Chaotic Tunneling in a Laser Field

We study the driven tunneling of a one-dimensional charged particle confined to a rectangular double-well. The numerical simulation of the Schrödinger 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.