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.
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