  We describe a possibility of creating non-stationary electron wave packets in
zigzag carbon nanotubes (CNT) illuminated by short laser pulses. After
disappearance of the pulse the packet experiences the trembling motion
(Zitterbewegung, ZB). The band structure of CNT is calculated using the
tight-binding approximation generalized for the presence of radiation.
Employing realistic pulse and CNT parameters we obtain the ZB oscillations with
inter-band frequencies corresponding to specific pairs of energy bands. A
choice of optimal parameters is presented in order to observe the phenomenon of
ZB experimentally. The use of Gaussian wave packets to trigger the electron
Zitterbewegung, as used in the literature, is critically reexamined.
