  We explain the origin and the nature of a special nonlinear supersymmetry of
a reflectionless Poschl-Teller system by the Aharonov-Bohm effect for a
nonrelativistic particle on the AdS_2. A key role in the supersymmetric
structure appearing after reduction by a compact generator of the AdS_2
isometry is shown to be played by the discrete symmetries related to the space
and time reflections in the ambient Minkowski space. We also observe that a
correspondence between the two quantum non-relativistic systems is somewhat of
the AdS/CFT holography nature.
