Heavily Damped Motion of One-Dimensional Bose Gases in an Optical Lattice

We study the dynamics of strongly correlated one-dimensional Bose gases in a combined harmonic and optical lattice potential subjected to sudden displacement of the confining potential. Using the time-evolving block decimation method, we perform a first-principles quantum many-body simulation of the experiment of Fertig et al. [Phys. Rev. Lett. 94, 120403 (2005)] across different values of the lattice depth ranging from the superfluid to the Mott insulator regimes. We find good quantitative agreement with this experiment: the damping of the dipole oscillations is significant even for shallow lattices, and the motion becomes overdamped with increasing lattice depth as observed. We show that the transition to overdamping is attributed to the decay of superfluid flow accelerated by quantum fluctuations, which occurs well before the emergence of Mott insulator domains.

Figure 1

Results at four values of $V_0/E_{\mathrm{R}}$: 2 (a) and (e), 3 (b) and (f), 4 (c) and (g), and 8 (d) and (h). In the left four figures, we show the local densities $n_j\equiv ⟨{\widehat{n}}_j⟩$ (squares) and fluctuations ${\sigma }_j$ (triangles) of the ground states. The dashed lines in (c) and (d) represent the fluctuations for the unit-filling in the homogeneous Bose-Hubbard system, calculated with the use of the infinite-size version of the TEBD [27]. In the right four figures, we show the time evolution of the c.m. position $x_{\mathrm{c}.\mathrm{m}.}(t)$ for a small displacement $x_0=d$. In (f), ${\dot{x}}_{\mathrm{c}.\mathrm{m}.}(t)$ is also plotted by a dotted line.

Figure 2

Damping rate $b/b_0$ versus $V_0/E_{\mathrm{R}}$ for $x_0=d$ (diamonds) and $x_0=8d$ (squares). The triangles are the experimental results of Ref. 7.

Figure 3

Maximum c.m. velocities ${\overline{v}}_{\mathrm{cm}}^{\max }\equiv |B_1|$ (a) and damping rates $b/b_0$ (b) for $V_0/E_{\mathrm{R}}=2$ (triangles), 3 (diamonds), and 4 (squares) as functions of $x_0/d$.

Figure 4

(a) Time evolution of the noncondensate fraction ${\overline{n}}_{\mathrm{non}}(t)$ at $V_0=2E_{\mathrm{R}}$ for different values of the displacement. (b) Time evolution of $d{\overline{n}}_{\mathrm{non}}/dt$ (solid line) and ${\overline{v}}_{\mathrm{c}.\mathrm{m}.}$ (dashed line) for $V_0=2E_{\mathrm{R}}$ and $x_0=8d$.

Figure 5

Maximum growth rates $d{\widehat{n}}_{\mathrm{non}}/dt{|}_{\max }$ of the noncondensate fraction for $V_0/E_{\mathrm{R}}=2$ (triangles), 3 (diamonds), and 4 (squares) as functions of ${\overline{v}}_{\mathrm{c}.\mathrm{m}.}^{\max }$.