  We have constructed an asymmetric matter-wave beam splitter and a ring
potential on an atom chip with Bose-Einstein condensates using radio-frequency
dressing. By applying rf-field parallel to the quantization axis in the
vicinity of the static trap minima added to perpendicular rf-fields, versatile
controllability on the potentials is realized. Asymmetry of the rf-induced
double well is manipulated without discernible displacement of the each well
along horizontal and vertical direction. Formation of an isotropic ring
potential on an atom chip is achieved by compensating the gradient due to
gravity and inhomogeneous coupling strength. In addition, position and rotation
velocity of a BEC along the ring geometry are controlled by the relative phase
and the frequency difference between the rf-fields, respectively.
