147 research outputs found
Towards new understanding of nuclear rotation
Properties of time evolution of wave packets built up from rotator
eigenstates are discussed. The mechanism of perfect cloning of the initial wave
packet for "circular states" at fractional revival times is explained. The
smooth transition from "circular" to "linear" through intermediate "elliptic"
is described. Example of time evolution of a nuclear wave packet created in
Coulomb excitation mechanism is presented.Comment: 4 pages, 2 figures, LaTeX (appb.sty included), Presented at the
XXXIII Zakopane School of Physics, Zakopane, Poland, September 1-9, 1998. To
appear in Acta Phys. Polon. B (1999
Geometrical properties of intelligent spin states and time evolution of coherent states
We remind the properties of the intelligent (and quasi-intelligent) spin
states introduced by Aragone et al. We use these states to construct families
of coherent wave packets on the sphere and we sketch the time evolution of
these wave packets for a rigid body molecule.Comment: 7 pages + 4 figures (11p), LaTeX2e, Paper accepted for publication in
J.Phys.A: Math.Ge
New mechanism of collapse and revival in wave packet dynamics due to spin-orbit interaction
The article discusses the properties of time evolution of wave packets in a
few systems. Dynamics of wave packet motion for Rydberg atoms with the
hierarchy of collapses and revivals is briefly reviewed. The main part of the
paper focuses on the new mechanism of quantum reccurrences in wave packet
dynamics. This mechanism can occur (in principle) in any physical system with
strong enough spin-orbit interaction. We discuss here the SPIN_ORBIT PENDULUM
effect that consists in different motions of subpackets possessing different
spin fields and results in oscillations of a fraction of average angular
momentum between spin and ordinary subspaces. The evolution of localized wave
packet into toroidal objects and backwards (for other class of initial
conditions) is also subject to discussion.Comment: 10 pages, LaTeX, 7 PS figures (in 6 separate files), to appear in
Acta Phys. Polon. (Invited lecture at XXXI Zakopane School of Physics,
Zakopane, Poland, September 3-11, 1996
Controlling Quantum Rotation With Light
Semiclassical catastrophes in the dynamics of a quantum rotor (molecule)
driven by a strong time-varying field are considered. We show that for strong
enough fields, a sharp peak in the rotor angular distribution can be achieved
via time-domain focusing phenomenon, followed by the formation of angular
rainbows and glory-like angular structures. Several scenarios leading to the
enhanced angular squeezing are proposed that use specially designed and
optimized sequences of pulses. The predicted effects can be observed in many
processes, ranging from molecular alignment (orientation) by laser fields to
heavy-ion collisions, and the squeezing of cold atoms in a pulsed optical
lattice.Comment: 8 pages, Latex, 8 figures, based on the talk given at the Eighth
Rochester Conference on Coherence and Quantum Optics (June 13-16, 2001). To
appear in the proceedings of CQO8 (Plenum, 2002
Pictures of quantum nuclear rotation beyond the correspondence principle
We analyze the time evolution of simple nuclear rotational wave packets (WP) called circular, linear or elliptic assuming that rotational energies are proportional to I(I+1). The scenario of fractional revivals found by Averbukh and Perelman is adapted to symmetric WP and compared to that which holds for asymmetric WP. In both cases various shapes are identified under these lines in particular many cases of cloning. 'Mutants' WP are found most often
Spin dynamics of wave packets evolving with the Dirac Hamiltonian in atoms with high Z
The motion of circular WP for one electron in central Coulomb field with high
Z is calculated. The WP is defined in terms of solutions of the Dirac equation
in order to take into account all possible relevant effects in particular the
spin-orbit potential. A time scale is defined within which spin dynamics must
be taken into account mainly in the atoms with high Z. Within this time scale
there exists a mechanism of collapses and revivals of the spin already shown by
the authors for harmonic oscillator potential and called the 'spin-orbit
pendulum'. However this effect has not the exact periodicity of the simpler
model, but the WP's spatial motion is nevertheless quite similar.Comment: 17 pages, 9 figures, LaTeX2e, uses IOP style files (included). Title
changed, one reference adde
Semiclassical catastrophes and cumulative angular squeezing of a kicked quantum rotor
We present a detailed theory of spectacular semiclassical catastrophes happening during the time evolution of a kicked quantum rotor (Phys.Rev. Lett. {\bf 87}, 163601 (2001)). Both two- and three-dimensional rotational systems are analyzed. It is shown that the wave function of the rotor develops a {\em cusp} at a certain delay after a kick, which results in a sharply focused rotational wave packet. The {\em cusp} is followed by a fold-type catastrophe manifested in the {\em rainbow}-like moving angular singularities. In the three-dimensional case, the rainbows are accompanied by additional singular features similar to {\em glory} structures known in wave optics. These catastrophes in the time-dependent angular wave function are well described by the appropriate tools of the quasiclassical wave mechanics, i.e. by Airy and Bessel approximations and Pearcey's functions. A scenario of "accumulative squeezing" is also presented in which a specially designed train of short kicks produces an unlimited narrowing of the rotor angular distribution. This scenario is relevant for the molecular alignment by short laser pulses, and also for atom lithography schemes in which cold atoms are focused by an optical standing wave
CLASSICAL PROPERTIES AND SEMICLASSICAL CALCULATIONS IN A SPHERICAL NUCLEAR AVERAGE POTENTIAL
We study the relation between the classical properties of an average nuclear potential and its spectral properties. We have drawn the energy-action surface of this potential and related its properties to the spectral ones in the framework of the EBK semiclassical method. We also describe a method allowing us to get the evolution of the spectrum with the mass number
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.
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