  The pulse-train technique within ultrafast pump-probe spectroscopy is
theoretically investigated to enhance a specific coherent phonon mode while
suppressing the other phonon modes generated in single wall carbon nanotubes
(SWNTs). In particular, we focus on the selectivity of the radial breathing
mode (RBM) and the G-band for a given SWNT. We find that if the repetition
period of the pulse train matches with integer multiple of the RBM phonon
period, the RBM amplitude could be kept while the amplitudes of the other modes
are suppressed. As for the G-band, when we apply a repetition period of
half-integer multiple of the RBM period, the RBM could be suppressed because of
destructive interference, while the G-band still survives. It is also possible
to keep the G-band and suppress the RBM by applying a repetition period that
matches with integer multiple of the G-band phonon period. However, in this
case we have to use a large number of laser pulses having a property of "magic
ratio" of the G-band and RBM periods.
