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note
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The observed shift of the quadrupole mode frequency cannot be attributed to the heating the condensate is suffering during the excitation procedure of this mode. As a matter of fact, the timing for the experiments at various lattice depths differs only by 150 ms, so that the temperature does not vary significantly as we change the lattice potential. In the case of the dipole mode, the excitation is created by suddenly displacing the minimum of the magnetic field, and the evolution of the center of mass position is followed for 200 ms during which the oscillation is undamped in all the series of data we are discussing in this work.
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(private communication)
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