Zitterbewegung of Dirac quasiparticles emerged in a Su-Schrieffer–Heeger lattice

doi:10.1088/1674-1056/abb45b

Abstract

We analytically and numerically investigate the dynamical properties of the tilted dispersion relativistic quasiparticles emerged in a cold atomic optical lattice system. By introducing the next nearest neighboring (NNN) hopping term into Su–Schrieffer–Heeger (SSH) model, the Dirac quasiparticles with tilted dispersion relation are realized. The results show that the tilted dispersion causes a drift in relativistic quasiparticles rather than affecting interference behavior between inner states. To be specific, the relativistic phenomena of the quasiparticles induced by the inner state interference (such as Zitterbewegung, Klein paradox, etc.) is completely unaffected by the tilted dispersion. In order to distinguish the drift induced by tilted dispersion and common initial velocity, we calculate the momentum distribution of the relativistic quasiparticles. We obtain the difference between the drift induced by initial velocity and tilted dispersion. The former affects the ZB, while the latter does not. By using this character, we propose a quench dynamics scheme to obtain a stable mono-spin state. The proposed cold atomic lattice system would provide a promising platform in exploring the intrinsic exotic physics of relativistic quasiparticles and the related systems.

Keywords: tilted dispersion wave-packet dynamics quantum quench

Received: 09 June 2020
Revised: 23 July 2020
Accepted manuscript online: 02 September 2020

Fund: the National Key Research and Development Program of China (Grant Nos. 2016YFA0301803 and 2016YFA0302800), the National Natural Science Foundation of China (Grant Nos. 11604103, 11704132, 11822403, and 91636218), the NSAF, China (Grant Nos. U1801661 and U1830111), the PCSIRT, China (Grant No. IRT1243), the Natural Science Foundation of Guangdong Province, China (Grant Nos. 2016A030313436, 2018A030313322, and 2018A0303130066), the KPST of Guangzhou (Grant No. 201804020055), China Postdoctoral Science Foundation (Grant No. 2018M633063), and the Startup Foundation of SCNU.

Corresponding Authors: ^†Corresponding author. E-mail: zhongzeming_scut@163.com ^‡Corresponding author. E-mail: lizhi_nju@163.com

Cite this article:

Yue Hu(胡玥), Zheng-Xin Guo(郭政鑫), Ze-Ming Zhong(钟泽明), and Zhi Li(李志) Zitterbewegung of Dirac quasiparticles emerged in a Su-Schrieffer–Heeger lattice 2020 Chin. Phys. B 29 110302

Fig. 1.

(a) The proposed one-dimensional chain optical lattice scheme and atomic hopping configuration between the different A (or B) sublattice sites. t₁ (t₂) denotes the hopping between sites of the same (different) type atoms, a = 1 is the lattice constant. θ = π/2 is the hopping phase factor. (b) and (c) Dispersion relationship in the condition of Bloch Hamiltonian with v₀ = 0 and v₀ = 1, respectively. (d)–(h) Dispersion relationship with different v₀ in the condition of the low-energy effective Hamiltonian [Eq. (5)].

Fig. 2.

(a)–(e) Numerically calculated probability distributions, |Ψ(x,t)|², with different time. The width of the initial wave packet L = 2, effective mass m = 1, effective light speed v_x = 1.

Fig. 3.

Analytically (lines) and numerically (symbols) calculated ZB effect. The expectation value $\bar{x} (t)$ with different v₀ (m) is shown in (a) [(b)]. The corresponding frequency (c) and amplitude (d) of ZB with different m are provided. Throughout the calculation, the width of the initial wavepacket L = 2 and effective fermi velocity v_x = 1.

Fig. 4.

The expectation value $\bar{x} (t)$ for the cases of (a) v₀ = 0.5 and (b) q₀ = 0.5. The lines (symbols) correspond to the exact solution (numerical results).

Fig. 5.

Momentum distributions of the positive and negative energy parts of the wave packet: (a) v₀ = −0.5, (b) v₀ = 0, (c) v₀ = 0.5 with q₀ = 0; (d) q₀ = −0.5, (e) q₀ = 0, (f) q₀ = 0.5 with v₀ = 0.

Fig. 6.

The relationship of q₀ and v₀ for a stable single pure component wave packet. Insert: Visualized wavepacket for the condition of red star. Through the numerical calculation, the other parameters L = 2, q₀ = 0.5, m = 1, and v_x = 1.

[1]	Schrödinger E 1930 Sizungsber. Preuss. Akad. Wiss. Phys. Math. Kl. 24 418
[2]	Gerritsma R, Kirchmair G, Zähringer F et al. 2010 Nature 463 68 DOI: 10.1038/nature08688
[3]	Barut A O, Bracken A J 1981 Phys. Rev. D 23 2454 DOI: 10.1103/PhysRevD.23.2454
[4]	Schliemann J, Loss D, Westervelt R M 2005 Phys. Rev. Lett. 94 206801 DOI: 10.1103/PhysRevLett.94.206801
[5]	Katsnelson M I 2006 Eur. Phys. J. B 51 157 DOI: 10.1140/epjb/e2006-00203-1
[6]	Zhang X D 2008 Phys. Rev. Lett. 100 113903 DOI: 10.1103/PhysRevLett.100.113903
[7]	Vaishnav J Y, Clark C W 2008 Phys. Rev. Lett. 100 153002 DOI: 10.1103/PhysRevLett.100.153002
[8]	Zawadzki W, Rusin T M 2011 J. Phys.: Condens. Matter 23 143201 DOI: 10.1088/0953-8984/23/14/143201
[9]	Li Z, Wang H Q, Zhang D W, Zhu S L, Xing D Y 2016 Phys. Rev. A 94 043617 DOI: 10.1103/PhysRevA.94.043617
[10]	Huang T Y, Ma T, Wang L 2018 J. Phys.: Condens. Matter 30 245501 DOI: 10.1088/1361-648X/aac23b
[11]	Zhang D W, Zhu Y Q, Zhao Y X, Yan H, Zhu S L 2018 Adv. Phys. 67 253 DOI: 10.1080/00018732.2019.1594094
[12]	Su W P, Schrieffer J R, Heeger A J 1979 Phys. Rev. Lett. 42 1698 DOI: 10.1103/PhysRevLett.42.1698
[13]	Meier E J, An F A, Gadway B 2016 Nat. Commun. 7 13986 DOI: 10.1038/ncomms13986
[14]	Schomerus H 2013 Opt. Lett. 38 1912 DOI: 10.1364/OL.38.001912
[15]	Engelhardt G, Benito M, Platero G, Brandes T 2017 Phys. Rev. Lett. 118 197702 DOI: 10.1103/PhysRevLett.118.197702
[16]	Zhu S L, Wang B G, Duan L M 2007 Phys. Rev. Lett. 98 260402 DOI: 10.1103/PhysRevLett.98.260402
[17]	Zhu S L, Zhang D W, Wang Z D 2009 Phys. Rev. Lett. 102 210403 DOI: 10.1103/PhysRevLett.102.210403
[18]	Zhu S L, Shao L B, Wang Z D, Duan L M 2011 Phys. Rev. Lett. 106 100404 DOI: 10.1103/PhysRevLett.106.100404
[19]	Cooper N R, Dalibard J, Spielman I B 2019 Rev. Mod. Phys. 91 015005 DOI: 10.1103/RevModPhys.91.015005
[20]	Lewenstein M, Sanpera A, Ahufinger V, Damski B, De A S, Sen U 2007 Adv. Phys. 56 243 DOI: 10.1080/00018730701223200
[21]	Dalibard J, Gerbier F, Juzeliūnas G, Öhberg P 2011 Rev. Mod. Phys. 83 1523 DOI: 10.1103/RevModPhys.83.1523
[22]	Goldman N, Juzeliūnas G, Öhberg P, Spielman I B 2014 Rep. Prog. Phys. 77 126401 DOI: 10.1088/0034-4885/77/12/126401
[23]	Islam R, Senko C, Campbell W C et al. 2013 Science 340 583 DOI: 10.1126/science.1232296
[24]	Zhao W L, Gong J B, Wang W G, Casati G, Liu J, Fu L B 2016 Phys. Rev. A 94 053631 DOI: 10.1103/PhysRevA.94.053631
[25]	Dou F Q, Cao H, Liu J, Fu L B 2016 Phys. Rev. A 93 043419 DOI: 10.1103/PhysRevA.93.043419
[26]	Zhao W L, Wang J Z, Xiaohui Wang X H, Tong P Q 2019 Phys. Rev. E 99 042201 DOI: 10.1103/PhysRevE.99.042201
[27]	Li S C, Fu L B, Liu J 2018 Phys. Rev. A 98 013601 DOI: 10.1103/PhysRevA.98.013601
[28]	Dou F Q, Liu J, Fu L B 2018 Phys. Rev. A 98 022102 DOI: 10.1103/PhysRevA.98.022102
[29]	Li Z, Cao H, Fu L B 2015 Phys. Rev. A 91 023623 DOI: 10.1103/PhysRevA.91.023623
[30]	Hu X D, Huang Y L, Shen X, Liao K Y, Li Z 2019 Phys. Lett. A 383 125982 DOI: 10.1016/j.physleta.2019.125982
[31]	Shen X, Li Z 2018 Phys. Rev. A 97 01360 DOI: 10.1103/PhysRevA.97.013608
[32]	Shen X, Wang F D, Li Z, Wu Z G 2019 Phys. Rev. A 100 062514 DOI: 10.1103/PhysRevA.100.062514
[33]	Shen X, Zhang D W, Yan H, Li Z, Zhu S L 2020 Phys. Rev. Research 2 013037 DOI: 10.1103/PhysRevResearch.2.013037
[34]	Thaller B 2004 arXiv quant-ph/0409079

[1]	Entanglement and thermalization in the extended Bose-Hubbard model after a quantum quench: A correlation analysis Xiao-Qiang Su(苏晓强), Zong-Ju Xu(许宗菊), and You-Quan Zhao(赵有权). Chin. Phys. B, 2023, 32(2): 020506.
[2]	Quantum quenches in the Dicke model: Thermalization and failure of the generalized Gibbs ensemble Xiao-Qiang Su(苏晓强) and You-Quan Zhao(赵有权). Chin. Phys. B, 2020, 29(12): 120506.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Zitterbewegung of Dirac quasiparticles emerged in a Su-Schrieffer–Heeger lattice

Cite this article:

Online attention