Abstract
Recent experimental studies have demonstrated the simulation of Dirac equation using the discrete-time quantum walks. In this work, we add the oscillator potential and consider the simulation of a one-dimensional Dirac oscillator. Based on the coin operator, we run the quantum walk simulation and consider the effects of oscillator parameters, initial phase shifts, and masses. Compared to the Dirac equation, the probability distribution of a Dirac oscillator becomes more classical. Additionally, we find the probability distribution jumps between two spin states by changing the initial phase shift, and attribute this to the coherent nature of the two spin states. These results are hopefully to be realized in trapped-ion experiments.
Similar content being viewed by others
References
S.E. Venegas-Andraca, Quantum Inf. Process 11, 1015 (2012)
R.P. Feynman, A.R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965)
D. Bouwmeester, I. Marzoli, G.P. Karman, W. Schleich, J.P. Woerdman, Phys. Rev. A 61, 013410 (1999)
C.A. Ryan, M. Laforest, J.C. Boileau, R. Laflamme, Phys. Rev. A 72, 062317 (2005)
M. Karski, L. Förster, J. Choi, A. Steffen, W. Alt, D. Meschede, A. Widera, Science 325, 174 (2009)
H. Schmitz, R. Matjeschk, C. Schneider, J. Glueckert, M. Enderlein, T. Huber, T. Schaetz, Phys. Rev. Lett. 103, 090504 (2009)
A. Schreiber, K.N. Cassemiro, V. Potoček, A. Gábris, P.J. Mosley, E. Andersson, I. Jex, C. Silberhorn, Phys. Rev. Lett. 104, 050502 (2010)
F.W. Strauch, Phys. Rev. A 73, 054302 (2006)
A.J. Bracken, D. Ellinas, I. Smyrnakis, Phys. Rev. A 75, 022322 (2007)
C.M. Chandrashekar, R. Srikanth, R. Laflamme, Phys. Rev. A 77, 032326 (2008)
C.M. Chandrashekar, S. Banerjee, R. Srikanth, Phys. Rev. A 81, 062340 (2010)
Y. Shikano, Interdisciplinary. Inf. Sci. 23, 33 (2017)
F. Zähringer, G. Kirchmair, R. Gerritsma, E. Solano, R. Blatt, C.F. Roos, Phys. Rev. Lett. 104, 100503 (2010)
R. Gerritsma, G. Kirchmair, F. Zähringer, E. Solano, R. Blatt, C.F. Roos, Nature 463, 68 (2010)
D. Ito, K. Mori, E. Carriere, Nuovo Cimento A 51, 1119 (1967)
P.A. Cook, Lett. Nuovo Cimento 1, 419 (1971)
M. Moshinsky, A. Szczepaniak, J. Phys. A Math. Gen. 22, L817 (1989)
M. Moshinsky, Y.F. Simon, The Harmonic Oscillator in Modern Physics (Harwood Academic, Amsterdam, 1996)
E. Sadurni, A.I.P. Conf, Proc. 1334, 249 (2011)
N. Ferkous, A. Bounames, Phys. Lett. A 325, 21 (2004)
S. Longhi, Opt. Lett. 35, 1302 (2010)
N. Nayak, A. Vishwanath, arXiv: quant-ph/0010117
N.B. Lovett, S. Cooper, M. Everitt, M. Trevers, V. Kendon, Phys. Rev. A 81, 042330 (2010)
X. Zhan, L. Xiao, Z. Bian, K. Wang, X. Qiu, B.C. Sanders, W. Yi, P. Xue, Phys. Rev. Lett. 119, 130501 (2017)
V.V. Ramasesh, E. Flurin, M. Rudner, I. Siddiqi, N.Y. Yao, Phys. Rev. Lett. 118, 130501 (2017)
E. Flurin, V.V. Ramasesh, S. Hacohen-Gourgy, L.S. Martin, N.Y. Yao, I. Siddiqi, Phys. Rev. X 7, 031023 (2017)
S. Barkhofen, T. Nitsche, F. Elster, L. Lorz, A. Gábris, I. Jex, C. Silberhorn, Phys. Rev. A 96, 033846 (2017)
L. Innocenti, H. Majury, T. Giordani, N. Spagnolo, F. Sciarrino, M. Paternostro, A. Ferraro, Phys. Rev. A 96, 062326 (2017)
T. Giordani, E. Polino, S. Emiliani, A. Suprano, L. Innocenti, H. Majury, L. Marrucci, M. Paternostro, A. Ferraro, N. Spagnolo, F. Sciarrino, Phys. Rev. Lett. 122, 020503 (2019)
J.P. Keating, N. Linden, J.C.F. Matthews, A. Winter, Phys. Rev. A 76, 012315 (2007)
Y. Shang, Y. Wang, M. Li, R. Lu, EuroPhys. Lett. 124, 60009 (2018)
Y. Yang, J. Yang, Y. Zhou, W. Shi, X. Chen, J. Li, H. Zuo, Sci. China Inf. Sci. 61, 042501 (2018)
S. Srikara, C.M. Chandrashekar, Quantum Inf. Process 19, 295 (2020)
E. Schrödinger, Sitz. Preuss. Akad. Wiss. Phys. Math. Kl 24, 418 (1930)
G.H. Low, T.J. Yoder, I.L. Chuang, Phys. Rev. Lett. 114, 100801 (2015)
A. Abragam, The Principles of Nuclear Magnetism (Oxford University, Oxford, 1961)
A.B. Bardon, S. Beattie, C. Luciuk, W. Cairncross, D. Fine, N.S. Cheng, G.J.A. Edge, E. Taylor, S. Zhang, S. Trotzky, J.H. Thywissen, Science 344, 722 (2014)
J. Xu, Q. Gu, E.J. Mueller, Phys. Rev. A 91, 043613 (2015)
M. Moshinsky, G. Loyola, A. Szczepaniak, C. Villegas, N. Aquino, The Dirac oscillator and its contribution to the baryon mass formula, in Relativistic Aspects of Nuclear Physics (World Scientific Press, Singapore, 1990), p. 271
J. Yang, J. Piekarewicz, Phys. Rev. C 102, 054308 (2020)
Acknowledgements
This research is supported by Fundamental Research Funds for the Central Universities (No. FRF-TP-19-013A3).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Jia, S., Jia, D., Song, Z. et al. Discrete-Time Quantum Walks of the One-Dimensional Dirac Oscillator. J Low Temp Phys 209, 44–53 (2022). https://doi.org/10.1007/s10909-022-02804-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10909-022-02804-x