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Chin. Phys. B, 2018, Vol. 27(7): 070303    DOI: 10.1088/1674-1056/27/7/070303

Observation of geometric phase in a dispersively coupled resonator-qutrit system

Libo Zhang(张礼博)1, Chao Song(宋超)1, H Wang(王浩华)1, Shi-Biao Zheng(郑仕标)2
1 Department of Physics, Zhejiang University, Hangzhou 310027, China;
2 Fujian Key Laboratory of Quantum Information and Quantum Optics, College of Physics and Information Engineering, Fuzhou University, Fuzhou 350116, China

We present an experiment of observing the geometric phase in a superconducting circuit where the resonator and the qutrit energy levels are dispersively coupled. The drive applied to the resonator displaces its state components associated with the qutrit's ground state and first-excited state along different circular trajectories in phase space. We identify the resonator's phase-space trajectories by Wigner tomography using an ancilla qubit, following which we observe the difference between the geometric phases associated with these trajectories using Ramsey interferometry. This geometric phase is further used to construct the single-qubit π-phase gate with a process fidelity of 0.851±0.001.

Keywords:  geometric phase      superconducting circuit      Wigner tomography  
Received:  04 March 2018      Revised:  26 April 2018      Accepted manuscript online: 
PACS:  03.65.Vf (Phases: geometric; dynamic or topological)  
  03.67.Lx (Quantum computation architectures and implementations)  
  42.50.Pq (Cavity quantum electrodynamics; micromasers)  

Project supported by the National Basic Research Program of China (Grant No. 2014CB921201) and the National Natural Science Foundation of China (Grant Nos. 11434008 and 11574380).

Corresponding Authors:  H Wang, Shi-Biao Zheng     E-mail:;

Cite this article: 

Libo Zhang(张礼博), Chao Song(宋超), H Wang(王浩华), Shi-Biao Zheng(郑仕标) Observation of geometric phase in a dispersively coupled resonator-qutrit system 2018 Chin. Phys. B 27 070303

[1] Anandan J 1992 Nature 360 307
[2] Aharonov Y and Anandan J 1987 Phys. Rev. Lett. 58 1593
[3] Zanardi P and Rasetti M 1999 Phys. Lett. A 264 94
[4] Jones J A, Vedral V, Ekert A and Castagnoli G 2000 Nature 403 869
[5] Falci G, Fazio R, Palma G M, Siewert J and Vedral V 2000 Nature 407 355
[6] Duan L M, Cirac J I and Zoller P 2001 Science 292 1695
[7] Wang X B and Keiji M 2001 Phys. Rev. Lett. 87 097901
[8] Zhu S L and Wang Z D 2002 Phys. Rev. Lett. 89 097902
[9] Leibfried D, DeMarco B, Meyer V, Lucas D, Barrett M, Britton J, Itano W M, Jelenkovic B, Langer C, Rosenband T and Winel D J 2003 Nature 422 412
[10] Zheng S B 2004 Phys. Rev. A 70 052320
[11] Sjöqvist E, Tong D M, Andersson L M, Hessmo B, Johansson M and Singh K 2012 New J. Phys. 14 103035
[12] Samuel J and Bhandari R 1988 Phys. Rev. Lett. 60 2339
[13] Tycko R 1987 Phys. Rev. Lett. 58 2281
[14] Suter D, Mueller K T and Pines A 1988 Phys. Rev. Lett. 60 1218
[15] Webb C L, Godun R M, Summy G S, Oberthaler M K, Featonby P D, Foot C J and Burnett K 1999 Phys. Rev. A 60 R1783
[16] Feng G, Xu G and Long G 2013 Phys. Rev. Lett. 110 190501
[17] Leek P J, Fink J M, Blais A, Bianchetti R, Göppl M, Gambetta J M, Schuster D I, Frunzio L, Schoelkopf R J and Wallraff A 2007 Science 318 1889
[18] Filipp S, Klepp J, Hasegawa Y, Plonka-Spehr C, Schmidt U, Geltenbort P and Rauch H 2009 Phys. Rev. Lett. 102 030404
[19] Pechal M, Berger S, Abdumalikov A A Jr, Fink J M, Mlynek J A, Steffen L, Wallraff A and Filipp S 2012 Phys. Rev. Lett. 108 170401
[20] Tan X, Zhang D, Zhang Z, Yu Y, Han S and Zhu S 2014 Phys. Rev. Lett. 112 027001
[21] Zhou H, Li Z, Wang H, Chen H, Peng X and Du J 2016 Chin. Phys. Lett. 33 060301
[22] Song C, Zheng S B, Zhang P, Xu K, Zhang L, Guo Q, Liu W, Xu D, Deng H, Huang K, Zheng D, Zhu X and Wang H 2017 Nat. Commun. 8 1061
[23] Paik H, Mezzacapo A, Sandberg M, McClure D T, Abdo B, Córcoles A D, Dial O, Bogorin D F, Plourde B L T, Steffen M, Cross A W, Gambetta J M and Chow Jerry M 2016 Phys. Rev. Lett. 117 250502
[24] Song C, Xu K, Liu W, Yang C, Zheng S B, Deng H, Xie Q, Huang K, Guo Q, Zhang L, Zhang P, Xu D, Zheng D, Zhu X, Wang H, Chen Y A, Lu C Y, Han S and Pan J W 2017 Phys. Rev. Lett. 119 180511
[25] Gu X, Kockumb A F, Miranowicz A, Liu Y X and Nori F 2017 Phys. Rep. 718 1
[26] Xu H K, Song C, Liu W Y, Xue G M, Su F F, Deng H, Tian Y, Zheng D N, Han S, Zhong Y P, Wang H, Liu Y and Zhao S P 2016 Nat. Commun. 7 11018
[27] Zhong Y, Li C, Wang H and Chen Y 2013 Chin. Phys. B 22 110313
[28] Wang H, Mariantoni M, Bialczak R C, Lenander M, Lucero E, Neeley M, O0Connell A D, Sank D, Weides M, Wenner J, Yamamoto T, Yin Y, Zhao J, Martinis John M and Cleland A N 2011 Phys. Rev. Lett. 106 060401
[29] Zheng S B 2002 Phys. Rev. A 66 060303
[30] Zheng S B 2012 Phys. Rev. A 85 022128
[31] Vacanti G, Fazio R, Kim M S, Palma G M, Paternostro M and Vedral V 2012 Phys. Rev. A 85 022129
[32] Cross A W and Gambetta J M 2015 Phys. Rev. A 91 032325
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