Abstract
We propose an inverse method to accelerate without final excitation the adiabatic transport of a Bose–Einstein condensate. The method is based on a partial extension of the Lewis–Riesenfeld invariants and provides transport protocols that satisfy exactly the no-excitation conditions without approximations. This inverse method is complemented by optimizing the trap trajectory with respect to different physical criteria and by studying the effect of perturbations such as anharmonicities and noise.
Highlights
Our starting point is the GPE for potentials whose Schrodinger dynamics admit a quadratic invariant in momentum [8, 14,15,16,17]
Without the nonlinear term, it follows from the Lewis–Riesenfeld invariant theory [18, 19] that the solution can be written as ψ
Optimal control theory (OCT) combined with the inverse method, see below, provides a way of designing trajectories taking these restrictions into account
Summary
Our starting point is the GPE for potentials whose Schrodinger (linear) dynamics admit a quadratic invariant in momentum [8, 14,15,16,17],. Τ satisfies an SE with a time-independent Hamiltonian. These results can be generalized partially for the GPE, and the extent of the generalization depends on the process type. Inserting (4) as an ansatz for a time-dependent solution of the GPE, φ(σ , τ ) must satisfy ih. Equation (5) is very general and applicable to compressions, expansions or transport driven by harmonic or anharmonic potentials. It is most useful when ρ2−DgD does not depend on time, since the physical solution of the time-dependent problem is mapped, via (4), to the solution of a much simpler stationary equation. Different time scalings combined with a Thomas–Fermi approximation lead to a stationary equation [11]
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