@article { doi:10.1126/science.abf6568,
	title = {Generating arbitrary topological windings of a non-Hermitian band},
	journal = {Science},
	volume = {371},
	number = {6535},
	year = {2021},
	pages = {1240-1245},
	abstract = {Controlling the topology of a system provides a route to develop devices that are robust against defects. Whereas earlier developments of topological band theory focused on Hermitian (closed) systems, recent efforts have been toward non-Hermitian (open) systems. K. Wang et al. report on the measurement and control of topologically nontrivial windings of a non-Hermitian energy band. By implementing non-Hermitian lattice Hamiltonians along a frequency synthetic dimension formed by optical frequency modes in a modulated ring-resonator, they directly visualized the nontrivial topological band winding and showed that the winding can be controlled. Such control provides a route for the experimental synthesis, characterization, and control of topologically nontrivial phases in open physical systems. Science, this issue p. 1240 Control of the topological properties of an open system is demonstrated in an optical ring resonator. The nontrivial topological features in the energy band of non-Hermitian systems provide promising pathways to achieve robust physical behaviors in classical or quantum open systems. A key topological feature of non-Hermitian systems is the nontrivial winding of the energy band in the complex energy plane. We provide experimental demonstrations of such nontrivial winding by implementing non-Hermitian lattice Hamiltonians along a frequency synthetic dimension formed in a ring resonator undergoing simultaneous phase and amplitude modulations, and by directly characterizing the complex band structures. Moreover, we show that the topological winding can be controlled by changing the modulation waveform. Our results allow for the synthesis and characterization of topologically nontrivial phases in nonconservative systems.},
	doi = {10.1126/science.abf6568},
	url = {https://www.science.org/doi/abs/10.1126/science.abf6568},
	author = {Kai Wang and Dutt, Avik and Yang, Ki Youl and Casey C. Wojcik and Vu{\v c}kovi{\'c}, Jelena and Fan, Shanhui}
}
