Millen, J. & Stickler, B. A. Quantum experiments with microscale particles. Contemp. Phys. 61, 155–168 (2020).
Gonzalez-Ballestero, C., Aspelmeyer, M., Novotny, L., Quidant, R. & Romero-Isart, O. Levitodynamics: levitation and control of microscopic objects in vacuum. Science 374, eabg3027 (2021).
Delić, U. et al. Cooling of a levitated nanoparticle to the motional quantum ground state. Science 367, 892–895 (2020).
Piotrowski, J. et al. Simultaneous ground-state cooling of two mechanical modes of a levitated nanoparticle. Nat. Phys. 19, 1009–1013 (2023).
Pontin, A., Fu, H., Toroš, M., Monteiro, T. S. & Barker, P. F. Simultaneous cavity cooling of all six degrees of freedom of a levitated nanoparticle. Nat. Phys. 19, 1003–1008 (2023).
Sukhov, S. & Dogariu, A. Non-conservative optical forces. Rep. Prog. Phys. 80, 112001 (2017).
Li, X., Liu, Y., Lin, Z., Ng, J. & Chan, C. T. Non-Hermitian physics for optical manipulation uncovers inherent instability of large clusters. Nat. Commun. 12, 6597 (2021).
Svak, V. et al. Transverse spin forces and non-equilibrium particle dynamics in a circularly polarized vacuum optical trap. Nat. Commun. 9, 5453 (2018).
Arita, Y., Simpson, S. H., Zemánek, P. & Dholakia, K. Coherent oscillations of a levitated birefringent microsphere in vacuum driven by nonconservative rotation-translation coupling. Sci. Adv. 6, eaaz9858 (2020).
Arita, Y. et al. Cooling the optical-spin driven limit cycle oscillations of a levitated gyroscope. Commun. Phys. 6, 1–7 (2023).
Hu, Y. et al. Structured transverse orbital angular momentum probed by a levitated optomechanical sensor. Nat. Commun. 14, 2638 (2023).
Rieser, J. et al. Tunable light-induced dipole-dipole interaction between optically levitated nanoparticles. Science 377, 987–990 (2022).
Simpson, S. H. & Hanna, S. First-order nonconservative motion of optically trapped nonspherical particles. Phys. Rev. E 82, 031141 (2010).
Simpson, S. H., Arita, Y., Dholakia, K. & Zemánek, P. Stochastic Hopf bifurcations in vacuum optical tweezers. Phys. Rev. A 104, 043518 (2021).
Brzobohatý, O. et al. Synchronization of spin-driven limit cycle oscillators optically levitated in vacuum. Nat. Commun. 14, 5441 (2023).
Ashida, Y., Gong, Z. & Ueda, M. Non-Hermitian physics. Adv. Phys. 69, 249–435 (2020).
El-Ganainy, R. et al. Non-Hermitian physics and PT symmetry. Nat. Phys. 14, 11–19 (2018).
Feng, L., El-Ganainy, R. & Ge, L. Non-Hermitian photonics based on parity-time symmetry. Nat. Photonics 11, 752–762 (2017).
Öztürk, F. E. et al. Observation of a non-Hermitian phase transition in an optical quantum gas. Science 372, 88–91 (2021).
Miri, M.-A. & Alù, A. Exceptional points in optics and photonics. Science 363, eaar7709 (2019).
Huber, S. D. Topological mechanics. Nat. Phys. 12, 621–623 (2016).
Mao, X. & Lubensky, T. C. Maxwell lattices and topological mechanics. Annu. Rev. Condens. Matter Phys. 9, 413–433 (2018).
Brandenbourger, M., Locsin, X., Lerner, E. & Coulais, C. Non-reciprocal robotic metamaterials. Nat. Commun. 10, 4608 (2019).
Zhang, X., Zhang, T., Lu, M.-H. & Chen, Y.-F. A review on non-Hermitian skin effect. Adv. Phys. X 7, 2109431 (2022).
Heugel, T. L., Oscity, M., Eichler, A., Zilberberg, O. & Chitra, R. Classical many-body time crystals. Phys. Rev. Lett. 123, 124301 (2019).
Sacha, K. & Zakrzewski, J. Time crystals: a review. Rep. Prog. Phys. 81, 016401 (2017).
Wilczek, F. Quantum time crystals. Phys. Rev. Lett. 109, 160401 (2012).
Shapere, A. & Wilczek, F. Classical time crystals. Phys. Rev. Lett. 109, 160402 (2012).
Liu, T., Ou, J.-Y., MacDonald, K. F. & Zheludev, N. I. Photonic metamaterial analogue of a continuous time crystal. Nat. Phys. 19, 986–991 (2023).
Raskatla, V., Liu, T., Li, J., MacDonald, K. F. & Zheludev, N. I. Continuous space-time crystal state driven by nonreciprocal optical forces. Preprint at https://doi.org/10.48550/arXiv.2310.10747 (2023).
Wilson, H. R. & Cowan, J. D. Excitatory and inhibitory interactions in localized populations of model neurons. Biophys. J. 12, 1–24 (1972).
Shen, R.-F. & Matzner, C. D. Evolution of accretion disks in tidal disruption events. Astrophys. J. 784, 87 (2014).
Liška, V. et al. Cold damping of levitated optically coupled nanoparticles. Optica 10, 1203 (2023).
Bender, C. M., Gianfreda, M. & Klevansky, S. P. Systems of coupled PT-symmetric oscillators. Phys. Rev. A 90, 022114 (2014).
Kuang, T. et al. Nonlinear multi-frequency phonon lasers with active levitated optomechanics. Nat. Phys. 19, 414–419 (2023).
Pettit, R. M. et al. An optical tweezer phonon laser. Nat. Photonics 13, 402–405 (2019).
Zheng, Y., Liu, L.-H., Chen, X.-D., Guo, G.-C. & Sun, F.-W. Arbitrary nonequilibrium steady-state construction with a levitated nanoparticle. Phys. Rev. Res. 5, 033101 (2023).
Vahala, K. et al. A phonon laser. Nat. Phys. 5, 682–686 (2009).
Sharma, S., Kani, A. & Bhattacharya, M. PT symmetry, induced mechanical lasing, and tunable force sensing in a coupled-mode optically levitated nanoparticle. Phys. Rev. A 105, 043505 (2022).
Tass, P. et al. Detection of n:m phase locking from noisy data: application to magnetoencephalography. Phys. Rev. Lett. 81, 3291–3294 (1998).
Bender, C. M., Berntson, B. K., Parker, D. & Samuel, E. Observation of PT phase transition in a simple mechanical system. Am. J. Phys. 81, 173–179 (2013).
Hodaei, H. et al. Enhanced sensitivity at higher-order exceptional points. Nature 548, 187–191 (2017).
Zhang, K., Yang, Z. & Fang, C. Universal non-Hermitian skin effect in two and higher dimensions. Nat. Commun. 13, 2496 (2022).
Liang, Q. et al. Dynamic signatures of Non-Hermitian skin effect and topology in ultracold atoms. Phys. Rev. Lett. 129, 070401 (2022).
Zou, D. et al. Observation of hybrid higher-order skin-topological effect in non-Hermitian topolectrical circuits. Nat. Commun. 12, 7201 (2021).
Reisenbauer, M. et al. Non-Hermitian dynamics and non-reciprocity of optically coupled nanoparticles. Nat. Phy. https://doi.org/10.1038/s41567-024-02589-8 (2024).
Leite, I. T. et al. Three-dimensional holographic optical manipulation through a high-numerical-aperture soft-glass multimode fibre. Nat. Photonics 12, 33–39 (2018).
Magrini, L. et al. Real-time optimal quantum control of mechanical motion at room temperature. Nature 595, 373–377 (2021).
Rudolph, H., Delić, U., Aspelmeyer, M., Hornberger, K. & Stickler, B. A. Force-gradient sensing and entanglement via feedback cooling of interacting nanoparticles. Phys. Rev. Lett. 129, 193602 (2022).
Liška, V. et al. Observations of a PT-like phase transition and limit cycle oscillations in non-reciprocally coupled optomechanical oscillators levitated in vacuum (2024). Zenodo https://doi.org/10.5281/zenodo.11119872 (2024).