Nonlinear dynamics and quasibound state formation in a driven Gaussian potential

We examine the classical and quantum dynamics of an electron in an anharmonic atomic potential well in the presence of monochromatic laser radiation. The atomic potential is modeled by the inverted Gaussian potential. The radiation induces nonlinear resonances and chaos in the electron phase space. As the laser amplitude increases, regions of chaos grow and a pitchfork bifurcation of a key electron periodic orbit occurs leading to the appearance of three dominant periodic orbits which move apart with increasing laser amplitude. Electron quasibound states in the quantum system are found using complex coordinate scaling and Floquet theory. We show that the bifurcation of periodic orbits in the classical phase space is a precursor to the creation of a new quasibound state in the quantum system. As we increase the laser amplitude, the residues of the quasibound states become contracted into regions near the fixed points of the bifurcation and cause stabilization of the electron.