Adiabatic Condition for Nonlinear Systems

Abstract

We revisit the adiabatic criterion in stimulated Raman adiabatic passage for the three-level $\Lambda$-system, and compare the situation with and without nonlinearity. In linear systems, the adiabatic condition is derived with the help of the instantaneous eigenvalues and eigenstates of the Hamiltonian, a procedure that breaks down in the presence of nonlinearity. Using an explicit example relevant to photoassociation of atoms into diatomic molecules, we demonstrate that the proper way to derive the adiabatic condition for the nonlinear systems is through a linearization procedure.

4 pages, 3 figures

References in corpus (4)

• Adiabatic Theory of Nonlinear Evolution of Quantum States
• Atom-molecule dark states in a Bose-Einstein condensate
• Semiclassical approach to Bose-Einstein condensates in a triple well potential
• Dynamical Instability in a Trimeric Chain of Interacting Bose-Einstein Condensates

Cited by in corpus (10)

• Nonlinear dynamics of a cigar-shaped Bose-Einstein condensate coupled with a single cavity mode
• Two-mode Bose-Einstein condensate in a high-frequency driving field that directly couples the two modes
• Integrability, stability, and adiabaticity in nonlinear stimulated Raman adiabatic passage
• Adiabatic Fidelity for Atom-Molecule Conversion in a Nonlinear Three-Level Λ-system
• Coherent atom-trimer conversion in a repulsive Bose-Einstein condensate
• Properties of a coupled two species atom-heteronuclear molecule condensate
• Discrete chaotic states of a Bose-Einstein condensate
• Loschmidt echo and Berry phase around degeneracies in nonlinear systems
• Quantum Noise in the Collective Abstraction Reaction A+B ${}_2\to$ AB+B
• Coherent bimolecular reactions with quantum-degenerate matter waves