Mean-chiral displacement in coherently driven photonic lattices and its application to synthetic frequency dimensions

Year: 2024

Authors: Villa G., Carusotto I., Ozawa T.

Autors Affiliation: Univ Konstanz, Dept Phys, D-78464 Constance, Germany; Univ Trento, Pitaevskii BEC Ctr, CNR INO, I-38123 Trento, Italy; Univ Trento, Dipartimento Fis, I-38123 Trento, Italy; Tohoku Univ, Adv Inst Mat Res WPI AIMR, Sendai 9808577, Japan.

Abstract: Characterizing topologically nontrivial photonic lattices by measuring their topological invariants is crucial in topological photonics. In conservative one-dimensional systems, a widely used observable to extract the winding number is the mean-chiral displacement. In many realistic photonic systems, however, losses can hardly be avoided, and little is known on how one can extend the mean-chiral displacement to a driven-dissipative context. Here we theoretically propose an experimentally viable method to directly detect the topological winding number of one-dimensional chiral photonic lattices. The method we propose is a generalization of the mean-chiral displacement to a driven-dissipative context with coherent illumination. By integrating the mean-chiral displacement of the steady state over the pump light frequency, one can obtain the winding number with a correction of the order of the loss rate squared. We demonstrate that this method can be successfully applied to lattices along synthetic frequency dimensions. While various photonic lattices with topologically nontrivial band structures have been realized, how to measure topological invariants in such systems with photon losses has not been clearly understood. We find that the topological winding number can be measured even in the presence of photon loss by generalizing the concept of the mean-chiral displacement originally developed for lossless systems.

Journal/Review: COMMUNICATIONS PHYSICS

Volume: 7 (1)      Pages from: 246-1  to: 246-8

More Information: We wish to acknowledge a continuous collaboration with Toshihiko Baba, Armandas Balcytis, Satoshi Iwamoto, Yasutomo Ota, Felix Pellerin, and Philippe St-Jean. I.C. acknowledges financial support from the PNRR-MUR project PE0000023-NQSTI project, co-funded by the European Union – NextGeneration EU, and from Provincia Autonoma di Trento (PAT), partly via the Q@TN initiative. G.V. acknowledges financial support from the Universita di Trento and Advanced Institute for Materials Research at Tohoku University. T.O. acknowledges financial support from JSPS KAKENHI Grant Nos. JP20H01845 and JP24K00548, JST PRESTO Grant No. JPMJPR2353, and JST CREST Grant No. JPMJCR19T1. DAS:All data in this work is generated by numerical simulation; see also the Code Availability below.
KeyWords: Wave
DOI: 10.1038/s42005-024-01727-1


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