Self-organized topological insulator due to cavity-mediated correlated tunneling
1Institute of Theoretical Physics, Jagiellonian University in Kraków, Łojasiewicza 11, 30-348 Kraków, Poland
2Theoretical Physics, Saarland University, Campus E2.6, D–66123 Saarbrücken, Germany
3Mark Kac Complex Systems Research Center, Jagiellonian University in Krakow, Łojasiewicza 11, 30-348 Kraków, Poland
Published: | 2021-07-13, volume 5, page 501 |
Eprint: | arXiv:2011.01687v3 |
Doi: | https://doi.org/10.22331/q-2021-07-13-501 |
Citation: | Quantum 5, 501 (2021). |
Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.
Abstract
Topological materials have potential applications for quantum technologies. Non-interacting topological materials, such as e.g., topological insulators and superconductors, are classified by means of fundamental symmetry classes. It is instead only partially understood how interactions affect topological properties. Here, we discuss a model where topology emerges from the quantum interference between single-particle dynamics and global interactions. The system is composed by soft-core bosons that interact via global correlated hopping in a one-dimensional lattice. The onset of quantum interference leads to spontaneous breaking of the lattice translational symmetry, the corresponding phase resembles nontrivial states of the celebrated Su-Schriefer-Heeger model. Like the fermionic Peierls instability, the emerging quantum phase is a topological insulator and is found at half fillings. Originating from quantum interference, this topological phase is found in "exact" density-matrix renormalization group calculations and is entirely absent in the mean-field approach. We argue that these dynamics can be realized in existing experimental platforms, such as cavity quantum electrodynamics setups, where the topological features can be revealed in the light emitted by the resonator.

Featured image: Interference-induced topological phases (with fractional particle-hole localizations on the edges) can be realized in a cavity quantum electrodynamics setup. The bosons are atoms (red spheres) confined by a one-dimensional optical lattice and dispersively interacting with a standing- wave mode of the cavity. The cavity standing-wave field is parallel to the lattice, its wavelength is twice the lattice periodicity, and the atoms are trapped at the nodes of the cavity mode. Correlated hopping originates from coherent scattering of laser light into the cavity, the laser Rabi frequency $\Omega$ controls the strength of the interactions. The field at the cavity output is emitted with rate $\kappa$ and provides information about the phase of the bosons.
Popular summary
► BibTeX data
► References
[1] K. v. Klitzing, G. Dorda, and M. Pepper, Phys. Rev. Lett. 45, 494 (1980).
https://doi.org/10.1103/PhysRevLett.45.494
[2] D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Phys. Rev. Lett. 49, 405 (1982).
https://doi.org/10.1103/PhysRevLett.49.405
[3] X.-G. Wen, Rev. Mod. Phys. 89, 041004 (2017).
https://doi.org/10.1103/RevModPhys.89.041004
[4] T. Senthil, Annual Review of Condensed Matter Physics 6, 299 (2015).
https://doi.org/10.1146/annurev-conmatphys-031214-014740
[5] X.-L. Qi and S.-C. Zhang, Rev. Mod. Phys. 83, 1057 (2011).
https://doi.org/10.1103/RevModPhys.83.1057
[6] A. P. Schnyder, S. Ryu, A. Furusaki, and A. W. W. Ludwig, Phys. Rev. B 78, 195125 (2008).
https://doi.org/10.1103/PhysRevB.78.195125
[7] A. Kitaev, V. Lebedev, and M. Feigel'man, in AIP Conference Proceedings (AIP, 2009).
https://doi.org/10.1063/1.3149495
[8] C.-K. Chiu, J. C. Y. Teo, A. P. Schnyder, and S. Ryu, Rev. Mod. Phys. 88, 035005 (2016).
https://doi.org/10.1103/RevModPhys.88.035005
[9] S. Raghu, X.-L. Qi, C. Honerkamp, and S.-C. Zhang, Phys. Rev. Lett. 100, 156401 (2008).
https://doi.org/10.1103/PhysRevLett.100.156401
[10] C. Weeks and M. Franz, Phys. Rev. B 81, 085105 (2010).
https://doi.org/10.1103/PhysRevB.81.085105
[11] E. V. Castro, A. G. Grushin, B. Valenzuela, M. A. H. Vozmediano, A. Cortijo, and F. de Juan, Phys. Rev. Lett. 107, 106402 (2011).
https://doi.org/10.1103/PhysRevLett.107.106402
[12] A. G. Grushin, E. V. Castro, A. Cortijo, F. de Juan, M. A. H. Vozmediano, and B. Valenzuela, Phys. Rev. B 87, 085136 (2013).
https://doi.org/10.1103/PhysRevB.87.085136
[13] A. Dauphin, M. Müller, and M. A. Martin-Delgado, Phys. Rev. A 86, 053618 (2012).
https://doi.org/10.1103/PhysRevA.86.053618
[14] D. González-Cuadra, P. R. Grzybowski, A. Dauphin, and M. Lewenstein, Phys. Rev. Lett. 121, 090402 (2018).
https://doi.org/10.1103/PhysRevLett.121.090402
[15] D. González-Cuadra, A. Dauphin, P. R. Grzybowski, P. Wójcik, M. Lewenstein, and A. Bermudez, Phys. Rev. B 99, 045139 (2019).
https://doi.org/10.1103/PhysRevB.99.045139
[16] D. González-Cuadra, A. Bermudez, P. R. Grzybowski, M. Lewenstein, and A. Dauphin, Nature Communications 10, 2694 (2019).
https://doi.org/10.1038/s41467-019-10796-8
[17] M. Hohenadler and F. F. Assaad, Journal of Physics: Condensed Matter 25, 143201 (2013).
https://doi.org/10.1088/0953-8984/25/14/143201
[18] S. Rachel, Reports on Progress in Physics 81, 116501 (2018).
https://doi.org/10.1088/1361-6633/aad6a6
[19] Z.-X. Gong, M. F. Maghrebi, A. Hu, M. L. Wall, M. Foss-Feig, and A. V. Gorshkov, Phys. Rev. B 93, 041102 (2016a).
https://doi.org/10.1103/PhysRevB.93.041102
[20] A. Y. Kitaev, Physics-Uspekhi 44, 131 (2001).
https://doi.org/10.1070/1063-7869/44/10s/s29
[21] O. Viyuela, D. Vodola, G. Pupillo, and M. A. Martin-Delgado, Phys. Rev. B 94, 125121 (2016).
https://doi.org/10.1103/PhysRevB.94.125121
[22] O. Viyuela, L. Fu, and M. A. Martin-Delgado, Phys. Rev. Lett. 120, 017001 (2018).
https://doi.org/10.1103/PhysRevLett.120.017001
[23] A. Alecce and L. Dell'Anna, Phys. Rev. B 95, 195160 (2017).
https://doi.org/10.1103/PhysRevB.95.195160
[24] S. B. Jäger, L. Dell'Anna, and G. Morigi, Phys. Rev. B 102, 035152 (2020).
https://doi.org/10.1103/PhysRevB.102.035152
[25] K. Patrick, T. Neupert, and J. K. Pachos, Phys. Rev. Lett. 118, 267002 (2017).
https://doi.org/10.1103/PhysRevLett.118.267002
[26] Z.-X. Gong, M. F. Maghrebi, A. Hu, M. Foss-Feig, P. Richerme, C. Monroe, and A. V. Gorshkov, Phys. Rev. B 93, 205115 (2016b).
https://doi.org/10.1103/PhysRevB.93.205115
[27] J. Sicks and H. Rieger, The European Physical Journal B 93, 104 (2020).
https://doi.org/10.1140/epjb/e2020-10109-3
[28] W. P. Su, J. R. Schrieffer, and A. J. Heeger, Phys. Rev. Lett. 42, 1698 (1979).
https://doi.org/10.1103/PhysRevLett.42.1698
[29] W. P. Su, J. R. Schrieffer, and A. J. Heeger, Phys. Rev. B 22, 2099 (1980).
https://doi.org/10.1103/PhysRevB.22.2099
[30] S. Kourtis and M. Daghofer, Phys. Rev. Lett. 113, 216404 (2014).
https://doi.org/10.1103/PhysRevLett.113.216404
[31] F. Mivehvar, H. Ritsch, and F. Piazza, Phys. Rev. Lett. 118, 073602 (2017).
https://doi.org/10.1103/PhysRevLett.118.073602
[32] H. Ritsch, P. Domokos, F. Brennecke, and T. Esslinger, Rev. Mod. Phys. 85, 553 (2013).
https://doi.org/10.1103/RevModPhys.85.553
[33] R. Landig, L. Hruby, N. Dogra, M. Landini, R. Mottl, T. Donner, and T. Esslinger, Nature 532, 476 (2016).
https://doi.org/10.1038/nature17409
[34] P. Zupancic, D. Dreon, X. Li, A. Baumgärtner, A. Morales, W. Zheng, N. R. Cooper, T. Esslinger, and T. Donner, Phys. Rev. Lett. 123, 233601 (2019).
https://doi.org/10.1103/PhysRevLett.123.233601
[35] J. G. Cosme, C. Georges, A. Hemmerich, and L. Mathey, Phys. Rev. Lett. 121, 153001 (2018).
https://doi.org/10.1103/PhysRevLett.121.153001
[36] C. Georges, J. G. Cosme, L. Mathey, and A. Hemmerich, Phys. Rev. Lett. 121, 220405 (2018).
https://doi.org/10.1103/PhysRevLett.121.220405
[37] F. Mivehvar, F. Piazza, T. Donner, and H. Ritsch, ``Cavity QED with Quantum Gases: New Paradigms in Many-Body Physics,'' arXiv:2102.04473.
arXiv:arXiv:2102.04473
[38] C. Maschler and H. Ritsch, Phys. Rev. Lett. 95, 260401 (2005).
https://doi.org/10.1103/PhysRevLett.95.260401
[39] H. Habibian, A. Winter, S. Paganelli, H. Rieger, and G. Morigi, Phys. Rev. Lett. 110, 075304 (2013a).
https://doi.org/10.1103/PhysRevLett.110.075304
[40] S. F. Caballero-Benitez and I. B. Mekhov, Phys. Rev. Lett. 115, 243604 (2015).
https://doi.org/10.1103/PhysRevLett.115.243604
[41] S. F. Caballero-Benitez and I. B. Mekhov, New Journal of Physics 18, 113010 (2016).
https://doi.org/10.1088/1367-2630/18/11/113010
[42] T. J. Elliott and I. B. Mekhov, Phys. Rev. A 94, 013614 (2016).
https://doi.org/10.1103/PhysRevA.94.013614
[43] A. J. Heeger, S. Kivelson, J. R. Schrieffer, and W. P. Su, Rev. Mod. Phys. 60, 781 (1988).
https://doi.org/10.1103/RevModPhys.60.781
[44] J. Larson, B. Damski, G. Morigi, and M. Lewenstein, Phys. Rev. Lett. 100, 050401 (2008).
https://doi.org/10.1103/PhysRevLett.100.050401
[45] H. Habibian, A. Winter, S. Paganelli, H. Rieger, and G. Morigi, Phys. Rev. A 88, 043618 (2013b).
https://doi.org/10.1103/PhysRevA.88.043618
[46] S. Fernández-Vidal, G. De Chiara, J. Larson, and G. Morigi, Phys. Rev. A 81, 043407 (2010).
https://doi.org/10.1103/PhysRevA.81.043407
[47] P. Sierant, K. Biedroń, G. Morigi, and J. Zakrzewski, SciPost Phys. 7, 8 (2019).
https://doi.org/10.21468/SciPostPhys.7.1.008
[48] V. Peano, C. Brendel, M. Schmidt, and F. Marquardt, Phys. Rev. X 5, 031011 (2015).
https://doi.org/10.1103/PhysRevX.5.031011
[49] E. Lustig, S. Weimann, Y. Plotnik, Y. Lumer, M. A. Bandres, A. Szameit, and M. Segev, Nature 567, 356 (2019).
https://doi.org/10.1038/s41586-019-0943-7
[50] C. Schneider, D. Porras, and T. Schaetz, Reports on Progress in Physics 75, 024401 (2012).
https://doi.org/10.1088/0034-4885/75/2/024401
[51] J. Ruostekoski, G. V. Dunne, and J. Javanainen, Phys. Rev. Lett. 88, 180401 (2002).
https://doi.org/10.1103/PhysRevLett.88.180401
[52] J. Javanainen and J. Ruostekoski, Phys. Rev. Lett. 91, 150404 (2003).
https://doi.org/10.1103/PhysRevLett.91.150404
[53] E. Alba, X. Fernandez-Gonzalvo, J. Mur-Petit, J. K. Pachos, and J. J. Garcia-Ripoll, Phys. Rev. Lett. 107, 235301 (2011).
https://doi.org/10.1103/PhysRevLett.107.235301
[54] L. Tarruell, D. Greif, T. Uehlinger, G. Jotzu, and T. Esslinger, Nature 483, 302 (2012).
https://doi.org/10.1038/nature10871
[55] N. Goldman, J. Beugnon, and F. Gerbier, Phys. Rev. Lett. 108, 255303 (2012).
https://doi.org/10.1103/PhysRevLett.108.255303
[56] M. Atala, M. Aidelsburger, J. T. Barreiro, D. Abanin, T. Kitagawa, E. Demler, and I. Bloch, Nature Physics 9, 795 (2013).
https://doi.org/10.1038/nphys2790
[57] X.-L. Deng, D. Porras, and J. I. Cirac, Phys. Rev. A 77, 033403 (2008).
https://doi.org/10.1103/PhysRevA.77.033403
[58] D. D. Solnyshkov, G. Malpuech, P. St-Jean, S. Ravets, J. Bloch, and A. Amo, ``Microcavity polaritons for topological photonics,'' arXiv:2011.03012.
arXiv:arXiv:2011.03012
[59] I. Carusotto and C. Ciuti, Rev. Mod. Phys. 85, 299 (2013).
https://doi.org/10.1103/RevModPhys.85.299
[60] S. R. White, Phys. Rev. Lett. 69, 2863 (1992).
https://doi.org/10.1103/PhysRevLett.69.2863
[61] S. R. White, Phys. Rev. B 48, 10345 (1993).
https://doi.org/10.1103/PhysRevB.48.10345
[62] U. Schollwöck, Annals of Physics 326, 96 (2011).
https://doi.org/10.1016/j.aop.2010.09.012
[63] R. Orús, Annals of Physics 349, 117 (2014).
https://doi.org/10.1016/j.aop.2014.06.013
[64] M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature 415, 39 (2002).
https://doi.org/10.1038/415039a
[65] V. A. Kashurnikov, N. V. Prokof'ev, and B. V. Svistunov, Phys. Rev. A 66, 031601 (2002).
https://doi.org/10.1103/PhysRevA.66.031601
[66] K. Baumann, R. Mottl, F. Brennecke, and T. Esslinger, Phys. Rev. Lett. 107, 140402 (2011).
https://doi.org/10.1103/PhysRevLett.107.140402
[67] D. S. Rokhsar and B. G. Kotliar, Phys. Rev. B 44, 10328 (1991).
https://doi.org/10.1103/PhysRevB.44.10328
[68] W. Krauth, M. Caffarel, and J.-P. Bouchaud, Phys. Rev. B 45, 3137 (1992).
https://doi.org/10.1103/PhysRevB.45.3137
[69] K. Sheshadri, H. R. Krishnamurthy, R. Pandit, and T. V. Ramakrishnan, Europhysics Letters (EPL) 22, 257 (1993).
https://doi.org/10.1209/0295-5075/22/4/004
[70] W. Zwerger, Journal of Optics B: Quantum and Semiclassical Optics 5, S9 (2003).
https://doi.org/10.1088/1464-4266/5/2/352
[71] J. Zakrzewski, Phys. Rev. A 71, 043601 (2005).
https://doi.org/10.1103/PhysRevA.71.043601
[72] F. Grusdt, M. Höning, and M. Fleischhauer, Phys. Rev. Lett. 110, 260405 (2013).
https://doi.org/10.1103/PhysRevLett.110.260405
[73] R. Peierls, Quantum theory of solids (Clarendon Press Oxford University Press, Oxford New York, 2001).
[74] D. Rossini and R. Fazio, New Journal of Physics 14, 065012 (2012).
https://doi.org/10.1088/1367-2630/14/6/065012
[75] F. Pollmann, A. M. Turner, E. Berg, and M. Oshikawa, Phys. Rev. B 81, 064439 (2010).
https://doi.org/10.1103/PhysRevB.81.064439
[76] M. V. Berry, Proc. Roy. Soc. London A 392, 45 (1984).
http://www.jstor.org/stable/2397741
[77] J. Zak, Phys. Rev. Lett. 62, 2747 (1989).
https://doi.org/10.1103/PhysRevLett.62.2747
[78] D. Xiao, M.-C. Chang, and Q. Niu, Rev. Mod. Phys. 82, 1959 (2010).
https://doi.org/10.1103/RevModPhys.82.1959
[79] Y. Hatsugai, Journal of the Physical Society of Japan 75, 123601 (2006).
https://doi.org/10.1143/JPSJ.75.123601
[80] O. Dutta, M. Gajda, P. Hauke, M. Lewenstein, D.-S. Luehmann, B. A. Malomed, T. Sowiński, and J. Zakrzewski, Rep. Prog. Phys. 78, 066001 (2015). https://doi.org/10.1088/0034-4885/78/6/066001.
https://doi.org/10.1088/0034-4885/78/6/066001
[81] K. Rojan, R. Kraus, T. Fogarty, H. Habibian, A. Minguzzi, and G. Morigi, Phys. Rev. A 94, 013839 (2016).
https://doi.org/10.1103/PhysRevA.94.013839
[82] J. Major, G. Morigi, and J. Zakrzewski, Phys. Rev. A 98, 053633 (2018).
https://doi.org/10.1103/PhysRevA.98.053633
[83] C. Maschler, I. B. Mekhov, and H. Ritsch, The European Physical Journal D 46, 545 (2008).
https://doi.org/10.1140/epjd/e2008-00016-4
[84] N. Dogra, F. Brennecke, S. D. Huber, and T. Donner, Phys. Rev. A 94, 023632 (2016).
https://doi.org/10.1103/PhysRevA.94.023632
[85] G. M. Crosswhite, A. C. Doherty, and G. Vidal, Phys. Rev. B 78, 035116 (2008).
https://doi.org/10.1103/PhysRevB.78.035116
[86] B. Pirvu, V. Murg, J. I. Cirac, and F. Verstraete, New Journal of Physics 12, 025012 (2010).
https://doi.org/10.1088/1367-2630/12/2/025012
Cited by
[1] Giuliano Chiriacò, Marcello Dalmonte, and Titas Chanda, "Critical light-matter entanglement at cavity mediated phase transitions", Physical Review B 106 15, 155113 (2022).
[2] Suman Mondal, Ashirbad Padhan, and Tapan Mishra, "Realizing a symmetry protected topological phase through dimerized interactions", Physical Review B 106 20, L201106 (2022).
[3] Titas Chanda, Daniel Gonzalez-Cuadra, Maciej Lewenstein, Luca Tagliacozzo, and Jakub Zakrzewski, "Devil's staircase of topological Peierls insulators and Peierls supersolids", SciPost Physics 12 2, 076 (2022).
[4] Rodrigo Rosa-Medina, Francesco Ferri, Fabian Finger, Nishant Dogra, Katrin Kroeger, Rui Lin, R. Chitra, Tobias Donner, and Tilman Esslinger, "Observing Dynamical Currents in a Non-Hermitian Momentum Lattice", Physical Review Letters 128 14, 143602 (2022).
[5] Poornima Shakya, Amulya Ratnakar, and Sankalpa Ghosh, "Dimensional cross-over in self-organised super-radiant phases of ultra-cold atoms inside a cavity", Journal of Physics B: Atomic, Molecular and Optical Physics 56 3, 035301 (2023).
[6] I. V. Lukin and A. G. Sotnikov, "Continuous matrix-product states in inhomogeneous systems with long-range interactions", Physical Review B 106 14, 144206 (2022).
[7] Ciaran McDonnell and Beatriz Olmos, "Subradiant edge states in an atom chain with waveguide-mediated hopping", Quantum 6, 805 (2022).
[8] Alessio Chiocchetta, Dominik Kiese, Carl Philipp Zelle, Francesco Piazza, and Sebastian Diehl, "Cavity-induced quantum spin liquids", Nature Communications 12 1, 5901 (2021).
[9] Anjun Chu, Asier Piñeiro Orioli, Diego Barberena, James K. Thompson, and Ana Maria Rey, "Photon-mediated correlated hopping in a synthetic ladder", Physical Review Research 5 2, L022034 (2023).
[10] Joana Fraxanet, Daniel González-Cuadra, Tilman Pfau, Maciej Lewenstein, Tim Langen, and Luca Barbiero, "Topological Quantum Critical Points in the Extended Bose-Hubbard Model", Physical Review Letters 128 4, 043402 (2022).
[11] Marie S. Rider, Álvaro Buendía, Diego R. Abujetas, Paloma A. Huidobro, José A. Sánchez-Gil, and Vincenzo Giannini, "Advances and Prospects in Topological Nanoparticle Photonics", ACS Photonics 9 5, 1483 (2022).
[12] Javier Argüello-Luengo, Alejandro González-Tudela, and Daniel González-Cuadra, "Tuning Long-Range Fermion-Mediated Interactions in Cold-Atom Quantum Simulators", Physical Review Letters 129 8, 083401 (2022).
[13] Titas Chanda, Rebecca Kraus, Jakub Zakrzewski, and Giovanna Morigi, "Bond order via cavity-mediated interactions", Physical Review B 106 7, 075137 (2022).
[14] Farokh Mivehvar, Francesco Piazza, Tobias Donner, and Helmut Ritsch, "Cavity QED with quantum gases: new paradigms in many-body physics", Advances in Physics 70 1, 1 (2021).
[15] Yongguan Ke, Jiaxuan Huang, Wenjie Liu, Yuri Kivshar, and Chaohong Lee, "Topological Inverse Band Theory in Waveguide Quantum Electrodynamics", Physical Review Letters 131 10, 103604 (2023).
The above citations are from Crossref's cited-by service (last updated successfully 2023-09-21 17:22:36) and SAO/NASA ADS (last updated successfully 2023-09-21 17:22:37). The list may be incomplete as not all publishers provide suitable and complete citation data.
This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.