Quantized Nonlinear Transport with Ultracold Atoms

Fan Yang and Hui Zhai

Institute for Advanced Study, Tsinghua University, Beijing 100084, China

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In this letter, we propose how to measure the quantized nonlinear transport using two-dimensional ultracold atomic Fermi gases in a harmonic trap. This scheme requires successively applying two optical pulses in the left and lower half-planes and then measuring the number of extra atoms in the first quadrant. In ideal situations, this nonlinear density response to two successive pulses is quantized, and the quantization value probes the Euler characteristic of the local Fermi sea at the trap center. We investigate the practical effects in experiments, including finite pulse duration, finite edge width of pulses, and finite temperature, which can lead to deviation from quantization. We propose a method to reduce the deviation by averaging measurements performed at the first and third quadrants, inspired by symmetry considerations. With this method, the quantized nonlinear response can be observed reasonably well with experimental conditions readily achieved with ultracold atoms.

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

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

[3] B. A. Bernevig and T. Hughes, Topological insulators and topological superconductors (Princeton University Press 2013). https:/​/​doi.org/​10.1515/​9781400846733.

[4] E. Witten, Three lectures on topological phases of matter, Riv. del Nuovo Cim. 39, 313 (2016). https:/​/​doi.org/​10.1393/​ncr/​i2016-10125-3.

[5] X.-G. Wen, Colloquium: Zoo of quantum-topological phases of matter, Rev. Mod. Phys. 89, 041004 (2017). https:/​/​doi.org/​10.1103/​RevModPhys.89.041004.

[6] N. P. Armitage, E. J. Mele, and A. Vishwanath, Weyl and Dirac semimetals in three-dimensional solids, Rev. Mod. Phys. 90, 015001 (2018). https:/​/​doi.org/​10.1103/​RevModPhys.90.015001.

[7] R. Moessner and J. E. Moore, Topological phases of matter (Cambridge University Press 2021). https:/​/​doi.org/​10.1017/​9781316226308.

[8] R. Landauer, Spatial variation of currents and fields due to localized scatterers in metallic conduction, IBM J. Res. Dev. 1, 223 (1957). https:/​/​doi.org/​10.1147/​rd.13.0223.

[9] D. S. Fisher and P. A. Lee, Relation between conductivity and transmission matrix, Phys. Rev. B 23, 6851 (1981). https:/​/​doi.org/​10.1103/​PhysRevB.23.6851.

[10] B. J. van Wees, H. van Houten, C. W. J. Beenakker, J. G. Williamson, L. P. Kouwenhoven, D. van der Marel, and C. T. Foxon, Quantized conductance of point contacts in a two-dimensional electron gas, Phys. Rev. Lett. 60, 848 (1988). https:/​/​doi.org/​10.1103/​PhysRevLett.60.848.

[11] D. A. Wharam, T. J. Thornton, R. Newbury, M. Pepper, H. Ahmed, J. E. F Frost, D. G. Hasko, D. C. Peacock, D. A. Ritchie, and G. A. C. Jones, One-dimensional transport and the quantisation of the ballistic resistance, J. Phys. C: Solid State Phys. 21 L209 (1988). https:/​/​dx.doi.org/​10.1088/​0022-3719/​21/​8/​002.

[12] T. Honda, S. Tarucha, T. Saku, and Y. Tokura, Quantized conductance observed in quantum wires 2 to 10 $\mu$m long, Jpn. J. Appl. Phys. 34, L72 (1995). https:/​/​dx.doi.org/​10.1143/​JJAP.34.L72.

[13] I. van Weperen, S. R. Plissard, E. P. A. M. Bakkers, S. M. Frolov, and L. P. Kouwenhoven, Quantized conductance in an InSb nanowire, Nano Lett. 13, 387 (2013). https:/​/​doi.org/​10.1021/​nl3035256.

[14] S. Frank, P. Poncharal, Z. L. Wang, and W. A. de Heer, Carbon nanotube quantum resistors, Science 280, 1744 (1998). https:/​/​doi.org/​10.1126/​science.280.5370.1744.

[15] S. Krinner, D. Stadler, D. Husmann, J.-P. Brantut, and T. Esslinger, Observation of quantized conductance in neutral matter, Nature 517, 64 (2015). https:/​/​doi.org/​10.1038/​nature14049.

[16] S. Krinner, T. Esslinger, and J.-P. Brantut, Two-terminal transport measurements with cold atoms, J. Phys.: Condens. Matter 29 343003 (2017). https:/​/​doi.org/​10.1088/​1361-648X/​aa74a1.

[17] M. Lebrat, S. Häusler, P. Fabritius, D. Husmann, L. Corman, and T. Esslinger, Quantized conductance through a spin-selective atomic point contact, Phys. Rev. Lett. 123, 193605 (2019). https:/​/​doi.org/​10.1103/​PhysRevLett.123.193605.

[18] K. v. Klitzing, G. Dorda, and M. Pepper, New method for high-accuracy determination of the fine-structure constant based on quantized hall resistance, Phys. Rev. Lett. 45, 494, (1980). https:/​/​doi.org/​10.1103/​PhysRevLett.45.494.

[19] D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Quantized Hall conductance in a two-dimensional periodic potential, Phys. Rev. Lett. 49, 405 (1982). https:/​/​doi.org/​10.1103/​PhysRevLett.49.405.

[20] 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). https:/​/​doi.org/​10.1103/​PhysRevLett.61.2015.

[21] C.-Z. Chang, et al. Experimental observation of the quantum anomalous Hall effect in a magnetic topological insulator, Science 340, 167 (2013). https:/​/​doi.org/​10.1126/​science.1234414.

[22] C. L. Kane and E. J. Mele, $Z_2$ topological order and the quantum spin Hall effect, Phys. Rev. Lett. 95 146802 (2005); https:/​/​doi.org/​10.1103/​PhysRevLett.95.146802 Quantum Spin Hall Effect in Graphene, Phys. Rev. Lett. 95, 226801 (2005). https:/​/​doi.org/​10.1103/​PhysRevLett.95.226801.

[23] B. A. Bernevig and S.-C. Zhang, Quantum spin Hall effect, Phys. Rev. Lett. 96, 106802 (2006). https:/​/​doi.org/​10.1103/​PhysRevLett.96.106802.

[24] M. König, S. Wiedmann, C. Brüne, A. Roth, H. Buhmann, L W. Molenkamp, X.-L. Qi, and S.-C. Zhang, Quantum spin Hall insulator state in HgTe quantum wells, Science 318, 766 (2007). https:/​/​doi.org/​10.1126/​science.1148047.

[25] C. L Kane, Quantized nonlinear conductance in ballistic metals, Phys. Rev. Lett. 128, 076801 (2022). https:/​/​doi.org/​10.1103/​PhysRevLett.128.076801.

[26] M. Rodriguez-Vega, A quantized surprise from Fermi surface topology, Physics, 15 s19 (2022).

[27] A. S. Schwartz, Topology for Physicists (Springer 1994). https:/​/​doi.org/​10.1007/​978-3-662-02998-5.

[28] I. M. Lifshitz, Anomalies of electron characteristics of a metal in the high pressure region, Sov. Phys. JETP 11, 1130 (1960).

[29] P. Wang, Z.-Q. Yu, Z. Fu, J. Miao, L. Huang, S. Chai, H. Zhai, and J. Zhang, Spin-orbit coupled degenerate Fermi gases, Phys. Rev. Lett. 109, 095301 (2012). https:/​/​doi.org/​10.1103/​PhysRevLett.109.095301.

[30] L. Tarruell, D. Greif, T. Uehlinger, G. Jotzu, and T. Esslinger, Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice, Nature 483, 302 (2012). https:/​/​doi.org/​10.1038/​nature10871.

[31] D. B. Hume, I. Stroescu, M. Joos, W. Muessel, H. Strobel, and M. K. Oberthaler, Accurate Atom Counting in Mesoscopic Ensembles, Phys. Rev. Lett. 111, 253001 (2013). https:/​/​doi.org/​10.1103/​PhysRevLett.111.253001 See also, V. Vuletic, Physics, 6, 137 (2013).

[32] The numerical program can be found at https:/​/​github.com/​YangFan403/​Quantized-nonlinear-transport-with-ultracold-atoms/​tree/​main.

[33] P. K. Tam, M. Claassen, and C. L. Kane, Topological multipartite entanglement in a Fermi liquid, Phys. Rev. X 12, 031022 (2022). https:/​/​doi.org/​10.1103/​PhysRevX.12.031022.

Cited by

[1] Pengfei Zhang, "Quantized Topological Response in Trapped Quantum Gases", arXiv:2207.02382.

[2] Pok Man Tam and Charles L. Kane, "Probing Fermi sea topology by Andreev state transport", arXiv:2210.08048.

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