Stability of linear and non-linear lambda and tripod systems in the presence of amplitude damping

Abstract

We present the stability analysis of the dark states in the adiabatic passage for the linear and non-linear lambda and tripod systems in the presence of amplitude damping (losses). We perform an analytic evaluation of the real parts of eigenvalues of the corresponding Jacobians, the non-zero eigenvalues of which are found from the quadratic characteristic equations, as well as by the corresponding numerical simulations. For non-linear systems, we evaluate the Jacobians at the dark states. Similarly to the linear systems, here we also find the non-zero eigenvalues from the characteristic quadratic equations. We reveal a common property of all the considered systems showing that the evolution of the real parts of eigenvalues can be split into three stages. In each of them the evolution of the stimulated Raman adiabatic passage (STIRAP) is characterized by different effective dimension. This results in a possible adiabatic reduction of one or two degrees of freedom.

30 pages, 12 figures

References in corpus (10)

• Adiabatic Theory of Nonlinear Evolution of Quantum States
• Adiabatic approximation in open quantum systems
• Atom-molecule dark states in a Bose-Einstein condensate
• Adiabatic Condition for Nonlinear Systems
• High-fidelity local addressing of trapped ions and atoms by composite sequences of laser pulses
• 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
• Dephasing effects on stimulated Raman adiabatic passage in tripod configurations
• Slow-light probe of Fermi pairing through an atom-molecule dark state