FINDINGS FROM A. ISHKHANYAN AND CO-RESEARCHERS ADVANCE KNOWLEDGE IN OPTICAL PHYSICS

News of Science
January 24, 2010

"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.