- Open Access
Antibunching in locally driven dissipative Lieb lattices
Phys. Rev. B 114, 185306 – Published 22 September, 2026
DOI: https://doi.org/10.1103/g22d-99w7
Abstract
In Lieb lattices, geometric frustration and destructive interference of hopping cancels the occupation of certain sites, leading to flat-band physics. Here, we show numerically how, in the driven-dissipative Bose-Hubbard model arranged into Lieb lattices and related geometries, specific localized driving schemes can repurpose this interference to generate enhanced antibunching via a mechanism similar to the so-called unconventional photon blockade. Stochastic simulations using the positive-P method allow us to calculate occupations and second-order correlations exactly for extended lattices. We use this to optimize the parameters for the possible observation of this effect in polariton micropillar experiments. This work demonstrates the possibility of using localized driving and interference effects to generate nontrivial quantum correlations in open quantum lattice systems—specifically, producing antibunching in the dark sites of the flat-band system rather than the usual and less useful bunching.
Physics Subject Headings (PhySH)
Article Text
References (59)
- I. Carusotto and C. Ciuti, Quantum fluids of light, Rev. Mod. Phys. 85, 299 (2013).
- J. M. Raimond, M. Brune, and S. Haroche, Manipulating quantum entanglement with atoms and photons in a cavity, Rev. Mod. Phys. 73, 565 (2001).
- H. Walther, B. T. H. Varcoe, B.-G. Englert, and T. Becker, Cavity quantum electrodynamics, Rep. Prog. Phys. 69, 1325 (2006).
- A. Reiserer and G. Rempe, Cavity-based quantum networks with single atoms and optical photons, Rev. Mod. Phys. 87, 1379 (2015).
- S. Schmidt and J. Koch, Circuit QED lattices: Towards quantum simulation with superconducting circuits, Ann. Phys. 525, 395 (2013).
- A. A. Houck, H. E. Türeci, and J. Koch, On-chip quantum simulation with superconducting circuits, Nat. Phys. 8, 292 (2012).
- J. M. Fink, A. Dombi, A. Vukics, A. Wallraff, and P. Domokos, Observation of the photon-blockade breakdown phase transition, Phys. Rev. X 7, 011012 (2017).
- M. Fitzpatrick, N. M. Sundaresan, A. C. Y. 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).
- A. J. Kollár, M. Fitzpatrick, and A. A. Houck, Hyperbolic lattices in circuit quantum electrodynamics, Nature (London) 571, 45 (2019).
- I. Carusotto, D. Gerace, H. E. Tureci, S. De Liberato, C. Ciuti, and A. Imamoǧlu, Fermionized photons in an array of driven dissipative nonlinear cavities, Phys. Rev. Lett. 103, 033601 (2009).
- R. O. Umucalılar and I. Carusotto, Fractional quantum Hall states of photons in an array of dissipative coupled cavities, Phys. Rev. Lett. 108, 206809 (2012).
- J. Kasprzak, S. Reitzenstein, E. A. Muljarov, C. Kistner, C. Schneider, M. Strauss, S. Höfling, A. Forchel, and W. Langbein, Up on the Jaynes–Cummings ladder of a quantum-dot/microcavity system, Nat. Mater. 9, 304 (2010).
- A. Amo and J. Bloch, Exciton-polaritons in lattices: A non-linear photonic simulator, C. R. Phys. 17, 934 (2016).
- C. Schneider, K. Winkler, M. D. Fraser, M. Kamp, Y. Yamamoto, E. A. Ostrovskaya, and S. Höfling, Exciton-polariton trapping and potential landscape engineering, Rep. Prog. Phys. 80, 016503 (2017).
- C. W. Lai, N. Y. Kim, S. Utsunomiya, G. Roumpos, H. Deng, M. D. Fraser, T. Byrnes, P. Recher, N. Kumada, T. Fujisawa, and Y. Yamamoto, Coherent zero-state and -state in an exciton–polariton condensate array, Nature (London) 450, 529 (2007).
- N. Y. Kim, K. Kusudo, C. Wu, N. Masumoto, A. Löffler, S. Höfling, N. Kumada, L. Worschech, A. Forchel, and Y. Yamamoto, Dynamical -wave condensation of exciton–polaritons in a two-dimensional square-lattice potential, Nat. Phys. 7, 681 (2011).
- D. Tanese, H. Flayac, D. Solnyshkov, A. Amo, A. Lemaître, E. Galopin, R. Braive, P. Senellart, I. Sagnes, G. Malpuech, and J. Bloch, Polariton condensation in solitonic gap states in a one-dimensional periodic potential, Nat. Commun. 4, 1749 (2013).
- D. Tanese, E. Gurevich, F. Baboux, T. Jacqmin, A. Lemaître, E. Galopin, I. Sagnes, A. Amo, J. Bloch, and E. Akkermans, Fractal energy spectrum of a polariton gas in a Fibonacci quasiperiodic potential, Phys. Rev. Lett. 112, 146404 (2014).
- B. Zhang, S. Brodbeck, Z. Wang, M. Kamp, C. Schneider, S. Höfling, and H. Deng, Coupling polariton quantum boxes in sub-wavelength grating microcavities, Appl. Phys. Lett. 106, 051104 (2015).
- F. Baboux, L. Ge, T. Jacqmin, M. Biondi, E. Galopin, A. Lemaître, L. Le Gratiet, I. Sagnes, S. Schmidt, H. E. Türeci, A. Amo, and J. Bloch, Bosonic condensation and disorder-induced localization in a flat band, Phys. Rev. Lett. 116, 066402 (2016).
- P. St-Jean, V. Goblot, E. Galopin, A. Lemaître, T. Ozawa, L. Le Gratiet, I. Sagnes, J. Bloch, and A. Amo, Lasing in topological edge states of a one-dimensional lattice, Nat. Photonics 11, 651 (2017).
- S. Klembt, T. H. Harder, O. A. Egorov, K. Winkler, H. Suchomel, J. Beierlein, M. Emmerling, C. Schneider, and S. Höfling, Polariton condensation in S- and P-flatbands in a two-dimensional Lieb lattice, Appl. Phys. Lett. 111, 231102 (2017).
- S. Klembt, T. Harder, O. Egorov, K. Winkler, R. Ge, M. Bandres, M. Emmerling, L. Worschech, T. Liew, M. Segev, et al., Exciton-polariton topological insulator, Nature (London) 562, 552 (2018).
- C. E. Whittaker, E. Cancellieri, P. M. Walker, D. R. Gulevich, H. Schomerus, D. Vaitiekus, B. Royall, D. M. Whittaker, E. Clarke, I. V. Iorsh, I. A. Shelykh, M. S. Skolnick, and D. N. Krizhanovskii, Exciton polaritons in a two-dimensional Lieb lattice with spin-orbit coupling, Phys. Rev. Lett. 120, 097401 (2018).
- V. Goblot, B. Rauer, F. Vicentini, A. Le Boité, E. Galopin, A. Lemaître, L. Le Gratiet, A. Harouri, I. Sagnes, S. Ravets, C. Ciuti, A. Amo, and J. Bloch, Nonlinear polariton fluids in a flatband reveal discrete gap solitons, Phys. Rev. Lett. 123, 113901 (2019).
- M. Milićević, G. Montambaux, T. Ozawa, O. Jamadi, B. Real, I. Sagnes, A. Lemaître, L. Le Gratiet, A. Harouri, J. Bloch, and A. Amo, Type-III and tilted Dirac cones emerging from flat bands in photonic orbital graphene, Phys. Rev. X 9, 031010 (2019).
- R. Su, S. Ghosh, J. Wang, S. Liu, C. Diederichs, T. C. H. Liew, and Q. Xiong, Observation of exciton polariton condensation in a perovskite lattice at room temperature, Nat. Phys. 16, 301 (2020).
- N. H. M. Dang, D. Gerace, E. Drouard, G. Trippé-Allard, F. Lédée, R. Mazurczyk, E. Deleporte, C. Seassal, and H. S. Nguyen, Tailoring dispersion of room-temperature exciton-polaritons with perovskite-based subwavelength metasurfaces, Nano Lett. 20, 2113 (2020).
- M. Dusel, S. Betzold, O. Egorov, S. Klembt, J. Ohmer, U. Fischer, S. Höfling, and C. Schneider, Room temperature organic exciton-polariton condensate in a lattice, Nat. Commun. 11, 2863 (2020).
- F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Köhl, and T. Esslinger, Cavity QED with a Bose–Einstein condensate, Nature (London) 450, 268 (2007).
- G. Usaj, Localization engineering by resonant driving in dissipative polariton arrays, SciPost Phys. Core 7, 052 (2024).
- A. Muñoz de las Heras, A. Amo, and A. González-Tudela, Nonlinearity-enabled localization in driven-dissipative photonic lattices, Phys. Rev. A 109, 063523 (2024).
- M. Biondi, E. P. L. van Nieuwenburg, G. Blatter, S. D. Huber, and S. Schmidt, Incompressible polaritons in a flat band, Phys. Rev. Lett. 115, 143601 (2015).
- M. Hyrkäs, V. Apaja, and M. Manninen, Many-particle dynamics of bosons and fermions in quasi-one-dimensional flat-band lattices, Phys. Rev. A 87, 023614 (2013).
- W. Casteels, R. Rota, F. Storme, and C. Ciuti, Probing photon correlations in the dark sites of geometrically frustrated cavity lattices, Phys. Rev. A 93, 043833 (2016).
- P. Deuar, A. Ferrier, M. Matuszewski, G. Orso, and M. H. Szymańska, Fully quantum scalable description of driven-dissipative lattice models, PRX Quantum 2, 010319 (2021).
- C. Gardiner and P. Zoller, Quantum Noise (Springer, Berlin Heidelberg, 2004).
- G. Muñoz-Matutano, A. Wood, M. Johnsson, X. Vidal, B. Q. Baragiola, A. Reinhard, A. Lemaître, J. Bloch, A. Amo, G. Nogues, B. Besga, M. Richard, and T. Volz, Emergence of quantum correlations from interacting fibre-cavity polaritons, Nat. Mater. 18, 213 (2019).
- A. Delteil, T. Fink, A. Schade, S. Höfling, C. Schneider, and A. İmamoğlu, Towards polariton blockade of confined exciton–polaritons, Nat. Mater. 18, 219 (2019).
- T. C. H. Liew and V. Savona, Single photons from coupled quantum modes, Phys. Rev. Lett. 104, 183601 (2010).
- M. Bamba, A. Imamoğlu, I. Carusotto, and C. Ciuti, Origin of strong photon antibunching in weakly nonlinear photonic molecules, Phys. Rev. A 83, 021802(R) (2011).
- M. Bamba and C. Ciuti, Counter-polarized single-photon generation from the auxiliary cavity of a weakly nonlinear photonic molecule, Appl. Phys. Lett. 99, 171111 (2011).
- S. Ferretti, L. C. Andreani, H. E. Türeci, and D. Gerace, Photon correlations in a two-site nonlinear cavity system under coherent drive and dissipation, Phys. Rev. A 82, 013841 (2010).
- H. Flayac and V. Savona, Input-output theory of the unconventional photon blockade, Phys. Rev. A 88, 033836 (2013).
- S. Ferretti, V. Savona, and D. Gerace, Optimal antibunching in passive photonic devices based on coupled nonlinear resonators, New J. Phys. 15, 025012 (2013).
- T. C. H. Liew and V. Savona, Multimode entanglement in coupled cavity arrays, New J. Phys. 15, 025015 (2013).
- D. Gerace and V. Savona, Unconventional photon blockade in doubly resonant microcavities with second-order nonlinearity, Phys. Rev. A 89, 031803(R) (2014).
- X.-W. Xu and Y. Li, Strong photon antibunching of symmetric and antisymmetric modes in weakly nonlinear photonic molecules, Phys. Rev. A 90, 033809 (2014).
- M.-A. Lemonde, N. Didier, and A. A. Clerk, Antibunching and unconventional photon blockade with Gaussian squeezed states, Phys. Rev. A 90, 063824 (2014).
- H. Flayac and V. Savona, Single photons from dissipation in coupled cavities, Phys. Rev. A 94, 013815 (2016).
- H. Flayac and V. Savona, Unconventional photon blockade, Phys. Rev. A 96, 053810 (2017).
- H. J. Snijders, J. A. Frey, J. Norman, H. Flayac, V. Savona, A. C. Gossard, J. E. Bowers, M. P. van Exter, D. Bouwmeester, and W. Löffler, Observation of the unconventional photon blockade, Phys. Rev. Lett. 121, 043601 (2018).
- C. Vaneph, A. Morvan, G. Aiello, M. Féchant, M. Aprili, J. Gabelli, and J. Estève, Observation of the unconventional photon blockade in the microwave domain, Phys. Rev. Lett. 121, 043602 (2018).
- U. Naether, F. Quijandría, J. J. García-Ripoll, and D. Zueco, Stationary discrete solitons in a driven dissipative Bose-Hubbard chain, Phys. Rev. A 91, 033823 (2015).
- S. Mandt, D. Sadri, A. A. Houck, and H. E. Türeci, Stochastic differential equations for quantum dynamics of spin-boson networks, New J. Phys. 17, 053018 (2015).
- G. R. Dennis, J. J. Hope, and M. T. Johnsson, XMDS2: Fast, scalable simulation of coupled stochastic partial differential equations, Comput. Phys. Commun. 184, 201 (2013).
- P. Deuar, Multi-time correlations in the positive-P, Q, and doubled phase-space representations, Quantum 5, 455 (2021).
- Y. Wang, X. Zheng, T. C. H. Liew, and Y. D. Chong, Long-lived photon blockade with weak optical nonlinearity, npj Quantum Inf. (2026).
- A. Ferrier, Online GitHub repository, 2026, https://github.com/A-Ferrier/DDBHPP.