Abstract
A mathematical framework for optimal bilinear control of nonlinear Schrodinger equations of Gross--Pitaevskii type arising in the description of Bose--Einstein condensates is presented. The obtaine...
Highlights
The function U (x) describes an external trapping potential which is necessary for the experimental realization of a Bose– Einstein condensates (BECs)
We find that the algorithm converges well even if we invoke only the first order gradient method
We have introduced a rigorous mathematical framework for optimal quantum control of linear and nonlinear Schrodinger equations of Gross–Pitaevskii type
Summary
From the physical point of view, this is important since it implies continuous (in time) dependence of ψ∗ upon a given initial data ψ0 To this end, one should note that H1(0, T ) → C(0, T ) (using Sobolev embeddings), and the obtained optimal control parameter α∗(t) is a continuous function on [0, T ]. The resulting Cauchy problems for Schrodinger-type equations are solved by a time-splitting spectral method of second order (Strangsplitting), as can be found in [1] This computational approach is unconditionally stable and allows for spectral accuracy in the resolution of the wave function ψ(t, x).
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