Optimal Strategies for Sending Atoms Around the Bend

In this presentation, I will discuss classical and quantum-based optimization schemes to minimize the transverse excitations of a guided cold atom matter wave after that wave has completed a bend, changing direction by a fixed bending angle $\theta_0$ over a pre-determined distance. The waveguide potential is constrained to two dimensions. We carry out the minimization with respect to the trajectory of the waveguide’s potential minimum. To determine the trajectory, we solve for the curvature function $\kappa(s)$ as a function of arc-length that minimizes the transverse excitation energy after the bend. The curved part of the waveguide is treated as a scattering perturbation in curvilinear coordinates. The waveguide that is defined by the minimal $\kappa(s)$-function causes transverse excitations with energy-values that that are orders of magnitude smaller than the transverse energy caused by transition bends with the standard circular or Euler's type (clothoid) curvatures. In the limit of a nearly plane-wave shapes incoming wave, the final transverse excitation energy after the bend can be chosen to vanish.

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