227 research outputs found
The hydrogen atom in electric and magnetic fields : Pauli's 1926 article
The results obtained by Pauli, in his 1926 article on the hydrogen atom, made
essential use of the dynamical so(4) symmetry of the bound states. Pauli used
this symmetry to compute the perturbed energy levels of an hydrogen atom in a
uniform electric field (Stark effect) and in uniform electric and magnetic
fields. Although the experimental check of the single Stark effect on the
hydrogen atom has been studied experimentally, Pauli's results in mixed fields
have been studied only for Rydberg states of rubidium atoms in crossedfields
and lithium atoms in parallel fields.Comment: 11 pages, latex file, 2 figure
Femtosecond pulses and dynamics of molecular photoexcitation: RbCs example
We investigate the dynamics of molecular photoexcitation by unchirped
femtosecond laser pulses using RbCs as a model system. This study is motivated
by a goal of optimizing a two-color scheme of transferring
vibrationally-excited ultracold molecules to their absolute ground state. In
this scheme the molecules are initially produced by photoassociation or
magnetoassociation in bound vibrational levels close to the first dissociation
threshold. We analyze here the first step of the two-color path as a function
of pulse intensity from the low-field to the high-field regime. We use two
different approaches, a global one, the 'Wavepacket' method, and a restricted
one, the 'Level by Level' method where the number of vibrational levels is
limited to a small subset. The comparison between the results of the two
approaches allows one to gain qualitative insights into the complex dynamics of
the high-field regime. In particular, we emphasize the non-trivial and
important role of far-from-resonance levels which are adiabatically excited
through 'vertical' transitions with a large Franck-Condon factor. We also point
out spectacular excitation blockade due to the presence of a quasi-degenerate
level in the lower electronic state. We conclude that selective transfer with
femtosecond pulses is possible in the low-field regime only. Finally, we extend
our single-pulse analysis and examine population transfer induced by coherent
trains of low-intensity femtosecond pulses.Comment: 25 pages, 12 figure
Laser and microwave spectroscopy of even-parity Rydberg states of neutral ytterbium and Multichannel Quantum Defect Theory analysis
New measurements of high-lying even parity and
levels of neutral Yb are presented in this paper.
Spectroscopy is performed by a two-step laser excitation from the ground state
, and the Rydberg levels are detected by using the
field ionization method. Additional two-photon microwave spectroscopy is used
to improve the relative energy accuracy where possible. The spectroscopic
measurements are complemented by a multichannel quantum defect theory (MQDT)
analysis for the J=0 and the two-coupled J=2 even parity series. We compare our
results with the previous analysis of Aymar {\it{et al}} \cite{Aymar_1980} and
analyze the observed differences. From the new MQDT models, a revised value for
the first ionization limit cm is proposed.Comment: 15 pages, 3 figure
Optimizing the photoassociation of cold atoms by use of chirped laser pulses
Photoassociation of ultracold atoms induced by chirped picosecond pulses is
analyzed in a non-perturbative treatment by following the wavepackets dynamics
on the ground and excited surfaces. The initial state is described by a
Boltzmann distribution of continuum scattering states. The chosen example is
photoassociation of cesium atoms at temperature T=54 from the continuum to bound levels in the external well of the
potential. We study how the modification of the pulse
characteristics (carrier frequency, duration, linear chirp rate and intensity)
can enhance the number of photoassociated molecules and suggest ways of
optimizing the production of stable molecules.Comment: 40 pages, 12 figures, submitted to Eur. Phys. J.
Photoassociation of cold atoms with chirped laser pulses: time-dependent calculations and analysis of the adiabatic transfer within a two-state model
This theoretical paper presents numerical calculations for photoassociation
of ultracold cesium atoms with a chirped laser pulse and detailed analysis of
the results. In contrast with earlier work, the initial state is represented by
a stationary continuum wavefunction. In the chosen example, it is shown that an
important population transfer is achieved to vibrational levels in
the vicinity of the v=98 bound level in the external well of the
potential. Such levels lie in the energy range swept by
the instantaneous frequency of the pulse, thus defining a ``photoassociation
window''. Levels outside this window may be significantly excited during the
pulse, but no population remains there after the pulse. Finally, the population
transfer to the last vibrational levels of the ground (6s + 6s)
is significant, making stable molecules. The results are interpreted in the
framework of a two state model as an adiabatic inversion mechanism, efficient
only within the photoassociation window. The large value found for the
photoassociation rate suggests promising applications. The present chirp has
been designed in view of creating a vibrational wavepacket in the excited state
which is focussing at the barrier of the double well potential.Comment: 49 pages, 9 figures, submitted to Phys. Rev.
Application of B-splines to determining eigen-spectrum of Feshbach molecules
The B-spline basis set method is applied to determining the rovibrational
eigen-spectrum of diatomic molecules. A particular attention is paid to a
challenging numerical task of an accurate and efficient description of the
vibrational levels near the dissociation limit (halo-state and Feshbach
molecules). Advantages of using B-splines are highlighted by comparing the
performance of the method with that of the commonly-used discrete variable
representation (DVR) approach. Several model cases, including the Morse
potential and realistic potentials with 1/R^3 and 1/R^6 long-range dependence
of the internuclear separation are studied. We find that the B-spline method is
superior to the DVR approach and it is robust enough to properly describe the
Feshbach molecules. The developed numerical method is applied to studying the
universal relation of the energy of the last bound state to the scattering
length. We numerically illustrate the validity of the quantum-defect-theoretic
formulation of such a relation for a 1/R^6 potential.Comment: submitted to can j phys: Walter Johnson symposu
Resummation of the Divergent Perturbation Series for a Hydrogen Atom in an Electric Field
We consider the resummation of the perturbation series describing the energy
displacement of a hydrogenic bound state in an electric field (known as the
Stark effect or the LoSurdo-Stark effect), which constitutes a divergent formal
power series in the electric field strength. The perturbation series exhibits a
rich singularity structure in the Borel plane. Resummation methods are
presented which appear to lead to consistent results even in problematic cases
where isolated singularities or branch cuts are present on the positive and
negative real axis in the Borel plane. Two resummation prescriptions are
compared: (i) a variant of the Borel-Pade resummation method, with an
additional improvement due to utilization of the leading renormalon poles (for
a comprehensive discussion of renormalons see [M. Beneke, Phys. Rep. vol. 317,
p. 1 (1999)]), and (ii) a contour-improved combination of the Borel method with
an analytic continuation by conformal mapping, and Pade approximations in the
conformal variable. The singularity structure in the case of the LoSurdo-Stark
effect in the complex Borel plane is shown to be similar to (divergent)
perturbative expansions in quantum chromodynamics.Comment: 14 pages, RevTeX, 3 tables, 1 figure; numerical accuracy of results
enhanced; one section and one appendix added and some minor changes and
additions; to appear in phys. rev.
Ballistic matter waves with angular momentum: Exact solutions and applications
An alternative description of quantum scattering processes rests on
inhomogeneous terms amended to the Schroedinger equation. We detail the
structure of sources that give rise to multipole scattering waves of definite
angular momentum, and introduce pointlike multipole sources as their limiting
case. Partial wave theory is recovered for freely propagating particles. We
obtain novel results for ballistic scattering in an external uniform force
field, where we provide analytical solutions for both the scattering waves and
the integrated particle flux. Our theory directly applies to p-wave
photodetachment in an electric field. Furthermore, illustrating the effects of
extended sources, we predict some properties of vortex-bearing atom laser beams
outcoupled from a rotating Bose-Einstein condensate under the influence of
gravity.Comment: 42 pages, 8 figures, extended version including photodetachment and
semiclassical theor
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