Spin-Orbit Pendulum: the Microscopic Stern-Gerlach Effect

The motion of a particle with a spin in spherical harmonic oscillator potential with spin-orbit interaction is studied. We have focus our attention on spatial motion of wave packets, giving a description complementary to motion of spin discussed already in [1]. The particular initial conditions studied here lead to the most transparent formulas and can be treated analytically. A strong analogy with the Stern-Gerlach experiment is suggested. [1] R.Arvieu and P.Rozmej, Phys.Rev.A50 (1994) 4376.Comment: 4 pages, LaTeX (precisely RevTeX), attached 4 complicated Postscript figures , Paper submitted to Phys.Rev.

Wave packet revivals in a graphene quantum dot in a perpendicular magnetic field

We study the time-evolution of localized wavepackets in graphene quantum dots under a perpendicular magnetic field, focusing on the quasiclassical and revival periodicities, for different values of the magnetic field intensities in a theoretical framework. We have considered contributions of the two inequivalent points in the Brillouin zone. The revival time has been found as an observable that shows the break valley degeneracy.Comment: 5 pages, 4 figures, corrected typo, To appear in Phys. Rev.

Electric Deflection of Rotating Molecules

We provide a theory of the deflection of polar and non-polar rotating molecules by inhomogeneous static electric field. Rainbow-like features in the angular distribution of the scattered molecules are analyzed in detail. Furthermore, we demonstrate that one may efficiently control the deflection process with the help of short and strong femtosecond laser pulses. In particular the deflection process may by turned-off by a proper excitation, and the angular dispersion of the deflected molecules can be substantially reduced. We study the problem both classically and quantum mechanically, taking into account the effects of strong deflecting field on the molecular rotations. In both treatments we arrive at the same conclusions. The suggested control scheme paves the way for many applications involving molecular focusing, guiding, and trapping by inhomogeneous fields

Time dependent partial waves and vortex rings in the dynamics of wave packets

We have found a new class of time dependent partial waves which are solutions of time dependent Schr\"odinger equation for three dimensional harmonic oscillator. We also showed the decomposition of coherent states of harmonic oscillator into these partial waves. This decomposition appears perticularly convenient for a description of the dynamics of a wave packet representing a particle with spin when the spin--orbit interaction is present in the hamiltonian. An example of an evolution of a localized wave packet into a torus and backwards, for a particular initial conditions is analysed in analytical terms and shown with a computer graphics.Comment: 10 pages, LaTeX, 6 postscript figures, submitted to J. Phys. A: Math. Ge

Factorization of numbers with Gauss sums: II. Suggestions for implementations with chirped laser pulses

We propose three implementations of the Gauss sum factorization schemes discussed in part I of this series: (i) a two-photon transition in a multi-level ladder system induced by a chirped laser pulse, (ii) a chirped one-photon transition in a two-level atom with a periodically modulated excited state, and (iii) a linearly chirped one-photon transition driven by a sequence of ultrashort pulses. For each of these quantum systems we show that the excitation probability amplitude is given by an appropriate Gauss sum. We provide rules how to encode the number N to be factored in our system and how to identify the factors of N in the fluorescence signal of the excited state.Comment: 22 pages, 7 figure

Non-classical properties of quantum wave packets propagating in a Kerr-like medium

We investigate non-classical effects such as fractional revivals, squeezing and higher-order squeezing of photon-added coherent states propagating through a Kerr-like medium.The Wigner functions corresponding to these states at the instants of fractional revivals are obtained, and the extent of non-classicality quantified.Comment: 8 pages, 10 figure

Relativistic precession and spin dynamics of an elliptic Rydberg wave packet

Time evolution of wave packets built from the eigenstates of the Dirac equation for a hydrogenic system is considered. We investigate the space and spin motion of wave packets which, in the non-relativistic limit, are stationary states with a probability density distributed uniformly along the classical, elliptical orbit (elliptic WP). We show that the precession of such a WP, due to relativistic corrections to the energy eigenvalues, is strongly correlated with the spin motion. We show also that the motion is universal for all hydrogenic systems with an arbitrary value of the atomic number Z.Comment: Latex2e, uses IOP style files (included), 10 pages, 5 jpg figures, 1 postscript figure. Relation between precession time and radiative liftime added (eq.(12)). Accepted for publication in J. Phys.

Controlling Molecular Scattering by Laser-Induced Field-Free Alignment

We consider deflection of polarizable molecules by inhomogeneous optical fields, and analyze the role of molecular orientation and rotation in the scattering process. It is shown that molecular rotation induces spectacular rainbow-like features in the distribution of the scattering angle. Moreover, by preshaping molecular angular distribution with the help of short and strong femtosecond laser pulses, one may efficiently control the scattering process, manipulate the average deflection angle and its distribution, and reduce substantially the angular dispersion of the deflected molecules. We provide quantum and classical treatment of the deflection process. The effects of strong deflecting field on the scattering of rotating molecules are considered by the means of the adiabatic invariants formalism. This new control scheme opens new ways for many applications involving molecular focusing, guiding and trapping by optical and static fields