Frequency beating and damping of breathing oscillations of a harmonically trapped one-dimensional quasicondensate

We study the breathing (monopole) oscillations and their damping in a harmonically trapped one-dimensional (1D) Bose gas in the quasicondensate regime using a finite-temperature classical field approach. By characterizing the oscillations via the dynamics of the density profile's rms width over long time, we find that the rms width displays beating of two distinct frequencies. This means that 1D Bose gas oscillates not at a single breathing mode frequency, as found in previous studies, but as a superposition of two distinct breathing modes, one oscillating at frequency close to $\sim\!\sqrt{3}\omega$ and the other at $\sim\!2\omega$, where $\omega$ is the trap frequency. The breathing mode at $\sim\!\sqrt{3}\omega$ dominates the beating at lower temperatures, deep in the quasicondensate regime, and can be attributed to the oscillations of the bulk of the density distribution comprized of particles populating low-lying, highly-occupied states. The breathing mode at $\sim\!2\omega$, on the other hand, dominates the beating at higher temperatures, close to the nearly ideal Bose gas regime, and is attributed to the oscillations of the tails of the density distribution comprized of thermal particles in higher energy states. The two breathing modes have distinct damping rates, with the damping rate of the bulk component being an order of magnitude larger than that of the tails component, and at least 2--3 times smaller than the damping rate predicted by Landau's theory of damping in 1D.Comment: 11 pages, 8 figure