Lie transformation on shortcut to adiabaticity in parametric driving quantum systems

doi:10.1088/1674-1056/abd747

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.

Keywords: shortcut to adiabaticity parametric driving Lewis-Riesenfeld invariants

Received: 10 October 2020
Revised: 28 November 2020
Accepted manuscript online: 30 December 2020

PACS:	03.65.Xp	(Tunneling, traversal time, quantum Zeno dynamics)
	03.65.Fd	(Algebraic methods)
	42.50.Dv	(Quantum state engineering and measurements)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11447025 and 11847308).

Corresponding Authors: Lin Zhang
E-mail: zhanglincn@snnu.edu.cn

Cite this article:

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 2021 Chin. Phys. B 30 060302

[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

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