Landau-Zener Problem for Trilinear Hamiltonians
arXiv:physics/0205018 · doi:10.1103/PhysRevA.69.043612
Abstract
We consider a nonlinear version of the Landau-Zener problem, focusing on photoassociation of a Bose-Einstein condensate as a specific example. Contrary to the exponential rate dependence obtained for the linear problem, a series expansion technique indicates that, when the resonance is crossed slowly, the probability for failure of adiabaticity is directly proportional to the rate at which the resonance is crossed.
4.5 pages, 1 figure, transferred to PRA; v2 adds discussion, clarification, and explicit numbers for Na and 87Rb
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Cited by in corpus (23)
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- Nonlinear adiabatic passage from fermion atoms to boson molecules
- Superparabolic Level Glancing Models for Two-State Quantum Systems
- Adiabatic passage through chaos
- Variational ansatz for the nonlinear Landau-Zener problem for cold atom association
- Detuning-induced robustness of a three-state Lanzau-Zener model against dissipation
- Interaction induced Landau-Zener transitions
- Three-state Landau-Zener model in the presence of dissipation
- Generalized formula for the Landau-Zener transition in interacting Bose-Einstein condensates
- Dynamics of a two-state system through a real level crossing
- Many-body adiabatic passage: Quantum detours around chaos
- Semiclassical Spectrum of Small Bose-Hubbard Chains: A Normal Form Approach
- Weak coupling regime of the Landau-Zener transition for association of an atomic Bose-Einstein condensate
- Rosen-Zener model in cold molecule formation
- Strong-coupling limit in cold-molecule formation via photoassociation or Feshbach resonance through Nikitin exponential resonance crossing
- Landau-Zener transition in quadratic-nonlinear two-state systems
- Interaction-induced instability and chaos in the photoassociative stimulated Raman adiabatic passage from atomic to molecular Bose-Einstein condensates
- Master equation approach to the three-state open Majorana model
- Degenerate Landau-Zener model in the presence of quantum noise
- Open multistate Majorana model
- Demkov-Kunike model in cold molecule formation