CONTROLLING THE QUANTUM ROTOR WITH A TIME-DEPENDENT MAGNETIC FLUX

We study the possibility of controlling a quantum rotor interacting with a time-dependent external field, namely, using a continuous or a piecewise continuous (bang-bang control) magnetic flux. Using the exact eigenfunctions we show how to steer a wave-packet constructed as a superposition of these eigenstates. In the first case we show how to steer a Gaussian wave-packet (GWP) to two other positions: one of them which would not be realized if the evolution were free, and the second is the one where wave-packet revival takes place. In the piecewise approach we implement a kind of tracking control, i.e. before steering it to the final target we achieve another given GWP.

Spin-Orbit Entanglement in Time Evolution of Radial Wave Packets in Hydrogenic Systems

Time evolution of radial wave packets built from the eigenstates of Dirac equation for a hydrogenic system is considered. Radial wave packets are constructed from the states of different n quantum numbers and the same lowest angular momentum. In general they exhibit a kind of breathing motion with dispersion and (partial) revivals. Calculations show that for some particular preparations of the wave packet one can observe interesting effects in spin motion, coming from inherent entanglement of spin and orbital degrees of freedom. These effects manifest themselves through some oscillations in the mean values of spin operators and through changes of spatial probability density carried by upper and lower components of the wave function. It is also shown that the characteristic time scale of predicted effects (called T ls ) is much smaller for radial wave packets than in other cases, reaching values comparable to (or even less than) the time scale for the wave packet revival.