Research ArticlePHYSICS

Energy redistribution and spatiotemporal evolution of correlations after a sudden quench of the Bose-Hubbard model

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Science Advances  30 Sep 2020:
Vol. 6, no. 40, eaba9255
DOI: 10.1126/sciadv.aba9255
  • Fig. 1 Energy redistribution after the quench in 1D.

    The kinetic-energy term (red), the onsite interaction energy term (blue), and the sum of them (green) are shown as functions of the hold time t after a rapid quench into a Mott insulator region with U/J = 6.8 in 1D optical lattice tubes. The solid lines show the results of the numerical calculation at zero temperature with the MPS method using the time-dependent variational principle and local density approximation. The error bars for the kinetic-energy and onsite interaction energy terms denote the SE of 15 independent measurements.

  • Fig. 2 Spatiotemporal evolution of the single-particle correlation after the quench in 1D.

    (A and B) The single-particle correlations for the distance in the unit of the lattice constant Δ up to 4 are shown as functions of the hold time t. Note that the displayed correlations are normalized by the maximum value of the correlation Cmax,Δ(1D) during 0 < t < 1.6ℏ/J for each distance Δ; (A) experiment and (B) numerical calculation. (C to F) Time evolution of the single-particle correlation KΔ after the quench. Solid blue lines show the results of numerical calculation. (C) Δ = 1, (D) Δ = 2, (E) Δ = 3, and (F) Δ = 4. The error bars denote the SE of five independent measurements. (G) Time of the first peak of the single-particle correlation is plotted as a function of the distance Δ. A fit with a linear function with a nonzero offset is shown as a solid line. The error bars denote the SE of five independent measurements.

  • Fig. 3 Energy redistribution after the quench in 3D.

    The kinetic-energy term (red), the onsite interaction energy term (blue), and the sum of them (green) are shown as functions of the hold time t after a rapid quench into a superfluid region with U/J = 3.4 in a 3D optical lattice. The solid lines show the results of the numerical calculation obtained using the TWA (29). The error bars for the kinetic-energy (onsite-interaction energy) terms denote the SE of 15 (3) independent measurements.

  • Fig. 4 Spatiotemporal evolution of the single-particle correlation after the quench in 2D.

    (A to D) 2D plots of the single-particle correlation as functions of the distances Δx and Δy for several hold times of tJ/ℏ = 0 (A), 0.12 (B), 0.23 (C), and 0.35 (D). Data with Δx2+Δy24 are shown. Note that the displayed correlations are normalized by the maximum value of the correlation Cmax,Δ(2D) during 0 < t < 1.0ℏ/J for each distance (Δx, Δy). (E to G) Time evolution of the single-particle correlation KΔ after the quench for (Δx, Δy) = (1,0) [(E), red square], (2,0) [(E), green circle], (3,0) [(E), yellow diamond], (0,1) [(F), red square], (0,2) [(F), green circle], (0,3) [(F), yellow diamond], (1,1) [(G), green circle], and (2,2) [(G), yellow diamond]. The solid lines are the numerical results obtained using the TWA method. The error bars denote the SE of 15 independent measurements. (H and I) Time at the first peak (H) or the first trough (I) of the single-particle correlation as a function of the Euclidean distance Δ=Δx2+Δy2. A fit with a linear function with a nonzero offset is shown as a solid line both in (H) and (I). The first peak and trough are obtained by fitting the experimental data with the empirical function described in section S6. The error bars denote the fitting errors.

Supplementary Materials

  • Supplementary Materials

    Energy redistribution and spatiotemporal evolution of correlations after a sudden quench of the Bose-Hubbard model

    Yosuke Takasu, Tomoya Yagami, Hiroto Asaka, Yoshiaki Fukushima, Kazuma Nagao, Shimpei Goto, Ippei Danshita, Yoshiro Takahashi

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    This PDF file includes:

    • Sections S1 to S6
    • Figs. S1 to S7
    • Table S1
    • References

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