## Material properties in open engineered systems

We are interested in the interplay between topology, (quasi-)disorder, interaction, and parametric driving in engineered driven-dissipative photonic crystals and ultracold-atomic systems. Conjoining any pair of the above ingredients leads to very active fields of research, such as, topological light, Floquet topological insulators, topological quasicrystals, and many-body localization. Highlights of our contribution to this emerging field include illustrating a deep connection between quasi-periodic materials and topological pumps, which was experimentally demonstrated in photonic waveguide arrays and cold atoms in optical superlattices.

**Dynamical gauge fields with bosonic codes**, J. del Pino and OZ, [arXiv:2211.12119].**A semiclassical treatment of spinor topological effects in driven, inhomogeneous insulators under external electromagnetic fields**, I. Petrides and OZ, Phys. Rev. B**106**, 165130 (2022) [arXiv:2203.14902].**A tensor-based entanglement measure for mixed states**, C. Carisch and OZ [arXiv:2202.07420].**Roadmap on Topological Photonics**, H. Price, Y. Chong, A. Khanikaev, H. Schomerus, L. J. Maczewsky, M. Kremer, M. Heinrich, A. Szameit, OZ, Y. Yang, B. Zhang, A. Alù, R. Thomale, I. Carusotto, P. St-Jean, A. Amo, A. Dutt, L. Yuan, S. Fan, X. Yin, C. Peng, T. Ozawa, and A. Blanco-Redondo J. Phys. Phot.**4**, 032501 (2022) [arXiv:2201.06315].**Many-body localization in the interpolating Aubry-André-Fibonacci model**, A. Štrkalj, E. V. H. Doggen, I. V. Gornyi, and OZ, Phys. Rev. Research**3**, 033257 (2021) [arXiv:2106.13841].**Emerging dissipative phases in a superradiant quantum gas with tunable decay**, F. Ferri, R. Rosa-Medina, F. Finger, N. Dogra, M. Soriente, OZ, T. Donner, and T. Esslinger Phys. Rev. X**11**, 041046 (2021) [arXiv:2104.12782].**Second-order topological modes in 2D continuous media**, J. Košata and OZ, Phys. Rev. Research**3**, L032029 (2021) [arXiv:2103.05403].**A distinctive class of dissipation-induced phase transitions and their universal characteristics**, M. Soriente, T. L. Heugel, K. Arimitsu, R. Chitra, and OZ, Phys. Rev. Research**3**, 023100 (2021) [arXiv:2101.12227].**Topology in quasicrystals**, OZ, Opt. Mat. Express**11**, 1143 (2021) [arXiv:2012.03644].**Spontaneous valley spirals in magnetically encapsulated twisted bilayer graphene**, T. M. R. Wolf, OZ, G. Blatter, and J. L. Lado, Phys. Rev. Lett.**126**, 056803 (2021) [arXiv:2008.06441].**Anti-chiral states in twisted graphene multilayers**, M. M. Denner, J. L. Lado, and OZ, Phys. Rev. Research**2**, 043190 (2020) [arXiv:2006.13903].**Optical circuits cross dimensions**, A. Amo and OZ, Nat. Phot. 14, 68 (2020).**High-order topological insulators from high-dimensional Chern insulators**, I. Petrides and OZ, Phys. Rev. Research**2**, 022049(R) (2020) [arXiv:1911.08461].**Emergence of criticality through a cascade of delocalization transitions in quasiperiodic chains**, V. Goblot, A. Štrkalj, N. Pernet, J. L. Lado, C. Dorow, A. Lemaître, L. Le Gratiet, A. Harouri, I. Sagnes, S. Ravets, A. Amo, J. Bloch, and OZ, Nature Phys. (2020) [arXiv:1911.07809].**Dynamical phase transitions in driven-dissipative light-matter systems**, M. Soriente, R. Chitra, and OZ, Phys. Rev. A**101**, 023823 (2020) [arXiv:1909.09550].**Topological spin excitations in Harper-Heisenberg spin chains**, J. L. Lado and OZ, Phys. Rev. Research**1**, 033009 (2019) [arXiv:1906.07090].**Electrically-tunable flat bands and magnetism in twisted bilayer graphene**, T. M. R. Wolf, J. L. Lado, G. Blatter, and OZ, [arXiv:1905.07651].**Quantum interference of topological states of light**, J.-L. Tambasco, G. Corrielli, R. J. Chapman, A. Crespi, OZ, R. Osellame, and A. Peruzzo, Science Advances**4**, aat3187 (2018).**Substrate-induced topological mini-bands in graphene**, T. M. R. Wolf, OZ, I. Levkivskyi, and G. Blatter, Phys. Rev. B**98**, 125408 (2018) [arXiv:1805.10670].**Non-quantized square-root topological insulators: a realization in photonic Aharonov-Bohm cages**, M. Kremer, I. Petrides, E. Meyer, M. Heinrich, OZ, and A. Szameit, Nature Communications**11**, 907 (2020) [arXiv:1805.05209].**The 6D quantum Hall effect and 3D topological pumps**, I. Petrides, H. M. Price, and OZ, Phys. Rev. B**98**, 125431 (2018) [arXiv:1804.01871].**Entanglement spectrum of mixed states**, E. van Nieuwenburg and OZ, Phys. Rev. A**98**, 012327 (2018) [arXiv:1803.09842].**Topological photonics**, T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. Rechtsman, D. Schuster, J. Simon, OZ, and I. Carusotto, Rev. Mod. Phys.**91**, 015006 (2019) [arXiv:1802.04173].**Dissipation-induced anomalous multicritical phenomena**, M. Soriente, T. Donner, R. Chitra, and OZ, Phys. Rev. Lett.**120**, 183603 (2018) [arXiv:1712.09671].**Exploring 4D Quantum Hall Physics with a 2D Topological Charge Pump**, M. Lohse, C. Schweizer, H. M. Price, OZ, and I. Bloch, Nature**553**, 55 (2018) [arXiv:1705.08371].**Photonic topological pumping through the edges of a dynamical four-dimensional quantum Hall system**, OZ, S. Huang, J. Guglielmon, M. Wang, K. Chen, Y. E. Kraus, and M. C. Rechtsman, Nature**553**, 59 (2018) [arXiv:1705.08361].**Parametric symmetry breaking in a nonlinear resonator**, A. Leuch, L. Papariello, OZ, C. Degen, R. Chitra, and A. Eichler, Phys. Rev. Lett.**117**, 214101 (2016) [arXiv:1608.08896].**Quasiperiodicity and topology transcend dimensions**, Y. E. Kraus and OZ, Nature Phys.**12**, 624 (2016).**Ultrasensitive hysteretic force sensing with parametric nonlinear oscillators**, L. Papariello, OZ, A. Eichler, and R. Chitra, Phys. Rev. E**94**, 022201 (2016) [arXiv:1603.07774].**On the measurement of Chern numbers through center-of-mass responses**, H. M. Price, OZ, T. Ozawa, I. Carusotto, and N. Goldman, Phys. Rev. B**93**, 245113 (2016) (Editor's suggestion) [arXiv:1602.01696].**Synthetic dimensions in integrated photonics: From optical isolation to 4D quantum Hall physics**, T. Ozawa, H. M. Price, N. Goldman, OZ, and I. Carusotto, Phys. Rev. A**93**, 043827 (2016) [arXiv:1510.03910].**A Thouless quantum pump with ultracold bosonic atoms in an optical superlattice**, M. Lohse, C. Schweizer, OZ, M. Aidelsburger, and I. Bloch, Nature Phys.**12**, 350 (2016) [arXiv:1507.02225].**Four-dimensional quantum Hall effect with ultracold atoms**, H. M. Price, OZ, T. Ozawa, I. Carusotto, and N. Goldman, Phys. Rev. Lett.**115**, 195303 (2015) (Editor's suggestion) [arXiv:1505.04387]. Featured in a Physics synopsis: The Quantum Hall Effect Leaves Flatland.**Dynamical many-body phases of the parametrically driven, dissipative Dicke model**, R. Chitra and OZ, Phys. Rev. A**92**, 023815 (2015) [arXiv:1501.07098].**Topological pumping over a photonic Fibonacci quasicrystal**, M. Verbin, OZ, Y. Lahini, Y. E. Kraus, and Y. Silberberg, Phys. Rev. B**91**, 064201 (2015) [arXiv:1403.7124].**Measuring topological invariants in small photonic lattices**, C.-E. Bardyn, S. D. Huber, and OZ, New J. Phys.**16**, 123013 (2014) [arXiv:1312.6894].**Enhanced compressibility due to repulsive interaction in the Harper model**, Y. E. Kraus, OZ, and R. Berkovits, Phys. Rev. B**89**, 161106(R) (2014) [arXiv:1311.4711].**Comment on "Topological equivalence of crystal and quasicrystal band structures"**, Y. E. Kraus, Z. Ringel, and OZ, arXiv:1308.2378.**Four-dimensional quantum Hall effect in a two-dimensional quasicrystal**, Y. E. Kraus, Z. Ringel, and OZ, Phys. Rev. Lett.**111**, 226401 (2013) [arXiv:1302.2647].**Observation of topological phase transitions in photonic quasicrystals**, M. Verbin, OZ, Y. E. Kraus, Y. Lahini, and Y. Silberberg, Phys. Rev. Lett.**110**, 076403 (2013) (Editor's suggestion) [arXiv:1211.4476].**Topological equivalence between the Fibonacci quasicrystal and The Harper Model**, Y. E. Kraus and OZ, Phys. Rev. Lett.**109**, 116404 (2012) [arXiv:1204.3517].**Topological states and adiabatic pumping in quasicrystals**, Y. E. Kraus, Y. Lahini, Z. Ringel, M. Verbin, and OZ, Phys. Rev. Lett.**109**, 106402 (2012) (Editor's suggestion) [arXiv:1109.5983]. It received a Physics viewpoint: Physics**5**, 99 (2012) and was chosen as highlighted research in Science**338**, 444 (2012) and Nature Physics**8**, 702 (2012). It has also featured in physicsworld and has an invited article in 2Physics.