Decay of superfluid currents in the interacting one-dimensional Bose gas

We examine the superfluid properties of a one-dimensional (1D) Bose gas in a ring trap based on the model of Lieb and Liniger. While the 1D Bose gas has nonclassical rotational inertia and exhibits quantization of velocities, the metastability of currents depends sensitively on the strength of interactions in the gas: the stronger the interactions, the faster the current decays. It is shown that the Landau critical velocity is zero in the thermodynamic limit due to the first supercurrent state, which has zero energy and finite probability of excitation. We calculate the energy dissipation rate of ring currents in the presence of weak defects, which should be observable on experimental time scales.

Figure 1

(Color online) The dimensionless drag force versus the velocity (relative to $v_{\text{F}}=\hslash \pi n/m$) of the impurity at various values of the coupling parameter. The solid (blue) lines represent the force obtained with Eqs. (1, 4); open circles are the numerical data obtained using ABACUS [18].

Figure 2

(Color online) Schematic of the excitation spectrum of the 1D Bose gas in a perfectly isotropic ring. The supercurrent states $I$ lie on the parabola ${\hslash }^2{k}^2/\left(2Nm\right)$ (dotted line). Excitations occur in the shaded area; the discrete structure of the spectrum is not shown for simplicity. The blue (dark) area represents particle-hole excitations [21]. Motion of the impurity with respect to the gas causes transitions from the ground state to the states lying on the straight (red) line.

Figure 3

(Color online) Dynamic structure factor of the 1D Bose gas from [18] for $N=100$. Dimensionless values of $S\left(k,\omega \right){\epsilon }_{\text{F}}/N$ are shown in shades of gray between 0 (white) and 0.7 (black). The full (blue) lines represent the limiting dispersion relations ${\omega }_{\pm }$ and the straight (red) line is the line of integration in Eq. (1). Only one point at $k=k_G$, shown in full (red) circle, contributes to the integral when the perturber is a shallow cosine potential with a reciprocal vector $k_G$.

Figure 4

(Color online) Decay of the ring current velocity of 1D bosons from the initial velocity of $1.1v_{\text{F}}$ at $t=0$. The solid (blue) and dashed (red) lines represent the results obtained with the approximate formula and ABACUS, respectively. The time scale is $\tau =N\pi {\hslash }^3/\left(2m{g}_{\text{i}}^2\right)$.