We study experimentally the line of a single quantized vortex in a rotating prolate Bose-Einstein condensate of Rb atoms confined by a harmonic potential. Exciting the two transverse quadrupole modes of the single vortex condensate, we show that the counterrotating mode is more strongly damped than in the absence of a vortex, whereas the corotating mode is not affected appreciably by the vortex. We interpret this result as a decay of the counterrotating quadrupole mode into two excitations of the vortex line, the so-called Kelvin modes. This is supported by direct observation of the vortex line.
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