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 (13)

• Superchemistry: dynamics of coupled atomic and molecular Bose-Einstein condensates
• Theory of nonlinear Landau-Zener tunneling
• Adiabatic Theory of Nonlinear Evolution of Quantum States
• Inconsistency in the application of the adiabatic theorem
• Atom-molecule dark states in a Bose-Einstein condensate
• Bose-Stimulated Raman Adiabatic Passage in Photoassociation
• Creating stable molecular condensate using a generalized Raman adiabatic passage scheme
• Accurate determination of the scattering length of metastable Helium atoms using dark resonances between atoms and exotic molecules
• Semiclassical approach to Bose-Einstein condensates in a triple well potential
• Dynamical Instability in a Trimeric Chain of Interacting Bose-Einstein Condensates
• Sub-Natural-Linewidth Quantum Interference Features Observed in Photoassociation of a Thermal Gas
• Comment on "Stimulated Raman adiabatic passage from an atomic to a molecular Bose-Einstein condensate"
• Coherent population trapping and dynamical instability in the nonlinearly coupled atom-molecule system

Cited by in corpus (38)

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• Quantized Fractional Thouless Pumping of Solitons
• The effect of nonlinearity on adiabatic evolution of light
• Nonlinear quantum interferometry with Bose condensed atoms
• Nonlinear dynamics of a cigar-shaped Bose-Einstein condensate coupled with a single cavity mode
• The Chern Number Governs Soliton Motion in Nonlinear Thouless Pumps
• Efficient, Broadband and Robust Frequency Conversion by Fully Nonlinear Adiabatic Three Wave Mixing
• Topological Invariant and Anomalous Edge Modes of Strongly Nonlinear Systems
• 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
• Two dimensional bright solitons in dipolar Bose-Einstein condensates with tilted dipoles
• Berry Phase in Atom-Molecule Conversion Systems and Fractional Monopole
• Coherent atom-trimer conversion in a repulsive Bose-Einstein condensate
• Adiabaticity in nonreciprocal Landau-Zener tunneling
• Properties of a coupled two species atom-heteronuclear molecule condensate
• Dark solitons generation and their instability dynamics in two dimensional condensates
• Broadband sum frequency generation via chirped quasi-phase-matching
• Discrete chaotic states of a Bose-Einstein condensate
• Adiabatic and high-fidelity quantum gates with hybrid Rydberg-Rydberg interactions
• Second order tunneling of two interacting bosons in a driven triple well
• Achieving ground-state polar molecular condensates by chainwise atom-molecule adiabatic passage
• Loschmidt echo and Berry phase around degeneracies in nonlinear systems
• Anomalous Monopole In an Interacting Boson System
• Quantum Noise in the Collective Abstraction Reaction A+B ${}_2\to$ AB+B
• Quantum phase transition in a three-level atom-molecule system
• Interaction-induced instability and chaos in the photoassociative stimulated Raman adiabatic passage from atomic to molecular Bose-Einstein condensates
• Efficient production of polar molecular Bose-Einstein condensates via an all-optical R-type atom-molecule adiabatic passage
• Efficiency limitation for realizing an atom-molecule adiabatic transfer based on a chainwise system
• Coherent bimolecular reactions with quantum-degenerate matter waves
• Deterministic entanglement generation between a pair of atoms on different Rydberg states via chirped adiabatic passage
• Quantum Hamiltonian daemons: unitary analogs of combustion engines
• Stability, Adiabaticity and Transfer efficiency in a nonlinear Λ-system
• Robust switching of superposition-states via a coherent double stimulated Raman adiabatic passage
• Stability of linear and non-linear lambda and tripod systems in the presence of amplitude damping
• Robust stability of quantum interference realized by coexisting detuned and resonant STIRAPs