2006/12/20 by Artur Ishkhanyan, А. М. Ishkhanyan, Hiroki Nakamura · 2 citations
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Coupling (piping) #Coupling constant #Exponential function #Feshbach resonance #Limit (mathematics) #Mathematical analysis #Mathematics #Molecule #Nonlinear system #Optical properties and cooling technologies in crystalline materials #Physics #Population #Quantum #Quantum electrodynamics #Quantum mechanics #Resonance (particle physics) #Semiclassical physics #Strong Light-Matter Interactions #cond-mat.quant-gas
paper · pdf · doi:10.1103/physreva.74.063414
published as Phys. Rev. A 74, 063414 (2006)
openalex publication_date 2006/12/20 · arxiv created 2009/09/02 · arxiv updated 2015/05/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The strong-coupling limit of molecule formation in an atomic Bose-Einstein condensate via two-mode one-color photoassociation or sweep across a Feshbach resonance is examined using a basic nonlinear time-dependent two-state model. For the general class of term-crossing models with constant coupling, a common strategy for attacking the problem is developed based on the reduction of the initial system of semiclassical equations for atom-molecule amplitudes to a third-order nonlinear differential equation for the molecular state probability. This equation provides deriving exact solution for a class of periodic level-crossing models. These models reveal much in common with the Rabi problem. Discussing the strong-coupling limit for the general case of variable detuning, the equation is further truncated to a limit first-order nonlinear equation. Using this equation, the strong nonlinearity regime for the first Nikitin exponential-crossing model is analyzed and accurate asymptotic expressions for the nonlinear transition probability to the molecular state are derived. It is shown that, because of a finite final detuning involved, this model displays essential deviations from the Landau-Zener behavior. In particular, it is shown that in the limit of strong coupling the final conversion probability tends to 1∕6. Thus, in this case the strong interaction limit is not optimal for molecule formation. We have found that if optimal field intensity is applied the molecular probability is increased up to 1∕4 (i.e., the half of the initial atomic population).