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Floquet band engineering with Bloch oscillations

Xi Liu, Senmao Tan, Qing-hai Wang, Longwen Zhou, and Jiangbin Gong
Phys. Rev. B 106, 224309 – Published 22 December 2022
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  • INTRODUCTION
  • THEORY
  • CONTINUOUSLY DRIVEN AAH MODEL WITH ONE…
  • CONTINUOUSLY DRIVEN AAH MODEL WITH TWO…
  • DISCUSSION AND SUMMARY
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    This work provides a convenient and powerful means towards the engineering of Floquet bands via Bloch oscillations, by adding a tilted linear potential to periodically driven lattice systems. The added linear field not only restricts the spreading of a time-evolving wave packet but also, depending on the ratio between the Bloch oscillation frequency and the modulation frequency of the periodic driving, dramatically modifies the band profile and topology. Specifically, we consider a driven Aubry-André-Harper model as a working example, in the presence of a linear field. Almost flat Floquet bands or Floquet bands with large Chern numbers due to the interplay between the periodic driving and Bloch oscillations can be obtained, with the band structure and topology extensively tunable by adjusting the ratio of two competing frequencies. To confirm our finding, we further execute the Thouless pumping of one and two interacting bosons in such a lattice system and establish its connection with the topological properties of single- and two-particle Floquet bands.

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    • Received 18 August 2022
    • Revised 30 October 2022
    • Accepted 14 December 2022

    DOI:https://doi.org/10.1103/PhysRevB.106.224309

    ©2022 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Quantum engineeringQuantum transportTopological insulatorsTopological phases of matter
    1. Physical Systems
    Floquet systems
    1. Techniques
    Adiabatic approximation
    Atomic, Molecular & OpticalCondensed Matter, Materials & Applied PhysicsStatistical Physics & Thermodynamics

    Authors & Affiliations

    Xi Liu1, Senmao Tan2, Qing-hai Wang2, Longwen Zhou3,*, and Jiangbin Gong2,4,†

    • 1NUS Graduate School-Integrative Sciences and Engineering Programme (ISEP), National University of Singapore, Singapore 119077, Singapore
    • 2Department of Physics, National University of Singapore, Singapore 117551, Singapore
    • 3College of Physics and Optoelectronic Engineering, Ocean University of China, Qingdao 266100, China
    • 4Center for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore

    • *zhoulw13@u.nus.edu
    • †phygj@nus.edu.sg

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    Issue

    Vol. 106, Iss. 22 — 1 December 2022

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    Images

    • Figure 1
      Figure 1

      Floquet spectrum under the PBC, the pumping of Wannier and Gaussian initial states in real space for T1=2, a=3, and b=1. (a) The three quasienergy bands with Chern numbers −2, 4, −2. (b) Pumping of Wannier states prepared in the three Floquet bands over an adiabatic cycle (t=2000T). (c) Pumping of Gaussian states initialized in the three Floquet bands over an adiabatic cycle (t=2000T). For each Wannier or Gaussian initial state, the shift of wave-packet center over an adiabatic cycle yields the Chern number of the corresponding Floquet band.

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    • Figure 2
      Figure 2

      Floquet spectrum under the PBC, pumping of Wannier states, and Floquet spectrum under the OBC for (T1=4,ωF=0) in (a)–(c) and T1/T2=(25,52) in (d)–(i). The legends in (a), (d), and (g) include the Chern numbers of three Floquet bands.

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    • Figure 3
      Figure 3

      Floquet spectrum under the PBC and adiabatic pumping of two interacting bosons. The driving period T1=2 and interaction strength U=20 are chosen for all panels. (a) Two-particle quasienergy spectrum for T1/T2=32 along ϕ=0. (b) Pumping of a Wannier initial state for T1/T2=32. (c) Pumping of a Gaussian initial state for T1/T2=32. (d) Quasienergy spectrum for ωF=0 along ϕ=0. (e) Pumping of two Wannier initial states for ωF=0.

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    • Figure 4
      Figure 4

      Floquet spectrum under the PBC along ϕ=0 in (a), (d), (g), (j), pumping of Wannier states in (b), (e), (h), (k), and Floquet spectrum under the OBC in (c), (f), (i), (l) for the interaction strengths U=2,10 and the driving period ratios T1/T2=11,12.

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    • Figure 5
      Figure 5

      Time evolution of the single-particle density distribution in momentum space. The chosen parameters are T=T1=2, T2=0.5, and J=V=2.5.

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    • Figure 6
      Figure 6

      Floquet bands under the PBC, pumping of Wannier states, and Floquet bands under the OBC for the single-particle case with T1=4 and T1/T2=57 [in (a), (b), (c)], 710 [in (d), (e), (f)], 811 [in (g), (h), (i)], respectively. The legends in (a), (d), and (g) include the Chern numbers of the three Floquet bands.

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