Classical and Quantum Dynamics of a Periodically Driven Particle in a Triangular Well

We investigate the correspondence between classical and quantum mechanics for periodically time dependent Hamiltonian systems, using the example of a periodically forced particle in a one-dimensional triangular well potential. In particular, we consider quantum mechanical Floquet states associated with resonances in the classical phase space. When the classical motion exhibits {\it sub}harmonic resonances, the corresponding Floquet states maintain the driving field's periodicity through dynamical tunneling. This principle applies both to Floquet states associated with classical invariant vortex tubes surrounding stable, elliptic periodic orbits and to Floquet states that are associated with unstable, hyperbolic periodic orbits. The triangular well model also poses a yet unsolved mathematical problem, related to perturbation theory for systems with a dense pure point spectrum. The present approximate analytical and numerical results indicate that quantum tunneling between different resonance zones is of crucial importance for the question whether the driven triangular well has a dense point or an absolutely continuous quasienergy spectrum, or whether there is a transition from the one to the other.Comment: revtex, 36 pages, 18 figures (available upon request), to appear in Annals of Physic

Electric-field control of a hydrogenic donor's spin in a semiconductor

An AC electric field applied to a donor-bound electron in a semiconductor modulates the orbital character of its wave function, which affects the electron's spin dynamics via the spin-orbit interaction. Numerical calculations of the spin dynamics of a hydrogenic donor (Si) embedded in GaAs, using a real-space multi-band k.p formalism, show the high symmetry of the hydrogenic donor state results in strongly nonlinear dependences of the electronic g tensor on applied fields. A nontrivial consequence is that the most rapid Rabi oscillations occur for electric fields modulated at a subharmonic of the Larmor frequency