The transverse breathing mode of an elongated Bose-Einstein condensate

We study experimentally the transverse monopole mode of an elongated rubidium condensate. Due to the scaling invariance of the non-linear Schr"odinger (Gross-Pitaevski) equation, the oscillation is monochromatic and sinusoidal at short times, even under strong excitation. For ultra-low temperatures, the quality factor $Q={\omega }_0\mathrm{/}{\gamma }_0$ can exceed 2000, where ${\omega }_0$ and ${\gamma }_0$ are the mode angular frequency and damping rate. This value is much larger than any previously reported for other eigenmodes of a condensate. We also present the temperature variation of ${\omega }_0$ and ${\gamma }_0$.