Magnetic field control of the Franck-Condon coupling of few-electron quantum states

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 sidebands in transport spectroscopy. We present data on such sidebands 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 parameter, different for different electronic base states and indicating a valley dependence. Reshaping of the electronic wave function by the magnetic field is discussed as a possible cause of our observations; its impact is demonstrated in a model calculation reproducing the field-dependent coupling.