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Journal of the Chinese Chemical Society

Resonance Scattering in the Three‐Body Systems of Atom‐diatom and Relevance to Condensed Matter Physics

Sung‐Ho Suck Salk

Published Jun 1, 2001• 0 citations
Publisher

Abstract

Abstract Three‐body resonance scattering of atom‐diatomic molecule systems involving internal excitations is discussed by fully allowing the topological phase (Berry phase) contribution. Earlier a generalized formalism (Phys. Rev. A 1996, 53, 2433) of the three‐body resonance scattering was presented by introducing the gauge potential (Berry connection). Based on this study we provide additional information on topological importance in resonance scattering involving the atom‐diatomic molecule systems. The massive gauge field (Berry connection) contribution which arises from a broken symmetry is discussed. Its relevance to condensed matter physics will be briefly high lighted in connection with our recent theory of super conductivity (Phys. Rev. B 1999, 60, 6324).

DOI
10.1002/jccs.200100059

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Abstract Three‐body resonance scattering of atom‐diatomic molecule systems involving internal excitations is discussed by fully allowing the topological phase (Berry phase) contribution. Earlier a generalized formalism (Phys. Rev. A 1996, 53, 2433) of the three‐body resonance scattering was presented by introducing the gauge potential (Berry connection). Based on this study we provide additional information on topological importance in resonance scattering involving the atom‐diatomic molecule systems. The massive gauge field (Berry connection) contribution which arises from a broken symmetry is discussed. Its relevance to condensed matter physics will be briefly high lighted in connection with our recent theory of super conductivity (Phys. Rev. B 1999, 60, 6324).
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We derive a resonance field-theory for ultra-cold Bose or Fermi gases that is valid when scattering resonances are present. Experiments with a ^85Rb condensate have shown new interesting physics close to resonance(N.R. Claussen, E.A. Donley, S.T. Thompson, C.E. Wieman, e-print cond-mat/0201400.). It is also expected that utilizing a Feshbach resonance can greatly enhance the critical temperature for superfluidity in a Fermi gas(M. Holland, S.J.J.M.F. Kokkelmans, M.L. Chiofalo, and R. Walser, Phys. Rev. Lett. 87), 120406 (2001).. Therefore it is important to treat the rich scattering physics properly inside a many-body theory. We show that the scattering length only is insufficient to describe a system close to resonance. Our many-body equations have build-in the two-body scattering equations, and we include the full scattering solution over the relevant energy range by means of a renormalized resonance scattering theory(S.J.J.M.F. Kokkelmans, J.N. Milstein, M.L. Chiofalo, R. Walser, and M.J. Holland, e-print cond-mat/0112283.).
The quantum three body problem generally has its own complexities and is difficult to solve. It requires rigorous steps and iterations to find the solution. We often encounter three body system in various branches of physics including Nuclear Physics, Particle, Atomic, Molecular physics, and condensed matter. The underlying physics involved is quite complicated. Faddeev in 1961 made a successful attempt and formulated theory of three particle scattering in a rather rigorous mathematical way. Efimov developed a method that enabled one to obtain the universal properties of three particle system and is quite independent of the two body potentials. This article attempts to introduce Efimov effect. The formalism and the salient features are also discussed.
We extend classical-field methods [Blakie et al., Adv. Phys. 57, 363 (2008)] to provide a description of atom-molecule systems. We use a model of Bose-Einstein condensation of atoms close to a Feshbach resonance, in which the tunable scattering length of the atoms is described using a system of coupled atom and molecule fields [Holland et al., Phys. Rev. Lett. 86, 1915 (2001)]. We formulate the basic theoretical methods for a coupled atom-molecule system, including the determination of the phenomenological parameters in our system, the Thomas-Fermi description of Bose-Einstein condensate, the Bogoliubov--de Gennes equations, and the Bogoliubov excitation spectrum for a homogenous condensed system. We apply this formalism to the special case of Bragg scattering from a uniform condensate and find that for moderate and large scattering lengths, there is a dramatic difference in the shift of the peak of the Bragg spectra, compared to that based on a structureless atom model. The result is compatible with the experimental results of Papp et al. [Phys. Rev. Lett 101, 135301 (2008)] for Bragg scattering from a nonuniform condensate.
In the mean-field theory of atom-molecule systems, where bosonic atoms combine to form molecules, there is no usual U(1)\text{U}(1)U(1) symmetry, presenting an apparent hurdle for defining the Berry phase and Berry curvature for these systems. We define a Berry connection for this system, with which the Berry phase and Berry curvature can be naturally computed. We use a three-level atom-molecule system to illustrate our results. In particular, we have computed the mean-field Berry curvature of this system analytically, and compared it to the Berry curvature computed with the second-quantized model of the same system. An excellent agreement is found, indicating the validity of our definition.