  Suspended carbon nanotubes display at cryogenic temperatures a distinct
interaction between the quantized longitudinal vibration of the macromolecule
and its embedded quantum dot, visible via Franck-Condon conductance side bands
in transport spectroscopy. We present data on such side bands at known absolute
number N=1 and N=2 of conduction band electrons and consequently well-defined
electronic ground and excited states in a clean nanotube device. The
interaction evolves only at a finite axial magnetic field and displays a
distinct magnetic field dependence of the Franck-Condon coupling, different for
different electronic base states and indicating a valley-dependent
electron-vibron coupling. A tentative cause of these effects, reshaping of the
electronic wavefunction by the magnetic field, is discussed and demonstrated in
a model.
