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 $6sns\, {}^1 \! S_0$ and $6snd\,{}^{3,1}\!D_2$ levels of neutral $^{174}$Yb are presented in this paper. Spectroscopy is performed by a two-step laser excitation from the ground state $4f^{14}6s^2 \, {}^1 \! S_0$, 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 $I_{6s}=50443.07041(25)$ cm$^{-1}$ 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 $\mu K$ from the $a^3 \Sigma_u^+(6s,6s)$ continuum to bound levels in the external well of the $0_g^-(6s+6p_{3/2})$ 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 $\approx 15$ vibrational levels in the vicinity of the v=98 bound level in the external well of the $0_g^-(6s+6p_{3/2})$ 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 $a^3\Sigma_u^+$(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