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Journal of Physics B Atomic Molecular and Optical Physics

Semiclassical description of collisionally induced rainbow satellites: a model study

Robert Beuc, Berislav Horvatić, Mladen Movre

Published Oct 22, 2010• 4 citations
Publisher

Abstract

We apply the uniform Airy approximation ( Beuc and Horvatic 1992 J. Phys. B: At. Mol. Opt. Phys. 25 1497 ) to the analytical model proposed by Devdariani et al ( 2002 J. Phys. B: At. Mol. Opt. Phys. 35 2469 ). The model describes asymptotically forbidden quasimolecular optical transitions within the frame of the semiclassical approach. Our results support conclusions that the uniform Airy approximation, originally developed for the asymptotically allowed transitions, is applicable to a broad class of asymptotically forbidden but collisionally assisted optical transitions as well. In addition, we present a new transitional formula and discuss some further approximations.

DOI
10.1088/0953-4075/43/21/215210

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Atoms to optics - the overlap betweenJ. Phys. B: At. Mol. Opt. Phys.andJ. Opt. B: Quantum Semiclass. Opt.explained

Following the recent publications of the special issues, `Coherent matter waves' in Journal of Physics B: Atomic, Molecular and Optical Physics and `Quantum transport of atoms in optical lattices' in Journal of Optics B: Quantum and Semiclassical Optics , we would like to take this opportunity to clarify the situation regarding the overlap of topics in the two journals. As a not-for-profit publisher we believe in serving the communities represented by the journals and wish to offer as much choice to the authors and readers as possible. For example, in relation to atoms and optics we are in an excellent position to offer this choice as we have two world-class journals that cover all aspects of atom optics, guaranteeing maximum exposure to the communities involved. Both journals have high impact factors and both are abstracted in INSPEC Information Services; Chemical Abstracts; ISI (Science Citation Index®, SciSearch®, ISI Alerting Services, Current Contents®/Physical, Chemical and Earth Sciences), to name but a few. The journal web sites are highly accessed with a combined average of over 20 000 views per month in 2000. Please feel free to view the journal information pages on www.iop.org/Journals/jb and www.iop.org/Journals/ob . We welcome submissions from all aspects of atom optics, coherent matter waves and Bose-Einstein condensation with atoms. We encourage authors to look at both journals and decide which journal would provide the best home for their article. We, at the Editorial Office, are happy to help if there is any doubt. Additionally Professor Arimondo (Editor-in-Chief, J. Opt. B: Quantum Semiclass. Opt. ) and Professor Burnett (Honorary Editor, J. Phys. B: At. Mol. Opt. Phys. ) have drawn up some basic guidelines as to which topics sit better in which journal. These are shown below and are meant to aid the author when deciding which journal to submit to, but are not meant to be prescriptive in any way. Ultimately it is the authors' decision and we will always respect that. If at anytime you have any queries or comments, please do contact us at the Editorial Office. Nicola Gulley Publisher J. Phys. B: At. Mol. Opt. Phys. Andrew Harmer Publisher J. Opt. B: Quantum Semiclass. Opt. General guide to suitable topics for J. Phys. B: At. Mol. Opt. Phys. and J. Opt. B: Quantum Semiclass. Opt. in atoms to optics research. J. Phys. B: At. Mol. Opt. Phys.: • cold collisions; • many-body wavefunctions; • interactions; • excitations of condensates; • computational techniques for condensates; • molecular condensates. J. Opt. B: Quantum Semiclass. Opt.: • atom optics; • matter--wave coherence; • optics of matter waves; • condensates phase issues; • lattices; • quantum information with BEC.

Journal of Optics B Quantum and Semiclassical Optics•Dec 1, 2000•0 citations
We apply the uniform Airy approximation ( Beuc and Horvatic 1992 J. Phys. B: At. Mol. Opt. Phys. 25 1497 ) to the analytical model proposed by Devdariani et al ( 2002 J. Phys. B: At. Mol. Opt. Phys. 35 2469 ). The model describes asymptotically forbidden quasimolecular optical transitions within the frame of the semiclassical approach. Our results support conclusions that the uniform Airy approximation, originally developed for the asymptotically allowed transitions, is applicable to a broad class of asymptotically forbidden but collisionally assisted optical transitions as well. In addition, we present a new transitional formula and discuss some further approximations.
A semiclassical formula that gives scattering cross sections down to an angular resolution of order ${\mathrm{\ensuremath{\Elzxh}}}^{4/5}$ is derived. The formula describes rainbow peaks, which have widths of order ${\mathrm{\ensuremath{\Elzxh}}}^{2/3}$, but not other interference effects, which give structure on a scale of order \ensuremath{\Elzxh}. For cross sections with many rainbow peaks, it can be easier to evaluate than conventional uniform approximations. As an example, the formula is applied to a simple two-dimensional model.
We present a detailed discussion of the semiclassical approximations to path integrals when there exist caustics in the relevant family of classical trajectories. We show carefully how the Airy functions arise from the post-semiclassical approximation of the path integral and interpret the coefficients in the Airy functions in terms of the flow of classical trajectories. Finally, we present a configuration-space path integral for the scattering matrix and extend our discussion of caustics to the case of rainbow scattering.
Semiclassical integral representations, analogous to initial value expressions for the propagator, are presented for the Clebsch-Gordan angular momentum coupling coefficients. Two forms (L and R types) of the approximation are presented. For each form, new non-Gaussian expressions, which are specifically adapted to the nature of angular momentum variables, are proposed in place of the familiar Gaussian coherent state functions. With these non-Gaussian kernels, it is found that the present treatments are capable of accuracy similar to that obtained from a uniform Airy approximation. Although the present semiclassical approximations involve only real-valued angle variables, associated with sets of angular momenta that are related by ordinary, real, classical transformations, the treatments produce accurate results not only for classically allowed choices of quantum numbers but also for very strongly classically forbidden values.
Perturbation theory for the interaction of light with a binary collisional system is applied to the calculation of line profiles, spontaneous emission rates and absorption or stimulated emission coefficients. For the usual radiation fields are perturber densities, this approximation is valid at all detunings Delta omega except the very narrow resonance region. Appropriate expansions of the total binary system wavefunctions give the emission and absorption profiles or rates, for atom-electron systems as well as for atom-atom systems, from the impact regime at small Delta omega up to the Born-Oppenheimer regime at very large Delta omega in collision-induced radiative transitions, the transitions being asymptotically allowed or forbidden. Emphasis is given to the proper averages and sums over initial and final states of the binary system which give rise to non-adiabatic effects. One shows that it is of crucial importance to include all dynamical effects during one collisional event before undertaking any calculation at small Delta omega where simultaneous collisions may occur.
We present a detailed analysis of the cold collision measurements performed in a high-gradient magneto-optical trap with a few trapped Cs atoms first presented in Ueberholz et al ( J. Phys. B: At. Mol. Opt. Phys. 33 (2000) L135 ). The ability to observe individual loss events allows us to identify two-body collisions that lead to the escape of only one of the colliding atoms (up to 10% of all collisional losses). Possible origins of these events are discussed here. We also observed strong modifications of the total loss rate with variations in the repumping laser intensity. This is explained by a simple semiclassical model based on optical suppression of hyperfine-changing collisions between ground-state atoms.
Following the recent publications of the special issues, `Coherent matter waves' in Journal of Physics B: Atomic, Molecular and Optical Physics and `Quantum transport of atoms in optical lattices' in Journal of Optics B: Quantum and Semiclassical Optics , we would like to take this opportunity to clarify the situation regarding the overlap of topics in the two journals. As a not-for-profit publisher we believe in serving the communities represented by the journals and wish to offer as much choice to the authors and readers as possible. For example, in relation to atoms and optics we are in an excellent position to offer this choice as we have two world-class journals that cover all aspects of atom optics, guaranteeing maximum exposure to the communities involved. Both journals have high impact factors and both are abstracted in INSPEC Information Services; Chemical Abstracts; ISI (Science Citation Index®, SciSearch®, ISI Alerting Services, Current Contents®/Physical, Chemical and Earth Sciences), to name but a few. The journal web sites are highly accessed with a combined average of over 20 000 views per month in 2000. Please feel free to view the journal information pages on www.iop.org/Journals/jb and www.iop.org/Journals/ob . We welcome submissions from all aspects of atom optics, coherent matter waves and Bose-Einstein condensation with atoms. We encourage authors to look at both journals and decide which journal would provide the best home for their article. We, at the Editorial Office, are happy to help if there is any doubt. Additionally Professor Arimondo (Editor-in-Chief, J. Opt. B: Quantum Semiclass. Opt. ) and Professor Burnett (Honorary Editor, J. Phys. B: At. Mol. Opt. Phys. ) have drawn up some basic guidelines as to which topics sit better in which journal. These are shown below and are meant to aid the author when deciding which journal to submit to, but are not meant to be prescriptive in any way. Ultimately it is the authors' decision and we will always respect that. If at anytime you have any queries or comments, please do contact us at the Editorial Office. Nicola Gulley Publisher J. Phys. B: At. Mol. Opt. Phys. Andrew Harmer Publisher J. Opt. B: Quantum Semiclass. Opt. General guide to suitable topics for J. Phys. B: At. Mol. Opt. Phys. and J. Opt. B: Quantum Semiclass. Opt. in atoms to optics research. J. Phys. B: At. Mol. Opt. Phys.: • cold collisions; • many-body wavefunctions; • interactions; • excitations of condensates; • computational techniques for condensates; • molecular condensates. J. Opt. B: Quantum Semiclass. Opt.: • atom optics; • matter--wave coherence; • optics of matter waves; • condensates phase issues; • lattices; • quantum information with BEC.