Lie transformation on shortcut to adiabaticity in parametric driving quantum systems

doi:10.1088/1674-1056/abd747

中国物理B ›› 2021, Vol. 30 ›› Issue (6): 60302-060302.doi: 10.1088/1674-1056/abd747

Lie transformation on shortcut to adiabaticity in parametric driving quantum systems

Jian-Jian Cheng(程剑剑), Yao Du(杜瑶), and Lin Zhang(张林)^†

School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710119, China

收稿日期:2020-10-10 修回日期:2020-11-28 接受日期:2020-12-30 出版日期:2021-05-18 发布日期:2021-05-18
通讯作者: Lin Zhang E-mail:zhanglincn@snnu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11447025 and 11847308).

Lie transformation on shortcut to adiabaticity in parametric driving quantum systems

Jian-Jian Cheng(程剑剑), Yao Du(杜瑶), and Lin Zhang(张林)^†

School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710119, China

Received:2020-10-10 Revised:2020-11-28 Accepted:2020-12-30 Online:2021-05-18 Published:2021-05-18
Contact: Lin Zhang E-mail:zhanglincn@snnu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11447025 and 11847308).

摘要/Abstract

摘要： Shortcut to adiabaticity (STA) is a speedway to produce the same final state that would result in an adiabatic, infinitely slow process. Two typical techniques to engineer STA are developed by either introducing auxiliary counterdiabatic fields or finding new Hamiltonians that own dynamical invariants to constraint the system into the adiabatic paths. In this paper, an efficient method is introduced to naturally cover the above two techniques with a unified Lie algebraic framework and neatly remove the design difficulties and loose assumptions in the two techniques. A general STA scheme for different potential expansions concisely achieves with the aid of squeezing transformations.

关键词: shortcut to adiabaticity, parametric driving, Lewis-Riesenfeld invariants

Abstract: Shortcut to adiabaticity (STA) is a speedway to produce the same final state that would result in an adiabatic, infinitely slow process. Two typical techniques to engineer STA are developed by either introducing auxiliary counterdiabatic fields or finding new Hamiltonians that own dynamical invariants to constraint the system into the adiabatic paths. In this paper, an efficient method is introduced to naturally cover the above two techniques with a unified Lie algebraic framework and neatly remove the design difficulties and loose assumptions in the two techniques. A general STA scheme for different potential expansions concisely achieves with the aid of squeezing transformations.

Key words: shortcut to adiabaticity, parametric driving, Lewis-Riesenfeld invariants

中图分类号: (Tunneling, traversal time, quantum Zeno dynamics)

03.65.Xp

03.65.Fd (Algebraic methods) 42.50.Dv (Quantum state engineering and measurements)

Jian-Jian Cheng(程剑剑), Yao Du(杜瑶), and Lin Zhang(张林). Lie transformation on shortcut to adiabaticity in parametric driving quantum systems[J]. 中国物理B, 2021, 30(6): 60302-060302.

Jian-Jian Cheng(程剑剑), Yao Du(杜瑶), and Lin Zhang(张林). Lie transformation on shortcut to adiabaticity in parametric driving quantum systems[J]. Chin. Phys. B, 2021, 30(6): 60302-060302.

参考文献

[1] Farhi E, Goldstone J, Gutmann S, Lapan J, Lundgren A and Preda D 2001 Science 292 472
[2] Guéry-Odelin D, Ruschhaupt A, Kiely A, Torrontegui E, Martínez-Garaot S and Muga J G 2019 Rev. Mod. Phys. 91 045001
[3] del Campo A and Kim K 2019 New J. Phys. 21 050201
[4] Masuda S and Nakamura K 2009 Proc. R. Soc. A 466 1135
[5] Martinez-Garaot S, Torrontegui E, Chen X and Muga J G 2014 Phys. Rev. A 89 053408
[6] Palmero M, Torrontegui E, Guéry-Odelin D and Muga J G 2013 Phys. Rev. A 88 053423
[7] Torrontegui E, Ibanez S, Chen X, Ruschhaupt A, Guéry-Odelin D and Muga J G 2011 Phys. Rev. A 83 013415
[8] Masuda S and Nakamura K 2011 Phys. Rev. A 84 043434
[9] Berry M V 2009 J. Phys. A: Math. Theor. 42 365303
[10] Torrontegui E, Martínez-Garaot S, Ruschhaupt A and Muga J G 2012 Phys. Rev. A 86 013601
[11] Chen X, Ruschhaupt A, Schmidt S, del Campo A, Guéry-Odelin D and Muga J G 2010 Phys. Rev. Lett. 104 063002
[12] Chen X, Torrontegui E and Muga J G 2011 Phys. Rev. A 83 062116
[13] Assis P E G and Fring A 2009 J. Phys. A: Math. Theor. 42 015203
[14] Zhang L and Zhang W 2016 Ann. Phys. 373 424
[15] Stefanatos D, Ruths J and Li J S 2010 Phys. Rev. A 82 063422
[16] Muga J G, Chen X, Ibáñez S, Lizuain I and Ruschhaupt A 2010 J. Phys. B: Atom. Mol. Opt. Phys. 43 085509
[17] Ibáñez S, Chen X, Torrontegui E, Muga J G and Ruschhaupt A 2012 Phys. Rev. Lett. 109 100403
[18] Torrontegui E, Martínez-Garaot S and Muga J G 2014 Phys. Rev. A 89 043408
[19] Deffner S, Jarzynski C and del Campo A 2014 Phys. Rev. X 4 021013
[20] del Campo A and Boshier M G 2012 Sci. Rep. 2 648
[21] Nakamura K, Avazbaev S K, Sobirov Z A, Matrasulov D U and Monnai T 2011 Phys. Rev. E 83 041133
[22] Berry M V and Klein G 1984 J. Phys. A: Math. Theor. 17 1805
[23] Landau L D and Lifshitz E M 1960 Mechanics (Oxford: Pergamon Press) Sec. 10
[24] del Campo A 2011 Europhys. Lett. 96 60005
[25] Tobalina A, Lizuain I and Muga J G 2019 Europhys. Lett. 127 20005

Lie transformation on shortcut to adiabaticity in parametric driving quantum systems

Lie transformation on shortcut to adiabaticity in parametric driving quantum systems

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 2

Metrics

本文评价

推荐阅读 0

[1]	Xin-Ping Dong(董新平), Zhi-Bo Feng(冯志波), Xiao-Jing Lu(路晓静), Ming Li(李明), and Zheng-Yin Zhao(赵正印). Fast population transfer with a superconducting qutrit via non-Hermitian shortcut to adiabaticity[J]. 中国物理B, 2023, 32(3): 34201-034201.
[2]	张林, 刘军鹏. The upper bound function of nonadiabatic dynamics in parametric driving quantum systems[J]. 中国物理B, 2019, 28(8): 80301-080301.