Physics – Quantum Physics
Scientific paper
2011-10-28
Physics
Quantum Physics
14 pages, 9 figures
Scientific paper
We present the stability analysis of the dark states in the adiabatic passage for the linear and nonlinear lambda and tripod systems. For the linear systems, using the basis comprising bright, excited and dark states the first two states can be adiabatically eliminated. Subsequently the system evolves in the 1D (the lambda system) or 2D (the tripod system) Hilbert subspaces. The validity of such approximations is confirmed by an analytic evaluation of the real parts of eigenvalues of the corresponding Jacobians, the non-zero eigenvalues of which are found from quadratic characteristic equations, as well as by the corresponding numerical simulations. The number of negative real parts dictates the number of variables that can be adiabatically eliminated. The number of zero real parts yields the dimensionality of the remaining system. In the cases of nonlinear 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. A distinctive feature of nonlinear systems is the absence of the principle of superposition making the stability analysis more complex.
Juzeliunas Gediminas
Pyragas Viktoras
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