomi, A. Osada, Y. Tabuchi, T. Ishikawa, A. Noguchi, R. Yamazaki, K. Usami, and Y. Nakamura, Bidirectional conversion between microwave and light via ferromagnetic magnons, Phys. Rev. B 93, 174427 (2016).
- Y. S. Ihn, S.-Y. Lee, D. Kim, S. H. Yim, and Z. Kim, Coherent multimode conversion from microwave to optical wave via a magnon-cavity hybrid system, Phys. Rev. B 102, 064418 (2020).
- M. Harder, L. Bai, P. Hyde, and C.-M. Hu, Topological properties of a coupled spin-photon system induced by damping, Phys. Rev. B 95, 214411 (2017).
- D. Zhang, X.-Q. Luo, Y.-P. Wang, T.-F. Li, and J. You, Observation of the exceptional point in cavity magnon-polaritons, Nat. Commun. 8, 1368 (2017).
- S. Zheng, Z. Wang, Y. Wang, F. Sun, Q. He, P. Yan, and H. Yuan, Tutorial: Nonlinear magnonics, J. Appl. Phys. 134, 151101 (2023).
- Y.-P. Wang, G.-Q. Zhang, D. Zhang, T.-F. Li, C.-M. Hu, and J. Q. You, Bistability of cavity magnon polaritons, Phys. Rev. Lett. 120, 057202 (2018).
- R.-C. Shen, Y.-P. Wang, J. Li, S.-Y. Zhu, G. S. Agarwal, and J. Q. You, Long-time memory and ternary logic gate using a multistable cavity magnonic system, Phys. Rev. Lett. 127, 183202 (2021).
- A. Gurevich and G. Melkov, Magnetization Oscillations and Waves (CRC Press, Boca Raton, FL, 1996).
- D. D. Stancil and A. Prabhakar, Spin Waves (Springer, New York, 2009), Vol. 5.
- V. A. S. V. Bittencourt, V. Feulner, and S. V. Kusminskiy, Magnon heralding in cavity optomagnonics, Phys. Rev. A 100, 013810 (2019).
- S. Sharma, V. A. S. V. Bittencourt, A. D. Karenowska, and S. V. Kusminskiy, Spin cat states in ferromagnetic insulators, Phys. Rev. B 103, L100403 (2021).
- H. Y. Yuan and R. A. Duine, Magnon antibunching in a nanomagnet, Phys. Rev. B 102, 100402(R) (2020).
- J. Li, S.-Y. Zhu, and G. S. Agarwal, Squeezed states of magnons and phonons in cavity magnomechanics, Phys. Rev. A 99, 021801(R) (2019).
- Z.-B. Yang, H. Jin, J.-W. Jin, J.-Y. Liu, H.-Y. Liu, and R.-C. Yang, Bistability of squeezing and entanglement in cavity magnonics, Phys. Rev. Res. 3, 023126 (2021).
- P. K. Gupta, S. Chakraborty, S. Kalita, and A. K. Sarma, Quantum signatures of bistability and limit cycle in Kerr-modified cavity magnomechanics, Phys. Rev. A 110, 063504 (2024).
- J. Li, S.-Y. Zhu, and G. S. Agarwal, Magnon-photon-phonon entanglement in cavity magnomechanics, Phys. Rev. Lett. 121, 203601 (2018).
- J. Li and S.-Y. Zhu, Entangling two magnon modes via magnetostrictive interaction, New J. Phys. 21, 085001 (2019).
- Z. Zhang, M. O. Scully, and G. S. Agarwal, Quantum entanglement between two magnon modes via Kerr nonlinearity driven far from equilibrium, Phys. Rev. Res. 1, 023021 (2019).
- H. Y. Yuan, S. Zheng, Z. Ficek, Q. Y. He, and M.-H. Yung, Enhancement of magnon-magnon entanglement inside a cavity, Phys. Rev. B 101, 014419 (2020).
- H. Y. Yuan, P. Yan, S. Zheng, Q. He, K. Xia, and M.-H. Yung, Steady Bell state generation via magnon-photon coupling, Phys. Rev. Lett. 124, 053602 (2020).
- A. Hidki, A. Lakhfif, J. El Qars, and M. Nassik, Quantifying quantum correlations in a double cavity–magnon system, Eur. Phys. J. D 76, 64 (2022).
- J.-X. Peng, S. K. Singh, N. Akhtar, Z. Gu, C. Wu, and J.-F. Li, Symmetric vs asymmetric magnon pairing: Comparative study of quantum entanglement and synchronization in the cavity-magnon system, Phys. Rev. A 112, 042430 (2025).
- N. Lambert, C. Emary, and T. Brandes, Entanglement and the phase transition in single-mode superradiance, Phys. Rev. Lett. 92, 073602 (2004).
- R. R. Soldati, M. T. Mitchison, and G. T. Landi, Multipartite quantum correlations in a two-mode Dicke model, Phys. Rev. A 104, 052423 (2021).
- M. Boneberg, I. Lesanovsky, and F. Carollo, Quantum fluctuations and correlations in open quantum Dicke models, Phys. Rev. A 106, 012212 (2022).
- P. C. Hohenberg and B. I. Halperin, Theory of dynamic critical phenomena, Rev. Mod. Phys. 49, 435 (1977).
- R. Bonifacio and P. Meystre, Critical slowing down in optical bistability, Opt. Commun. 29, 131 (1979).
- D. O. Krimer, M. Zens, and S. Rotter, Critical phenomena and nonlinear dynamics in a spin ensemble strongly coupled to a cavity. I. Semiclassical approach, Phys. Rev. A 100, 013855 (2019).
- C. Kuehn, Scaling of saddle-node bifurcations: Degeneracies and rapid quantitative changes, J. Phys. A: Math. Theor. 42, 045101 (2009).
- A. K. Sarma, S. Chakraborty, and S. Kalita, Continuous variable quantum entanglement in optomechanical systems: A short review, AVS Quantum Sci. 3, 015901 (2021).
- S. Olivares, Quantum optics in the phase space, Eur. Phys. J.: Spec. Top. 203, 3 (2012).
- G. Adesso, S. Ragy, and A. R. Lee, Continuous variable quantum information: Gaussian states and beyond, Open Syst. Inf. Dyn. 21, 1440001 (2014).
- L. Banchi, S. L. Braunstein, and S. Pirandola, Quantum fidelity for arbitrary Gaussian states, Phys. Rev. Lett. 115, 260501 (2015).