34 research outputs found
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
Quantum dynamics of a plane pendulum
A semi-analytical approach to the quantum dynamics of a plane pendulum is developed, based on Mathieu functions which appear as stationary wave functions. The time-dependent Schrödinger equation is solved for pendular analogues of coherent and squeezed states of a harmonic oscillator, induced by instantaneous changes of the periodic potential energy function. Coherent pendular states are discussed between the harmonic limit for small displacements and the inverted pendulum limit, while squeezed pendular states are shown to interpolate between vibrational and free rotational motion. In the latter case, full and fractional revivals as well as spatiotemporal structures in the time-evolution of the probability densities (quantum carpets) are quantitatively analyzed. Corresponding expressions for the mean orientation are derived in terms of Mathieu functions in time. For periodic double well potentials, different revival schemes and different quantum carpets are found for the even and odd initial states forming the ground tunneling doublet. Time evolution of the mean alignment allows the separation of states with different parity. Implications for external (rotational) and internal (torsional) motion of molecules induced by intense laser fields are discussed
A case study using the model H+H2 and F+H2 reactions with aligned and anti- aligned H2
We propose a method to steer the outcome of reactive atom-diatom scattering,
using rotational wavepackets excited by strong non-resonant laser pulses. Full
close-coupled quantum mechanical scattering calculations of the D+H2 and F+H2
reactions are presented, where the H2 molecule exists as a coherent
superposition of rotational states. The nuclear spin selective control over
the molecular bond axis alignment afforded by the creation of rotational
wavepackets is applied to reactive scattering systems, enabling a nuclear spin
selective influence to be exerted over the reactive dynamics. The extension of
the conventional eigenstate-to-eigenstate scattering problem to the case in
which the initial state is composed of a coherent superposition of rotational
states is detailed, and a selection of example calculations are discussed,
along with their mechanistic implications. The feasibility of the
corresponding experiments is considered, and a suitable simple two pulse laser
scheme is shown to strongly differentiate the reactivities of o-H2 and p-H2
Nuclear spin selective laser control of rotational and torsional dynamics
We explore the possibility of controlling rotational-torsional dynamics of
non-rigid molecules with strong, non-resonant laser pulses and demonstrate
that transient, laser-induced torsional alignment depends on the nuclear spin
of the molecule. Consequently, nuclear spin isomers can be manipulated
selectively by a sequence of time-delayed laser pulses. We show that two
pulses with different polarization directions can induce either overall
rotation or internal torsion, depending on the nuclear spin.Nuclear spin
selective control of the angular momentum distribution may open new ways to
separate and explore nuclear spin isomers of polyatomic molecules
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
Atom-diatom scattering dynamics of spinning molecules
We present full quantum mechanical scattering calculations using spinning
molecules as target states for nuclear spin selective atom-diatom scattering
of reactive D+H2 and F+H2 collisions. Molecules can be forced to rotate uni-
directionally by chiral trains of short, non-resonant laser pulses, with
different nuclear spin isomers rotating in opposite directions. The
calculations we present are based on rotational wavepackets that can be
created in this manner. As our simulations show, target molecules with
opposite sense of rotation are predominantly scattered in opposite directions,
opening routes for spatially and quantum state selective scattering of close
chemical species. Moreover, two-dimensional state resolved differential cross
sections reveal detailed information about the scattering mechanisms, which
can be explained to a large degree by a classical vector model for scattering
with spinning molecules
Molecular Symmetry Properties of Conical Intersections and Nonadiabatic Coupling Terms: Theory and Quantum Chemical Demonstration for Cyclopenta-2,4-dienimine (C5H4NH)
This paper discovers molecular symmetry (MS) properties of conical intersections (CIs) and the related
nonadiabatic coupling terms (NACTs) in molecules which allow large amplitude motions such as torsion, in
the frame of the relevant molecular symmetry group, focusing on groups with one-dimensional (1-d) irreducible
representations (IREPs). If one employs corresponding MS-adapted nuclear coordinates, the NACTs can be
classified according to those IREPs. The assignment is supported by theorems which relate the IREPs of
different NACTs to each other, and by properties of the NACTs related to the CIs. For example, planar
contour integrals of the NACTs evaluated along loops around the individual CIs are equal to +Ď€ or -Ď€,
depending on the IREP-adapted signs of the NACTs. The + or - signs for the contour integrals may also be
used to define the “charges” and IREPs of the CIs. We derive various general molecular symmetry properties
of the related NACTs and CIs. These provide useful applications; e.g., the discovery of an individual CI
allows one to generate, by means of all molecular symmetry operations, the complete set of CIs at different
symmetry-related locations. Also, we show that the seams of CIs with different IREPs may have different
topologies in a specific plane of MS-adapted coordinates. Moreover, the IREPs impose symmetrical nodes of
the NACTs, and this may support their calculations by quantum chemical ab initio methods, even far away
from the CIs. The general approach is demonstrated by application to an example. Specifically, we investigate
the CIs and NACTs of cyclopenta-2,4-dienimine (C5H4NH) which has C2V(M) molecular symmetry with 1-d
IREPs. The results are confirmed by quantum chemical calculations, starting from the location of a CI based
on the Longuet-Higgins phase change theorem, until a proof of self-consistency, i.e., the related symmetryadapted
NACTs fulfill quantization rules which have been derived in [Baer, M. Beyond Born-Oppenheimer:
Electronic non-Adiabatic Coupling Terms and Conical Intersections; Wiley & Sons Inc.: Hoboken, NJ, 2006].We thank Prof. Lluis Blancafort, Prof.
Dietrich Haase, Prof. Yehuda Haas, PD Dr. Dirk Andrae, Mr.
Thomas Grohmann, and Ms. Shireen Alfalah for advice and
stimulating discussions, and Mr. Dominik Sattler for preparing
Figures 1 and 2. This study was supported by the Deutsche
Forschungsgemeinschaft in the framework of Project No. MA
515/22-2, and by Fonds der Chemischen Industrie
Squeezing of Atoms in a Pulsed Optical Lattice
We study the process of squeezing of an ensemble of cold atoms in a pulsed
optical lattice. The problem is treated both classically and
quantum-mechanically under various thermal conditions. We show that a dramatic
compression of the atomic density near the minima of the optical potential can
be achieved with a proper pulsing of the lattice. Several strategies leading to
the enhanced atomic squeezing are suggested, compared and optimized.Comment: Latex, 9 pages, 10 figures, submitted to PR
Non-equilibrium dynamics of an unstable quantum pendulum
A pendulum prepared perfectly inverted and motionless is a prototype of
unstable equilibria and corresponds to an unstable hyperbolic fixed point in
the dynamical phase space. Unstable fixed points are central to understanding
Hamiltonian chaos in classical systems. In many-body quantum systems,
mean-field approximations fail in the vicinity of unstable fixed points and
lead to dynamics driven by quantum fluctuations. Here, we measure the
non-equilibrium dynamics of a many-body quantum pendulum initialized to a
hyperbolic fixed point of the phase space. The experiment uses a spin-1 Bose
condensate, which exhibits Josephson dynamics in the spin populations that
correspond in the mean-field limit to motion of a non-rigid mechanical
pendulum. The condensate is initialized to a minimum uncertainty spin state,
and quantum fluctuations lead to non-linear spin evolution along a separatrix
and non-Gaussian probability distributions that are measured to be in good
agreement with exact quantum calculations up to 0.25 s. At longer times, atomic
loss due to the finite lifetime of the condensate leads to larger spin
oscillation amplitudes compared to no loss case as orbits depart from the
separatrix. This demonstrates how decoherence of a many-body system can result
in more apparent coherent behaviour. This experiment provides new avenues for
studying macroscopic spin systems in the quantum limit and for investigations
of important topics in non-equilibrium quantum dynamics.Comment: Main text 6 pages, 5 figures; Supplement 4 pages, 1 figur