14 research outputs found
Quadratic-nonlinear Landau-Zener transition for association of an atomic Bose-Einstein condensate with inter-particle elastic interactions included
We study the strong coupling limit of a quadratic-nonlinear Landau-Zener
problem for coherent photo- and magneto-association of cold atoms taking into
account the atom-atom, atom-molecule, and molecule-molecule elastic scattering.
Using an exact third-order nonlinear differential equation for the molecular
state probability, we develop a variational approach which enables us to
construct a highly accurate and simple analytic approximation describing the
time dynamics of the coupled atom-molecule system. We show that the
approximation describing time evolution of the molecular state probability can
be written as a sum of two distinct terms; the first one, being a solution to a
limit first-order nonlinear equation, effectively describes the process of the
molecule formation while the second one, being a scaled solution to the linear
Landau-Zener problem (but now with negative effective Landau-Zener parameter as
long as the strong coupling regime is considered), corresponds to the remaining
oscillations which come up when the process of molecule formation is over.Comment: 19 pages, 7 figures, accepted for publication in Eur. Phys. J.
An ansatz for the nonlinear Demkov-Kunike problem for cold molecule formation
We study nonlinear mean-field dynamics of ultracold molecule formation in the
case when the external field configuration is defined by the level-crossing
Demkov-Kunike model, characterized by a bell-shaped coupling and finite
variation of the detuning. Analyzing the fast sweep rate regime of the strong
interaction limit, which models a situation when the peak value of the coupling
is large enough and the resonance crossing is sufficiently fast, we construct a
highly accurate ansatz to describe the temporal dynamics of the molecule
formation in the mentioned interaction regime. The absolute error of the
constructed approximation is less than 3*10^-6 for the final transition
probability while at certain time points it might increase up to 10^-3.
Examining the role of the different terms in the constructed approximation, we
prove that in the fast sweep rate regime of the strong interaction limit the
temporal dynamics of the atom-molecule conversion effectively consists of the
process of resonance crossing, which is governed by a nonlinear equation,
followed by atom-molecular coherent oscillations which are basically described
by a solution of the linear problem, associated with the considered nonlinear
one.Comment: Accepted for publication in J. Contemp. Phys. (Armenian National
Academy of Sciences) 8 pages, 4 figure