We theoretically evaluate changes in the magnetic potential arising from the magnetic field near superconducting thin films. An example of an atom chip based on a three-wire configuration has been simulated in the superconducting and the normal conducting state. Inhomogeneous current densities within the superconducting wires were calculated using an energy-minimization routine based on the London theory. The Meissner effect causes changes to both trap position and oscillation frequencies at short distances from the superconducting surface. Superconducting wires produce much shallower micro traps than normal conducting wires. The results presented in this paper demonstrate the importance of taking the Meissner effect into account when designing and carrying out experiments on magnetically trapped neutral atoms near superconducting surfaces.
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