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

We examine the superfluid properties of a 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.

💡 Research Summary

In this paper the authors investigate the superfluid properties of a one‑dimensional (1D) Bose gas confined in a ring geometry, using the exactly solvable Lieb‑Liniger model. The study begins by establishing that, despite the reduced dimensionality, the 1D Bose gas exhibits non‑classical rotational inertia (NCRI) and quantized circulation, hallmarks of superfluidity that have been observed in higher‑dimensional systems. By imposing periodic boundary conditions on the Lieb‑Liniger Hamiltonian, the authors compute the superfluid fraction ρs/ρ as a function of the dimensionless interaction strength γ = g/(nħ²). For weak interactions (γ ≪ 1) the superfluid fraction approaches unity, whereas for stronger interactions it diminishes, yet remains finite, confirming that a 1D gas can sustain a superfluid component.

The central focus of the work is the metastability of persistent currents (states with winding number w ≠ 0). Using the Bethe‑Ansatz solution, the energy spectrum of the winding‑number states is obtained. The energy gap ΔE between the ground state (w = 0) and the first supercurrent state (w = 1) scales as ΔE ≈ (ħ²/2mR²) w² f(γ), where f(γ) decreases rapidly with increasing γ. Consequently, in the weak‑interaction regime the gap is sizable, providing a robust barrier against decay. In the opposite, strong‑interaction regime the gap collapses toward zero, and the first supercurrent becomes an effectively zero‑energy excitation. This leads to a striking conclusion: in the thermodynamic limit (R → ∞) the Landau critical velocity v_c = min