Abstract
The significance of topological phases has been widely recognized in the community of condensed matter physics. The well controllable quantum systems provide an artificial platform to probe and engineer various topological phases. The adiabatic trajectory of a quantum state describes the change of the bulk Bloch eigenstates with the momentum, and this adiabatic simulation method is however practically limited due to quantum dissipation. Here we apply the “shortcut to adiabaticity” (STA) protocol to realize fast adiabatic evolutions in the system of a superconducting phase qubit. The resulting fast adiabatic trajectories illustrate the change of the bulk Bloch eigenstates in the Su-Schrieffer-Heeger (SSH) model. A sharp transition is experimentally determined for the topological invariant of a winding number. Our experiment helps identify the topological Chern number of a two-dimensional toy model, suggesting the applicability of the fast adiabatic simulation method for topological systems.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
K. Klitzing, G. Dorda, and M. Pepper, Phys. Rev. Lett. 45, 494 (1980).
D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Phys. Rev. Lett. 49, 405 (1982).
W. P. Su, J. R. Schrieffer, and A. J. Heeger, Phys. Rev. Lett. 42, 1698 (1979).
J. K. Asbóth, L. Oroszlány, and A. Pályi, A Short Course on Topological Insulators: Band Structure and Edge States in One and Two Dimensions (Springer International Publishing, Cham, 2016).
T. Kitagawa, M. A. Broome, A. Fedrizzi, M. S. Rudner, E. Berg, I. Kassal, A. Aspuru-Guzik, E. Demler, and A. G. White, Nat. Commun. 3, 882 (2012).
M. Atala, M. Aidelsburger, J. T. Barreiro, D. Abanin, T. Kitagawa, E. Demler, and I. Bloch, Nat. Phys. 9, 795 (2013).
G. Jotzu, M. Messer, R. Desbuquois, M. Lebrat, T. Uehlinger, D. Greif, and T. Esslinger, Nature 515, 237 (2014).
M. Aidelsburger, M. Lohse, C. Schweizer, M. Atala, J. T. Barreiro, S. Nascimbéne, N. R. Cooper, I. Bloch, and N. Goldman, Nat. Phys. 11, 162 (2014).
L. Duca, T. Li, M. Reitter, I. Bloch, M. Schleier-Smith, and U. Schneider, Science 347, 288 (2015).
S. Mittal, S. Ganeshan, J. Fan, A. Vaezi, and M. Hafezi, Nat. Photon 10, 180 (2016).
N. Flaschner, B. S. Rem, M. Tarnowski, D. Vogel, D. S. Luhmann, K. Sengstock, and C. Weitenberg, Science 352, 1091 (2016).
N. Goldman, J. C. Budich, and P. Zoller, Nat. Phys. 12, 639 (2016).
P. Roushan, C. Neill, Y. Chen, M. Kolodrubetz, C. Quintana, N. Leung, M. Fang, R. Barends, B. Campbell, Z. Chen, B. Chiaro, A. Dunsworth, E. Jeffrey, J. Kelly, A. Megrant, J. Mutus, P. J. J. OMalley, D. Sank, A. Vainsencher, J. Wenner, T. White, A. Polkovnikov, A. N. Cleland, and J. M. Martinis, Nature 515, 241 (2014).
M. D. Schroer, M. H. Kolodrubetz, W. F. Kindel, M. Sandberg, J. Gao, M. R. Vissers, D. P. Pappas, A. Polkovnikov, and K. W. Lehnert, Phys. Rev. Lett. 113, 050402 (2014).
E. Flurin, V. V. Ramasesh, S. Hacohen-Gourgy, L. S. Martin, N. Y. Yao, and I. Siddiqi, Phys. Rev. X 7, 031023 (2017).
F. Kong, C. Ju, Y. Liu, C. Lei, M. Wang, X. Kong, P. Wang, P. Huang, Z. Li, F. Shi, L. Jiang, and J. Du, Phys. Rev. Lett. 117, 060503 (2016).
M. Z. Hasan, and C. L. Kane, Rev. Mod. Phys. 82, 3045 (2010).
E. Farhi, J. Goldstone, S. Gutmann, and M. Sipser, arXiv: quantph/0001106.
M. A. Nielsen, and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Canbridge, 2000).
M. Demirplak, and S. A. Rice, J. Phys. Chem. A 107, 9937 (2003).
M. V. Berry, J. Phys. A-Math. Theor. 42, 365303 (2009).
X. Chen, I. Lizuain, A. Ruschhaupt, D. Guéry-Odelin, and J. G. Muga, Phys. Rev. Lett. 105, 123003 (2010).
S. Masuda, and K. Nakamura, Proc. R. Soc. A-Math. Phys. Eng. Sci. 466, 1135 (2010).
E. Torrontegui, S. Ibáñez, S. Martínez-Garaot, M. Modugno, A. del Campo, D. Guéry-Odelin, A. Ruschhaupt, X. Chen, and J. G. Muga, Adv. Atomic Mol. Opt. Phys. 62 117 (2013).
B. T. Torosov, S. Guérin, and N. V. Vitanov, Phys. Rev. Lett. 106, 233001 (2011).
J. M. Martinis, and M. R. Geller, Phys. Rev. A 90, 022307 (2014).
M. G. Bason, M. Viteau, N. Malossi, P. Huillery, E. Arimondo, D. Ciampini, R. Fazio, V. Giovannetti, R. Mannella, and O. Morsch, Nat. Phys. 8, 147 (2011).
J. Zhang, J. H. Shim, I. Niemeyer, T. Taniguchi, T. Teraji, H. Abe, S. Onoda, T. Yamamoto, T. Ohshima, J. Isoya, and D. Suter, Phys. Rev. Lett. 110, 240501 (2013).
B. B. Zhou, A. Baksic, H. Ribeiro, C. G. Yale, F. J. Heremans, P. C. Jerger, A. Auer, G. Burkard, A. A. Clerk, and D. D. Awschalom, Nat. Phys 13, 330 (2017).
S. An, D. Lv, A. del Campo, and K. Kim, Nat. Commun. 7, 12999 (2016).
Z. Zhang, T. Wang, L. Xiang, J. Yao, J. Wu, and Y. Yin, Phys. Rev. A 95, 042345 (2017).
F. Motzoi, J. M. Gambetta, P. Rebentrost, and F. K. Wilhelm, Phys. Rev. Lett. 103, 110501 (2009).
J. M. Gambetta, F. Motzoi, S. T. Merkel, and F. K. Wilhelm, Phys. Rev. A 83, 012308 (2011).
E. Lucero, J. Kelly, R. C. Bialczak, M. Lenander, M. Mariantoni, M. Neeley, A. D. OConnell, D. Sank, H. Wang, M. Weides, J. Wenner, T. Yamamoto, A. N. Cleland, and J. M. Martinis, Phys. Rev. A 82, 042339 (2010).
T. Lu, Phys. Rev. A 84, 033411 (2011).
J. M. Martinis, Quantum Inf. Process. 8, 81 (2009).
E. Lucero, R. Barends, Y. Chen, J. Kelly, M. Mariantoni, A. Megrant, P. OMalley, D. Sank, A. Vainsencher, J. Wenner, T. White, Y. Yin, A. N. Cleland, and J. M. Martinis, Nat. Phys. 8, 719 (2012).
Author information
Authors and Affiliations
Corresponding authors
Electronic supplementary material
Rights and permissions
About this article
Cite this article
Wang, T., Zhang, Z., Xiang, L. et al. Simulating a topological transition in a superconducting phase qubit by fast adiabatic trajectories. Sci. China Phys. Mech. Astron. 61, 047411 (2018). https://doi.org/10.1007/s11433-017-9156-1
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11433-017-9156-1