  We study the driven tunneling of a one-dimensional charged particle confined
to a rectangular double-well. The numerical simulation of the Schr\"odinger
equation based on the Cranck-Nicholson finite-difference scheme, shows that the
modulation of the amplitude of the external field may result in the parametric
resonance. The latter is accompanied by the breakdown of the quasi-periodic
motion characteristic of the usual driven tunneling, and the emergence of an
irregular dynamics. We describe the above breakdown with the occupation
probability for the ground state of the unperturbed system, and make the
visualization of the irregular dynamics with the help of Shaw-Takens'
reconstruction of the state-space. Both approaches agree as to the values of
the resonant frequency for the parametric excitation. Our results indicate that
the shape of the laser pulse could be essential for generating chaotic
tunneling.
