Probing superfluidity of a mesoscopic Tonks-Girardeau gas

TL;DR

This paper investigates superfluid-like behavior in a mesoscopic Tonks-Girardeau gas on a ring by analyzing its response to a moving barrier, revealing a velocity threshold for current generation indicative of superfluidity.

Contribution

It provides an exact solution for the dynamical response of a mesoscopic Tonks-Girardeau gas to a moving barrier, demonstrating superfluid-like behavior with a velocity threshold.

Findings

Zero current for velocities below critical velocity $v_c$

Nonzero drag force near $v_c$

Superfluid-like response in mesoscopic regime

Abstract

We study the dynamical response of a Tonks-Girardeau gas on a ring induced by a moving delta-barrier potential. An exact solution based on the time-dependent Bose-Fermi mapping allows to obtain the particle current, its fluctuations and the drag force acting on the barrier. The exact solution is analyzed numerically as well as analytically in the perturbative regime of weak barrier strength. In the weak barrier limit the stirring drives the system into a state with net zero current for velocities $v$ smaller than $v_c=\pi\hbar /mL$, with $m$ the atomic mass and $L$ the ring circumference. At $v$ approaching $v_c$ angular momentum can be transferred to the fluid and a nonzero drag force arises. The existence of a velocity threshold for current generation indicates superfluid-like behavior of the mesoscopic Tonks-Girardeau gas, different from the non-superfluid behavior predicted for Tonks-Girardeau gas in an infinite tube.