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News of Science
January 24, 2010
OPTICAL PHYSICS;
Findings from A. Ishkhanyan and co-researchers advance knowledge in
optical physics
"We present a rigorous analysis of the Landau-Zener linear-in-time
term crossing problem for quadratic-nonlinear systems relevant to the
coherent association of ultracold atoms in degenerate quantum gases.
Our treatment is based on an exact third-order nonlinear differential
equation for the molecular state probability," scientists in Armenia
report.
"Applying a variational two-term ansatz, we construct a simple
approximation that accurately describes the whole-time dynamics of the
coupled atom-molecular system for any set of involved parameters.
Ensuring an absolute error of less than 10(-5) for the final
transition probability, the resultant solution improves by several
orders of magnitude the accuracy of the previous approximations by A
Ishkhanyan et al developed separately for the weak coupling (2005 J.
Phys. A: Math. Gen. 38 3505) and strong interaction (2006 J. Phys. A:
Math. Gen. 39 14887) limits. In addition, the constructed
approximation covers the whole moderate-coupling regime, providing
this intermediate regime with the same accuracy as the two mentioned
limits. The obtained results reveal the remarkable observation, that
for the strong-coupling limit the resonance crossing is mostly
governed by the nonlinearity, while the coherent atom-molecular
oscillations arising soon after the resonance has been crossed are
basically of a linear nature," wrote A. Ishkhanyan and colleagues.
The researchers concluded: "This observation is supposed to be of a
general character, due to the basic attributes of the
resonance-crossing processes in the nonlinear quantum systems of the
discussed type of involved quadratic nonlinearity."
Ishkhanyan and colleagues published their study in the Journal of
Physics B - Atomic Molecular and Optical Physics (Variational ansatz
for the nonlinear Landau-Zener problem for cold atom association.
Journal of Physics B - Atomic Molecular and Optical Physics,
2009;42(22):21002).
For additional information, contact A. Ishkhanyan, NAS Armenia,
Institute Physics Research, Ashtarak 0203 2, Armenia.
The publisher's contact information for the Journal of Physics B -
Atomic Molecular and Optical Physics is: IOP Publishing Ltd., Dirac
House, Temple Back, Bristol BS1 6BE, England.
January 24, 2010
OPTICAL PHYSICS;
Findings from A. Ishkhanyan and co-researchers advance knowledge in
optical physics
"We present a rigorous analysis of the Landau-Zener linear-in-time
term crossing problem for quadratic-nonlinear systems relevant to the
coherent association of ultracold atoms in degenerate quantum gases.
Our treatment is based on an exact third-order nonlinear differential
equation for the molecular state probability," scientists in Armenia
report.
"Applying a variational two-term ansatz, we construct a simple
approximation that accurately describes the whole-time dynamics of the
coupled atom-molecular system for any set of involved parameters.
Ensuring an absolute error of less than 10(-5) for the final
transition probability, the resultant solution improves by several
orders of magnitude the accuracy of the previous approximations by A
Ishkhanyan et al developed separately for the weak coupling (2005 J.
Phys. A: Math. Gen. 38 3505) and strong interaction (2006 J. Phys. A:
Math. Gen. 39 14887) limits. In addition, the constructed
approximation covers the whole moderate-coupling regime, providing
this intermediate regime with the same accuracy as the two mentioned
limits. The obtained results reveal the remarkable observation, that
for the strong-coupling limit the resonance crossing is mostly
governed by the nonlinearity, while the coherent atom-molecular
oscillations arising soon after the resonance has been crossed are
basically of a linear nature," wrote A. Ishkhanyan and colleagues.
The researchers concluded: "This observation is supposed to be of a
general character, due to the basic attributes of the
resonance-crossing processes in the nonlinear quantum systems of the
discussed type of involved quadratic nonlinearity."
Ishkhanyan and colleagues published their study in the Journal of
Physics B - Atomic Molecular and Optical Physics (Variational ansatz
for the nonlinear Landau-Zener problem for cold atom association.
Journal of Physics B - Atomic Molecular and Optical Physics,
2009;42(22):21002).
For additional information, contact A. Ishkhanyan, NAS Armenia,
Institute Physics Research, Ashtarak 0203 2, Armenia.
The publisher's contact information for the Journal of Physics B -
Atomic Molecular and Optical Physics is: IOP Publishing Ltd., Dirac
House, Temple Back, Bristol BS1 6BE, England.