Strong-coupling regime of the nonlinear landau-zener problem for photo- and magnetoassociation of cold atoms

We discuss the strong-coupling regime of the nonlinear Landau-Zener problem occurring at coherent photo- and magneto-association of ultracold atoms. We apply a variational approach to an exact third-order nonlinear differential equation for the molecular state probability and construct an accurate a...

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Bibliographic Details
Published in:Journal of experimental and theoretical physics 2011-04, Vol.112 (4), p.543-550
Main Authors: Sokhoyan, R., Azizbekyan, H., Leroy, C., Ishkhanyan, A.
Format: Article
Language:English
Subjects:
APPROXIMATIONS
ATOMIC AND MOLECULAR PHYSICS
ATOMS
Classical and Quantum Gravitation
COUPLING
DIFFERENTIAL EQUATIONS
Elementary Particles
LANDAU-ZENER FORMULA
MAGNETISM
MATHEMATICAL SOLUTIONS
MOLECULES
NONLINEAR PROBLEMS
Optics
OSCILLATIONS
Particle and Nuclear Physics
Physics
Physics and Astronomy
PROBABILITY
Quantum Field Theory
Quantum Physics
Relativity Theory
RESONANCE
Solid State Physics
VARIATIONAL METHODS
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Summary:We discuss the strong-coupling regime of the nonlinear Landau-Zener problem occurring at coherent photo- and magneto-association of ultracold atoms. We apply a variational approach to an exact third-order nonlinear differential equation for the molecular state probability and construct an accurate approximation describing the time dynamics of the coupled atom-molecule system. The resultant solution improves the accuracy of the previous approximation [22]. The obtained results reveal a remarkable observation that in the strong-coupling limit, the resonance crossing is mostly governed by the nonlinearity, while the coherent atom-molecule oscillations occurring soon after crossing the resonance are principally of a linear nature. This observation is supposedly general for all nonlinear quantum systems having the same generic quadratic nonlinearity, due to the basic attributes of the resonance crossing processes in such systems. The constructed approximation turns out to have a larger applicability range than it was initially expected, covering the whole moderate-coupling regime for which the proposed solution accurately describes ail the main characteristics of the system evolution except the amplitude of the coherent atom-molecule oscillation, which is rather overestimated.
ISSN:1063-7761
1090-6509
DOI:10.1134/S1063776111020221