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Moдель демкова–кунике для ассоциации холодных атомов: режим слабого взаимодействия.

Claude Leroy, Ruzan Sokhoyan, H. H. Azizbekyan, Artur Mikhailovich Ishkhanyan

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

We examine the nonlinear dynamics of molecule formation at coherent photo- and magneto-association of an atomic Bose–Einstein condensate when the external field configuration is defined by the quasi-linear level crossing Demkov–Kunike model, characterized by a bell-shaped pulse and finite variation of the detuning. We present an approach to construct an approximation describing the temporal dynamics of the molecule formation in the weak interaction regime and apply the developed method to the nonlinear Demkov–Kunike problem. The presented approximation, written as a scaled solution to the linear problem associated to the nonlinear one we treat, contains adjustable parameters which are determined through a variational procedure. Assuming that the parameters include in the solution of the linear problem are not modified, we suggest an analytical relation for the scaling parameter.

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•Sep 7, 2010•0 citations
We examine the nonlinear dynamics of molecule formation at coherent photo- and magneto-association of an atomic Bose–Einstein condensate when the external field configuration is defined by the quasi-linear level crossing Demkov–Kunike model, characterized by a bell-shaped pulse and finite variation of the detuning. We present an approach to construct an approximation describing the temporal dynamics of the molecule formation in the weak interaction regime and apply the developed method to the nonlinear Demkov–Kunike problem. The presented approximation, written as a scaled solution to the linear problem associated to the nonlinear one we treat, contains adjustable parameters which are determined through a variational procedure. Assuming that the parameters include in the solution of the linear problem are not modified, we suggest an analytical relation for the scaling parameter.
We study the nonlinear mean-field dynamics of molecule formation at coherent photo- and magneto-association of an atomic Bose-Einstein condensate for the case when the external field configuration is defined by the quasi-linear level crossing Demkov-Kunike model, characterized by a bell-shaped pulse and finite variation of the detuning. We present a general approach to construct an approximation describing the temporal dynamics of the molecule formation in the weak interaction regime and apply the developed method to the nonlinear Demkov-Kunike problem. The presented approximation, written as a scaled solution to the linear problem associated to the nonlinear one we treat, contains fitting parameters which are determined through a variational procedure. Assuming that the parameters involved in the solution of the linear problem are not modified, we suggest an analytical expression for the scaling parameter.
We study the dynamics of cold molecule formation via photo- or magneto-association of quantum degenerate atomic gases for the case when the field configuration is defined by the quasi-linear level crossing Demkov-Kunike model, which is characterized by a bell-shaped pulse and finite variation of the frequency detuning. We generalize the approach developed for the Landau-Zener model and propose a cubic polynomial equation for the asymptotic transition probability at t → + ∞ applicable in the large detuning regime of the interaction process. The proposed approximation applies to all values of the Rabi frequency; hence, it presents a unified description of previously noticed weak, moderate, and strong interaction limits of the fast sweep regime. This cubic equation for the transition probability provides improvement of previous results by an order of the magnitude.
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.
We study a quadratic-nonlinear version of the level-crossing Demkov-Kunike problem relevant to coherent molecule formation via photo- or Feshbach-association of ultracold atoms. Using an exact third-order nonlinear differential equation for the molecular state probability, we construct an approximate solution to the problem in the fast sweep regime of the strong interaction limit. The constructed approximation, defined as a solution of a first-order nonlinear equation, contains a fitting parameter which we determine through a variational procedure. The suggested approach can be interpreted as a modification of the adiabatic approximation and can further be used for the treatment of analogous nonlinear two-state problems.
In the framework of a basic semiclassical time-dependent nonlinear two-state problem, we study the weak coupling limit of the nonlinear Landau-Zener transition at coherent photo- and magneto-association of an atomic Bose-Einstein condensate. Using an exact third-order nonlinear differential equation for the molecular state probability, we develop a variational approach which enables us to construct an accurate analytic approximation describing time dynamics of the coupled atom-molecular system for the case of weak coupling. The approximation is written in terms of the solution to an auxiliary linear Landau-Zener problem with some effective Landau-Zener parameter. The dependence of this effective parameter on the input Landau-Zener parameter is found to be unexpected: as the generic Landau-Zener parameter increases, the effective Landau-Zener parameter first monotonically increases (starting from zero), reaches its maximal value and then monotonically decreases again reaching zero at some point. The constructed approximation quantitatively well describes many characteristics of the time dynamics of the system, in particular, it provides a highly accurate formula for the final transition probability to the molecular state. The present result for the final transition probability improves the accuracy of the previous approximation by Ishkhanyan et al. [Phys. Rev. A 69 , 043612 (2004); J. Phys. A 38 , 3505 (2005)] by order of magnitude.
Using an exact third-order NL di®erential equation for the molecular state probability, we develop a variational approach which enables us to construct highly accurate analytic approximations describing time dynamics of the coupled atom-molecular system in each of the interaction regimes. We show that the approximation describing time evolution of the molecular state probability both in the weak interaction limit and in the large detuning regime of the strong interaction limit can be written as a sum of two distinct terms; the ¯rst one, being a solution to a limit ¯rst-order NL equation, e®ectively describes the process of the molecule formation while the second one, being a scaled solution to the linear DK problemb (but now with modi¯ed parameters), models the remaining oscillations which come up when the process of molecule formation is over. The graphs of the approximate and numerical solutions are practically indistinguishable for almost all the time range.