- Letter
- Open Access
Interaction-induced breakdown of chiral dynamics in the Su-Schrieffer-Heeger model
Phys. Rev. Research 5, L032035 – Published 13 September, 2023
DOI: https://doi.org/10.1103/PhysRevResearch.5.L032035
Abstract
The effect of interparticle interactions on topological properties is difficult to experimentally probe and quantitatively characterize. For ultracold atomic systems, although topological phases and phenomena have been recently observed in various settings, the effect of atomic interactions has so far remained largely unexplored. Here, we realize a Su-Schrieffer-Heeger model in the momentum lattice of a Bose-Einstein condensate with tunable atomic interactions and measure the bulk dynamics of atoms in a synthetic topological wire subjected to sudden quench under various interactions. We observe the breakdown of chiral dynamics in the atomic wire with increasing strength of interaction, where the atoms are localized at the initial injection site under the strong interaction. We show that the mean chiral displacement can be used to characterize the effect of interaction on the atomic chiral dynamics by studying its variation with the interaction. Our results provide a benchmark for exploring the interacting topological fluids.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (58)
- M. Z. Hasan and C. L. Kane, Colloquium: Topological insulators, Rev. Mod. Phys. 82, 3045 (2010).
- X.-L. Qi and S.-C. Zhang, Topological insulators and superconductors, Rev. Mod. Phys. 83, 1057 (2011).
- L. Lu, J. D. Joannopoulos, and M. Soljačić, Topological photonics, Nat. Photonics 8, 821 (2014).
- S. D. Huber, Topological mechanics, Nat. Phys. 12, 621 (2016).
- N. Goldman, J. C. Budich, and P. Zoller, Topological quantum matter with ultracold gases in optical lattices, Nat. Phys. 12, 639 (2016).
- N. R. Cooper, J. Dalibard, and I. B. Spielman, Topological bands for ultracold atoms, Rev. Mod. Phys. 91, 015005 (2019).
- S. Ryu, A. P. Schnyder, A. Furusaki, and A. W. W. Ludwig, Topological insulators and superconductors: tenfold way and dimensional hierarchy, New J. Phys. 12, 065010 (2010).
- C.-K. Chiu, J. C. Y. Teo, A. P. Schnyder, and S. Ryu, Classification of topological quantum matter with symmetries, Rev. Mod. Phys. 88, 035005 (2016).
- P. G. Harper, Single band motion of conduction electrons in a uniform magnetic field, Proc. Phys. Soc. A 68, 874 (1955).
- D. R. Hofstadter, Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields, Phys. Rev. B 14, 2239 (1976).
- F. D. M. Haldane, Model for a Quantum Hall Effect without Landau Levels: Condensed-Matter Realization of the “Parity Anomaly”, Phys. Rev. Lett. 61, 2015 (1988).
- M. Aidelsburger, M. Atala, M. Lohse, J. T. Barreiro, B. Paredes, and I. Bloch, Realization of the Hofstadter Hamiltonian with Ultracold Atoms in Optical Lattices, Phys. Rev. Lett. 111, 185301 (2013).
- H. Miyake, G. A. Siviloglou, C. J. Kennedy, W. C. Burton, and W. Ketterle, Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices, Phys. Rev. Lett. 111, 185302 (2013).
- M. Aidelsburger, M. Lohse, C. Schweizer, M. Atala, J. T. Barreiro, S. Nascimbène, N. R. Cooper, I. Bloch, and N. Goldman, Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms, Nat. Phys. 11, 162 (2015).
- G. Jotzu, M. Messer, R. Desbuquois, M. Lebrat, T. Uehlinger, D. Greif, and T. Esslinger, Experimental realization of the topological Haldane model with ultracold fermions, Nature (London) 515, 237 (2014).
- M. Mancini, G. Pagano, G. Cappellini, L. Livi, M. Rider, J. Catani, C. Sias, P. Zoller, M. Inguscio, M. Dalmonte, and L. Fallani, Observation of chiral edge states with neutral fermions in synthetic Hall ribbons, Science 349, 1510 (2015).
- B. K. Stuhl, H.-I. Lu, L. M. Aycock, D. Genkina, and I. B. Spielman, Visualizing edge states with an atomic Bose gas in the quantum Hall regime, Science 349, 1514 (2015).
- M. Atala, M. Aidelsburger, M. Lohse, J. T. Barreiro, B. Paredes, and I. Bloch, Observation of chiral currents with ultracold atoms in bosonic ladders, Nat. Phys. 10, 588 (2014).
- S. Kolkowitz, S. L. Bromley, T. Bothwell, M. L. Wall, G. E. Marti, A. P. Koller, X. Zhang, A. M. Rey, and J. Ye, Spin-orbit-coupled fermions in an optical lattice clock, Nature (London) 542, 66 (2017).
- F. A. An, E. J. Meier, and B. Gadway, Direct observation of chiral currents and magnetic reflection in atomic flux lattices, Sci. Adv. 3, e1602685 (2017).
- S. Nakajima, T. Tomita, S. Taie, T. Ichinose, H. Ozawa, L. Wang, M. Troyer, and Y. Takahashi, Topological Thouless pumping of ultracold fermions, Nat. Phys. 12, 296 (2016).
- M. Lohse, C. Schweizer, O. Zilberberg, M. Aidelsburger, and I. Bloch, A Thouless quantum pump with ultracold bosonic atoms in an optical superlattice, Nat. Phys. 12, 350 (2016).
- W. P. Su, J. R. Schrieffer, and A. J. Heeger, Solitons in Polyacetylene, Phys. Rev. Lett. 42, 1698 (1979).
- M. Atala, M. Aidelsburger, J. T. Barreiro, D. Abanin, T. Kitagawa, E. Demler, and I. Bloch, Direct measurement of the Zak phase in topological Bloch bands, Nat. Phys. 9, 795 (2013).
- E. J. Meier, F. A. An, and B. Gadway, Observation of the topological soliton state in the Su-Schrieffer-Heeger model, Nat. Commun. 7, 13986 (2016).
- E. J. Meier, F. A. An, A. Dauphin, M. Maffei, P. Massignan, T. L. Hughes, and B. Gadway, Observation of the topological Anderson insulator in disordered atomic wires, Science 362, 929 (2018).
- D. Z. Xie, W. Gou, T. Xiao, B. Gadway, and B. Yan, Topological characterizations of an extended Su-Schrieffer-Heeger model, npj Quantum Inf. 5, 55 (2019).
- D. Z. Xie, T.-S. Deng, T. Xiao, W. Gou, T. Chen, W. Yi, and B. Yan, Topological Quantum Walks in Momentum Space with a Bose-Einstein Condensate, Phys. Rev. Lett. 124, 050502 (2020).
- J. Maciejko and G. A. Fiete, Fractionalized topological insulators, Nat. Phys. 11, 385 (2015).
- S. Rachel, Interacting topological insulators: A review, Rep. Prog. Phys. 81, 116501 (2018).
- D.-W. Zhang, Y.-Q. Zhu, Y. X. Zhao, H. Yan, and S.-L. Zhu, Topological quantum matter with cold atoms, Adv. Phys. 67, 253 (2018).
- D. C. Tsui, H. L. Stormer, and A. C. Gossard, Two-Dimensional Magnetotransport in the Extreme Quantum Limit, Phys. Rev. Lett. 48, 1559 (1982).
- R. B. Laughlin, Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations, Phys. Rev. Lett. 50, 1395 (1983).
- 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).
- M. A. Bandres, S. Wittek, G. Harari, M. Parto, J. Ren, M. Segev, D. N. Christodoulides, and M. Khajavikhan, Topological insulator laser: Experiments, Science 359, eaar4005 (2018).
- S. Mukherjee and M. C. Rechtsman, Observation of Unidirectional Solitonlike Edge States in Nonlinear Floquet Topological Insulators, Phys. Rev. X 11, 041057 (2021).
- Y. V. Kartashov, A. A. Arkhipova, S. A. Zhuravitskii, N. N. Skryabin, I. V. Dyakonov, A. A. Kalinkin, S. P. Kulik, V. O. Kompanets, S. V. Chekalin, L. Torner, and V. N. Zadkov, Observation of Edge Solitons in Topological Trimer Arrays, Phys. Rev. Lett. 128, 093901 (2022).
- M. Jürgensen, S. Mukherjee, and M. C. Rechtsman, Quantized nonlinear Thouless pumping, Nature (London) 596, 63 (2021).
- C. Chin, R. Grimm, P. Julienne, and E. Tiesinga, Feshbach resonances in ultracold gases, Rev. Mod. Phys. 82, 1225 (2010).
- A.-S. Walter, Z. J. Zhu, M. Gächter, J. Minguzzi, S. Roschinski, K. Sandholzer, K. Viebahn, and T. Esslinger, Quantization and its breakdown in a Hubbard–Thouless pump, Nat. Phys. (2023), doi:10.1038/s41567-023-02145-w.
- T. Weber, J. Herbig, M. Mark, H.-C. Nägerl, and R. Grimm, Bose-Einstein condensation of cesium, Science 299, 232 (2003).
- T. Kraemer, J. Herbig, M. Mark, T. Weber, C. Chin, H.-C. Nägerl, and R. Grimm, Optimized production of a cesium Bose-Einstein condensate, Appl. Phys. B 79, 1013 (2004).
- Y. F. Wang, Y. Q. Li, J. Z. Wu, W. L. Liu, J. Z. Hu, J. Ma, L. T. Xiao, and S. T. Jia, Hybrid evaporative cooling of atoms to Bose-Einstein condensation, Opt. Express 29, 13960 (2021).
- E. J. Meier, F. A. An, and B. Gadway, Atom-optics simulator of lattice transport phenomena, Phys. Rev. A 93, 051602(R) (2016).
- F. A. An, E. J. Meier, and B. Gadway, Diffusive and arrested transport of atoms under tailored disorder, Nat. Commun. 8, 325 (2017).
- Y. Q. Li, J. H. Zhang, Y. F. Wang, H. Y. Du, J. Z. Wu, W. L. Liu, F. Mei, J. Ma, L. T. Xiao, and S. T. Jia, Atom-optically synthetic gauge fields for a noninteracting Bose gas, Light Sci. Appl. 11, 13 (2022).
- Y. F. Wang, J.-H. Zhang, Y. Q. Li, J. Z. Wu, W. L. Liu, F. Mei, Y. Hu, L. T. Xiao, J. Ma, C. Chin, and S. T. Jia, Observation of Interaction-Induced Mobility Edge in an Atomic Aubry-André Wire, Phys. Rev. Lett. 129, 103401 (2022).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.5.L032035 for details of our experiments, the single-particle topological edge states, the actual tunneling energies, the measurement of atomic population dynamics, the effect of interaction on the chiral dynamics for different dimerizations, the interaction of Bragg laser fields with atoms, the derivation of the Hamiltonian in a dimerized lattice, the real-space GPE simulation, the nonlinear SSH model, a comparison of the interaction effect on chiral dynamics with self-trapping, and the chiral dynamics under attractive interactions.
- C. J. Pethick and H. Smith, Bose-Einstein Condensation in Dilute Gases (Cambridge University Press, Cambridge, 2008).
- P. B. Blakie and R. J. Ballagh, Mean-field treatment of Bragg scattering from a Bose-Einstein condensate, J. Phys. B: At. Mol. Opt. Phys. 33, 3961 (2000).
- S. Pötting, M. Cramer, and P. Meystre, Momentum-state engineering and control in Bose-Einstein condensates, Phys. Rev. A 64, 063613 (2001).
- T. Chen, D. Z. Xie, B. Gadway, and B. Yan, A Gross-Pitaevskii-equation description of the momentum-state lattice: Roles of the trap and many-body interactions, arXiv:2103.14205 v2.
- F. A. An, E. J. Meier, J. Ang'ong'a, and B. Gadway, Correlated Dynamics in a Synthetic Lattice of Momentum States, Phys. Rev. Lett. 120, 040407 (2018).
- F. A. An, B. Sundar, J. P. Hou, X.-W. Luo, E. J. Meier, C. W. Zhang, K. R. A. Hazzard, and B. Gadway, Nonlinear Dynamics in a Synthetic Momentum-State Lattice, Phys. Rev. Lett. 127, 130401 (2021).
- S. Raghavan, A. Smerzi, S. Fantoni, and S. R. Shenoy, Coherent oscillations between two weakly coupled Bose-Einstein condensates: Josephson effects, oscillations, and macroscopic quantum self-trapping, Phys. Rev. A 59, 620 (1999).
- M. Albiez, R. Gati, J. Fölling, S. Hunsmann, M. Cristiani, and M. K. Oberthaler, Direct Observation of Tunneling and Nonlinear Self-Trapping in a Single Bosonic Josephson Junction, Phys. Rev. Lett. 95, 010402 (2005).
- F. Cardano, A. D'Errico, A. Dauphin, M. Maffei, B. Piccirillo, C. D. Lisio, G. D. Filippis, V. Cataudella, E. Santamato, L. Marrucci, M. Lewenstein, and P. Massignan, Detection of Zak phases and topological invariants in a chiral quantum walk of twisted photons, Nat. Commun. 8, 15516 (2017).
- Z.-Q. Jiao, S. Longhi, X.-W. Wang, J. Gao, W.-H. Zhou, Y. Wang, Y.-X. Fu, L. Wang, R.-J. Ren, L.-F. Qiao, and X.-M Jin, Experimentally Detecting Quantized Zak Phases without Chiral Symmetry in Photonic Lattices, Phys. Rev. Lett. 127, 147401 (2021).