Topological phonons in arrays of ultracold dipolar particles

Marco Di Liberto, Andreas Kruckenhauser, Peter Zoller, and Mikhail A. Baranov

Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, 6020 Innsbruck, Austria
Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.

Abstract

The notion of topology in physical systems is associated with the existence of a nonlocal ordering that is insensitive to a large class of perturbations. This brings robustness to the behaviour of the system and can serve as a ground for developing new fault-tolerant applications. We discuss how to design and study a large variety of topology-related phenomena for phonon-like collective modes in arrays of ultracold polarized dipolar particles. These modes are coherently propagating vibrational excitations, corresponding to oscillations of particles around their equilibrium positions, which exist in the regime where long-range interactions dominate over single-particle motion. We demonstrate that such systems offer a distinct and versatile tool to investigate a wide range of topological effects in a $\textit{single experimental setup}$ with a chosen underlying crystal structure by simply controlling the anisotropy of the interactions via the orientation of the external polarizing field. Our results show that arrays of dipolar particles provide a promising unifying platform to investigate topological phenomena with phononic modes.

► BibTeX data

► References

[1] M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. 82, 3045 (2010).
https:/​/​doi.org/​10.1103/​RevModPhys.82.3045

[2] X. Chen, Z.-C. Gu, Z.-X. Liu, and X.-G. Wen, Science 338, 1604 (2012).
https:/​/​doi.org/​10.1126/​science.1227224

[3] 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

[4] S. Rachel, Reports on Progress in Physics 81, 116501 (2018).
https:/​/​doi.org/​10.1088/​1361-6633/​aad6a6

[5] K. v. Klitzing, G. Dorda, and M. Pepper, Phys. Rev. Lett. 45, 494 (1980).
https:/​/​doi.org/​10.1103/​PhysRevLett.45.494

[6] R. B. Laughlin, Physical Review B 23, 5632 (1981).
https:/​/​doi.org/​10.1103/​PhysRevB.23.5632

[7] X.-L. Qi and S.-C. Zhang, Rev. Mod. Phys. 83, 1057 (2011).
https:/​/​doi.org/​10.1103/​RevModPhys.83.1057

[8] L. Fu, Phys. Rev. Lett. 106, 106802 (2011).
https:/​/​doi.org/​10.1103/​PhysRevLett.106.106802

[9] N. Goldman, J. C. Budich, and P. Zoller, Nature Physics 12, 639 (2016).
https:/​/​doi.org/​10.1038/​nphys3803

[10] N. R. Cooper, J. Dalibard, and I. B. Spielman, Rev. Mod. Phys. 91, 015005 (2019).
https:/​/​doi.org/​10.1103/​RevModPhys.91.015005

[11] T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, Rev. Mod. Phys. 91, 015006 (2019).
https:/​/​doi.org/​10.1103/​RevModPhys.91.015006

[12] C. H. Lee, S. Imhof, C. Berger, F. Bayer, J. Brehm, L. W. Molenkamp, T. Kiessling, and R. Thomale, Communications Physics 1, 39 (2018).
https:/​/​doi.org/​10.1038/​s42005-018-0035-2

[13] S. D. Huber, Nature Physics 12, 621 (2016).
https:/​/​doi.org/​10.1038/​nphys3801

[14] G. Ma, M. Xiao, and C. T. Chan, Nature Reviews Physics 1, 281 (2019).
https:/​/​doi.org/​10.1038/​s42254-019-0030-x

[15] T. Lahaye, C. Menotti, L. Santos, M. Lewenstein, and T. Pfau, Reports on Progress in Physics 72, 126401 (2009).
https:/​/​doi.org/​10.1088/​0034-4885/​72/​12/​126401

[16] H. Weimer, M. Müller, I. Lesanovsky, P. Zoller, and H. P. Büchler, Nature Physics 6, 382 (2010).
https:/​/​doi.org/​10.1038/​nphys1614

[17] M. A. Baranov, M. Dalmonte, G. Pupillo, and P. Zoller, Chemical Reviews 112, 5012 (2012).
https:/​/​doi.org/​10.1021/​cr2003568

[18] C. Gross and I. Bloch, Science 357, 995 (2017).
https:/​/​doi.org/​10.1126/​science.aal3837

[19] A. de Paz, A. Sharma, A. Chotia, E. Maréchal, J. H. Huckans, P. Pedri, L. Santos, O. Gorceix, L. Vernac, and B. Laburthe-Tolra, Phys. Rev. Lett. 111, 185305 (2013).
https:/​/​doi.org/​10.1103/​PhysRevLett.111.185305

[20] S. Baier, M. J. Mark, D. Petter, K. Aikawa, L. Chomaz, Z. Cai, M. Baranov, P. Zoller, and F. Ferlaino, Science 352, 201 (2016).
https:/​/​doi.org/​10.1126/​science.aac9812

[21] B. Yan, S. A. Moses, B. Gadway, J. P. Covey, K. R. A. Hazzard, A. M. Rey, D. S. Jin, and J. Ye, Nature 501, 521 (2013).
https:/​/​doi.org/​10.1038/​nature12483

[22] H. Labuhn, D. Barredo, S. Ravets, S. de Léséleuc, T. Macrì, T. Lahaye, and A. Browaeys, Nature 534, 667 (2016).
https:/​/​doi.org/​10.1038/​nature18274

[23] D. Peter, N. Y. Yao, N. Lang, S. D. Huber, M. D. Lukin, and H. P. Büchler, Phys. Rev. A 91, 053617 (2015).
https:/​/​doi.org/​10.1103/​PhysRevA.91.053617

[24] S. Weber, S. de Léséleuc, V. Lienhard, D. Barredo, T. Lahaye, A. Browaeys, and H. P. Büchler, Quantum Science and Technology 3, 044001 (2018).
https:/​/​doi.org/​10.1088/​2058-9565/​aaca47

[25] T. Schuster, F. Flicker, M. Li, S. Kotochigova, J. E. Moore, J. Ye, and N. Y. Yao, Phys. Rev. Lett. 127, 015301 (2021).
https:/​/​doi.org/​10.1103/​PhysRevLett.127.015301

[26] S. V. Syzranov, M. L. Wall, V. Gurarie, and A. M. Rey, Nature Communications 5, 5391 (2014).
https:/​/​doi.org/​10.1038/​ncomms6391

[27] S. V. Syzranov, M. L. Wall, B. Zhu, V. Gurarie, and A. M. Rey, Nature Communications 7, 13543 (2016).
https:/​/​doi.org/​10.1038/​ncomms13543

[28] G. Salerno, G. Palumbo, N. Goldman, and M. Di Liberto, Phys. Rev. Research 2, 013348 (2020).
https:/​/​doi.org/​10.1103/​PhysRevResearch.2.013348

[29] S. R. Manmana, E. M. Stoudenmire, K. R. A. Hazzard, A. M. Rey, and A. V. Gorshkov, Phys. Rev. B 87, 081106 (2013).
https:/​/​doi.org/​10.1103/​PhysRevB.87.081106

[30] N. Y. Yao, A. V. Gorshkov, C. R. Laumann, A. M. Läuchli, J. Ye, and M. D. Lukin, Phys. Rev. Lett. 110, 185302 (2013).
https:/​/​doi.org/​10.1103/​PhysRevLett.110.185302

[31] N. Y. Yao, M. P. Zaletel, D. M. Stamper-Kurn, and A. Vishwanath, Nature Physics 14, 405 (2018).
https:/​/​doi.org/​10.1038/​s41567-017-0030-7

[32] V. Lienhard, P. Scholl, S. Weber, D. Barredo, S. de Léséleuc, R. Bai, N. Lang, M. Fleischhauer, H. P. Büchler, T. Lahaye, and A. Browaeys, Phys. Rev. X 10, 021031 (2020).
https:/​/​doi.org/​10.1103/​PhysRevX.10.021031

[33] S. de Léséleuc, V. Lienhard, P. Scholl, D. Barredo, S. Weber, N. Lang, H. P. Büchler, T. Lahaye, and A. Browaeys, Science 365, 775 (2019).
https:/​/​doi.org/​10.1126/​science.aav9105

[34] X. Li and W. V. Liu, Reports on Progress in Physics 79, 116401 (2016).
https:/​/​doi.org/​10.1088/​0034-4885/​79/​11/​116401

[35] A. Isacsson and S. M. Girvin, Phys. Rev. A 72, 053604 (2005).
https:/​/​doi.org/​10.1103/​PhysRevA.72.053604

[36] T. Müller, S. Fölling, A. Widera, and I. Bloch, Phys. Rev. Lett. 99, 200405 (2007).
https:/​/​doi.org/​10.1103/​PhysRevLett.99.200405

[37] G. Wirth, M. Ölschläger, and A. Hemmerich, Nature Physics 7, 147 (2011).
https:/​/​doi.org/​10.1038/​nphys1857

[38] E. Prodan and C. Prodan, Phys. Rev. Lett. 103, 248101 (2009).
https:/​/​doi.org/​10.1103/​PhysRevLett.103.248101

[39] A. Bermudez, T. Schaetz, and D. Porras, Phys. Rev. Lett. 107, 150501 (2011).
https:/​/​doi.org/​10.1103/​PhysRevLett.107.150501

[40] C. L. Kane and T. C. Lubensky, Nature Physics 10, 39 (2014).
https:/​/​doi.org/​10.1038/​nphys2835

[41] R. Süsstrunk and S. D. Huber, Science 349, 47 (2015).
https:/​/​doi.org/​10.1126/​science.aab0239

[42] O. Stenull, C. L. Kane, and T. C. Lubensky, Phys. Rev. Lett. 117, 068001 (2016).
https:/​/​doi.org/​10.1103/​PhysRevLett.117.068001

[43] G. Salerno, T. Ozawa, H. M. Price, and I. Carusotto, Phys. Rev. B 93, 085105 (2016).
https:/​/​doi.org/​10.1103/​PhysRevB.93.085105

[44] J. Li, L. Wang, J. Liu, R. Li, Z. Zhang, and X.-Q. Chen, Phys. Rev. B 101, 081403 (2020).
https:/​/​doi.org/​10.1103/​PhysRevB.101.081403

[45] Q. Wei, X. Zhang, W. Deng, J. Lu, X. Huang, M. Yan, G. Chen, Z. Liu, and S. Jia, Nature Materials 20, 812 (2021).
https:/​/​doi.org/​10.1038/​s41563-021-00933-4

[46] L. Luo, H.-X. Wang, Z.-K. Lin, B. Jiang, Y. Wu, F. Li, and J.-H. Jiang, Nature Materials 20, 794 (2021).
https:/​/​doi.org/​10.1038/​s41563-021-00985-6

[47] G. F. Lange, A. Bouhon, B. Monserrat, and R.-J. Slager, Phys. Rev. B 105, 064301 (2022).
https:/​/​doi.org/​10.1103/​PhysRevB.105.064301

[48] H. Bruus and K. Flensberg, Many-Body Quantum Theory in Condensed Matter Physics: An Introduction (Oxford University Press, 2004).

[49] A. P. Schnyder, Topological Matter School (2018).
https:/​/​www.fkf.mpg.de/​6431357/​topo_lecture_notes_schnyder_TMS18.pdf

[50] X. Feng, J. Zhu, W. Wu, and S. A. Yang, Chinese Physics B 30, 107304 (2021).
https:/​/​doi.org/​10.1088/​1674-1056/​ac1f0c

[51] C. Wu and S. Das Sarma, Phys. Rev. B 77, 235107 (2008).
https:/​/​doi.org/​10.1103/​PhysRevB.77.235107

[52] T. Jacqmin, I. Carusotto, I. Sagnes, M. Abbarchi, D. D. Solnyshkov, G. Malpuech, E. Galopin, A. Lemaı̂tre, J. Bloch, and A. Amo, Phys. Rev. Lett. 112, 116402 (2014).
https:/​/​doi.org/​10.1103/​PhysRevLett.112.116402

[53] T. S. Gardenier, J. J. van den Broeke, J. R. Moes, I. Swart, C. Delerue, M. R. Slot, C. M. Smith, and D. Vanmaekelbergh, ACS Nano, ACS Nano 14, 13638 (2020).
https:/​/​doi.org/​10.1021/​acsnano.0c05747

[54] A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, Rev. Mod. Phys. 81, 109 (2009).
https:/​/​doi.org/​10.1103/​RevModPhys.81.109

[55] S. Park, Y. Hwang, H. C. Choi, and B.-J. Yang, Nature Communications 12, 6781 (2021).
https:/​/​doi.org/​10.1038/​s41467-021-27158-y

[56] B. A. Bernevig and T. L. Hughes, Topological Insulators and Topological Superconductors (Princeton University Press, 2013).

[57] K. Sun, H. Yao, E. Fradkin, and S. A. Kivelson, Phys. Rev. Lett. 103, 046811 (2009).
https:/​/​doi.org/​10.1103/​PhysRevLett.103.046811

[58] G. Montambaux, L.-K. Lim, J.-N. Fuchs, and F. Piéchon, Phys. Rev. Lett. 121, 256402 (2018).
https:/​/​doi.org/​10.1103/​PhysRevLett.121.256402

[59] Y. He, J. Moore, and C. M. Varma, Phys. Rev. B 85, 155106 (2012).
https:/​/​doi.org/​10.1103/​PhysRevB.85.155106

[60] G. Montambaux, F. Piéchon, J.-N. Fuchs, and M. O. Goerbig, Phys. Rev. B 80, 153412 (2009).
https:/​/​doi.org/​10.1103/​PhysRevB.80.153412

[61] L. Tarruell, D. Greif, T. Uehlinger, G. Jotzu, and T. Esslinger, Nature 483, 302 (2012).
https:/​/​doi.org/​10.1038/​nature10871

[62] M. Bellec, U. Kuhl, G. Montambaux, and F. Mortessagne, Phys. Rev. Lett. 110, 033902 (2013).
https:/​/​doi.org/​10.1103/​PhysRevLett.110.033902

[63] M. C. Rechtsman, Y. Plotnik, J. M. Zeuner, D. Song, Z. Chen, A. Szameit, and M. Segev, Phys. Rev. Lett. 111, 103901 (2013a).
https:/​/​doi.org/​10.1103/​PhysRevLett.111.103901

[64] M. Milićević, G. Montambaux, T. Ozawa, O. Jamadi, B. Real, I. Sagnes, A. Lemaı̂tre, L. Le Gratiet, A. Harouri, J. Bloch, and A. Amo, Phys. Rev. X 9, 031010 (2019).
https:/​/​doi.org/​10.1103/​PhysRevX.9.031010

[65] J. Kim, S. S. Baik, S. H. Ryu, Y. Sohn, S. Park, B.-G. Park, J. Denlinger, Y. Yi, H. J. Choi, and K. S. Kim, Science 349, 723 (2015).
https:/​/​doi.org/​10.1126/​science.aaa6486

[66] T. Kitagawa, E. Berg, M. Rudner, and E. Demler, Phys. Rev. B 82, 235114 (2010).
https:/​/​doi.org/​10.1103/​PhysRevB.82.235114

[67] S. Mukherjee, A. Spracklen, M. Valiente, E. Andersson, P. Öhberg, N. Goldman, and R. R. Thomson, Nature Communications 8, 13918 (2017).
https:/​/​doi.org/​10.1038/​ncomms13918

[68] L. J. Maczewsky, J. M. Zeuner, S. Nolte, and A. Szameit, Nature Communications 8, 13756 (2017).
https:/​/​doi.org/​10.1038/​ncomms13756

[69] K. Wintersperger, C. Braun, F. N. Ünal, A. Eckardt, M. Di Liberto, N. Goldman, I. Bloch, and M. Aidelsburger, Nature Physics 16, 1058 (2020).
https:/​/​doi.org/​10.1038/​s41567-020-0949-y

[70] A. Quelle, C. Weitenberg, K. Sengstock, and C. Morais Smith, New Journal of Physics 19, 113010 (2017).
https:/​/​doi.org/​10.1088/​1367-2630/​aa8646

[71] S. Giovanazzi, A. Görlitz, and T. Pfau, Phys. Rev. Lett. 89, 130401 (2002).
https:/​/​doi.org/​10.1103/​PhysRevLett.89.130401

[72] Y. Tang, W. Kao, K.-Y. Li, and B. L. Lev, Phys. Rev. Lett. 120, 230401 (2018).
https:/​/​doi.org/​10.1103/​PhysRevLett.120.230401

[73] A. Celi, P. Massignan, J. Ruseckas, N. Goldman, I. B. Spielman, G. Juzeliūnas, and M. Lewenstein, Phys. Rev. Lett. 112, 043001 (2014).
https:/​/​doi.org/​10.1103/​PhysRevLett.112.043001

[74] T. Ozawa and H. M. Price, Nature Reviews Physics 1, 349 (2019).
https:/​/​doi.org/​10.1038/​s42254-019-0045-3

[75] B. Bradlyn, J. Cano, Z. Wang, M. G. Vergniory, C. Felser, R. J. Cava, and B. A. Bernevig, Science 353, aaf5037 (2016).
https:/​/​doi.org/​10.1126/​science.aaf5037
https:/​/​science.sciencemag.org/​content/​353/​6299/​aaf5037

[76] D. Green, L. Santos, and C. Chamon, Phys. Rev. B 82, 075104 (2010).
https:/​/​doi.org/​10.1103/​PhysRevB.82.075104

[77] I. C. Fulga and A. Stern, Phys. Rev. B 95, 241116 (2017).
https:/​/​doi.org/​10.1103/​PhysRevB.95.241116

[78] Y.-Q. Zhu, D.-W. Zhang, H. Yan, D.-Y. Xing, and S.-L. Zhu, Phys. Rev. A 96, 033634 (2017).
https:/​/​doi.org/​10.1103/​PhysRevA.96.033634

[79] X. Tan, D.-W. Zhang, Q. Liu, G. Xue, H.-F. Yu, Y.-Q. Zhu, H. Yan, S.-L. Zhu, and Y. Yu, Phys. Rev. Lett. 120, 130503 (2018).
https:/​/​doi.org/​10.1103/​PhysRevLett.120.130503

[80] H. Hu and C. Zhang, Phys. Rev. A 98, 013627 (2018).
https:/​/​doi.org/​10.1103/​PhysRevA.98.013627

[81] N. Armitage, E. Mele, and A. Vishwanath, Reviews of Modern Physics 90, 015001 (2018).
https:/​/​doi.org/​10.1103/​RevModPhys.90.015001

[82] D. Xiao, M.-C. Chang, and Q. Niu, Rev. Mod. Phys. 82, 1959 (2010).
https:/​/​doi.org/​10.1103/​RevModPhys.82.1959

[83] Z.-Y. Wang, X.-C. Cheng, B.-Z. Wang, J.-Y. Zhang, Y.-H. Lu, C.-R. Yi, S. Niu, Y. Deng, X.-J. Liu, S. Chen, and J.-W. Pan, Science 372, 271 (2021).
https:/​/​doi.org/​10.1126/​science.abc0105

[84] S. Sugawa, F. Salces-Carcoba, A. R. Perry, Y. Yue, and I. B. Spielman, Science 360, 1429 (2018).
https:/​/​doi.org/​10.1126/​science.aam9031

[85] F. Guinea, M. I. Katsnelson, and A. K. Geim, Nature Physics 6, 30 (2010).
https:/​/​doi.org/​10.1038/​nphys1420

[86] M. C. Rechtsman, J. M. Zeuner, A. Tünnermann, S. Nolte, M. Segev, and A. Szameit, Nature Photonics 7, 153 (2013b).
https:/​/​doi.org/​10.1038/​nphoton.2012.302

[87] O. Jamadi, E. Rozas, G. Salerno, M. Milićević, T. Ozawa, I. Sagnes, A. Lemaı̂tre, L. Le Gratiet, A. Harouri, I. Carusotto, J. Bloch, and A. Amo, Light: Science & Applications 9, 144 (2020).
https:/​/​doi.org/​10.1038/​s41377-020-00377-6

[88] B. Tian, M. Endres, and D. Pekker, Phys. Rev. Lett. 115, 236803 (2015).
https:/​/​doi.org/​10.1103/​PhysRevLett.115.236803

[89] M. Jamotte, N. Goldman, and M. Di Liberto, Communications Physics 5, 30 (2022).
https:/​/​doi.org/​10.1038/​s42005-022-00802-9

[90] G. Salerno, T. Ozawa, H. M. Price, and I. Carusotto, 2D Materials 2, 034015 (2015).
https:/​/​doi.org/​10.1088/​2053-1583/​2/​3/​034015

[91] M. O. Goerbig, Rev. Mod. Phys. 83, 1193 (2011).
https:/​/​doi.org/​10.1103/​RevModPhys.83.1193

[92] L. Duca, T. Li, M. Reitter, I. Bloch, M. Schleier-Smith, and U. Schneider, Science 347, 288 (2015).
https:/​/​doi.org/​10.1126/​science.1259052

[93] P. T. Ernst, S. Götze, J. S. Krauser, K. Pyka, D.-S. Lühmann, D. Pfannkuche, and K. Sengstock, Nature Physics 6, 56 (2010).
https:/​/​doi.org/​10.1038/​nphys1476

[94] A. Frisch, Dipolar Quantum Gases of Erbium, Ph.D. thesis (2014).

[95] M. Aymar and O. Dulieu, The Journal of Chemical Physics, The Journal of Chemical Physics 122, 204302 (2005).
https:/​/​doi.org/​10.1063/​1.1903944

[96] I. Bloch, J. Dalibard, and W. Zwerger, Rev. Mod. Phys. 80, 885 (2008).
https:/​/​doi.org/​10.1103/​RevModPhys.80.885

[97] L.-K. Lim, J.-N. Fuchs, F. Piéchon, and G. Montambaux, Phys. Rev. B 101, 045131 (2020).
https:/​/​doi.org/​10.1103/​PhysRevB.101.045131

[98] N. Goldman and J. Dalibard, Phys. Rev. X 4, 031027 (2014).
https:/​/​doi.org/​10.1103/​PhysRevX.4.031027

Cited by

[1] Andreas Kruckenhauser, Rick van Bijnen, Torsten V. Zache, Marco Di Liberto, and Peter Zoller, "High-dimensional SO(4)-symmetric Rydberg manifolds for quantum simulation", arXiv:2206.01108.

[2] Maxime Jamotte, Nathan Goldman, and Marco Di Liberto, "Strain and pseudo-magnetic fields in optical lattices from density-assisted tunneling", Communications Physics 5 1, 30 (2022).

[3] Gunnar F. Lange, Adrien Bouhon, Bartomeu Monserrat, and Robert-Jan Slager, "Topological continuum charges of acoustic phonons in two dimensions and the Nambu-Goldstone theorem", Physical Review B 105 6, 064301 (2022).

The above citations are from SAO/NASA ADS (last updated successfully 2022-10-04 20:59:15). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref's cited-by service no data on citing works was found (last attempt 2022-10-04 20:59:14).