Fig. 1. (a) The wire layout to generate a ring potential on the chip and the definition of the azimuthal angle φ. The radius of the ring potential is 1000 μm and the separation distance between the successive turnings is 110 μm, which determines the height location of the ring potential. (b) The minimum of the magnetic field at a fixed azimuthal angle φ with a dc current of 1 A. Bmin (red line) is the magnetic field strength of the minimum. Br (purple line), Bφ (blue dashed line), and Bz (brown dashed line) are the three components of Bmin in the cylindrical coordinate system. The variation of the minimum of the magnetic field is about 1 G.

Fig. 2. Time-averaged magnetic field of the minimum at a fixed azimuthal angle φ with a rotation bias magnetic field. The magnitude of the bias magnetic field is 2 G. The variation of the minimum of magnetic field is 0.14 G.

Fig. 3. Locus of the position of the instantaneous zero points (blue lines), known as the circle of death, and the time-averaged minimum points (red line). The circles of death are two circles around the minimum of the ring waveguide. The image in the center shows a zoomed-in view of a slice of the circles of death. The radius of death is about 10 μm.

Fig. 4. Variation of the characteristics of the time-averaged potential as a function of the magnitude of the bias field B0. (a) The filed gradient in the z direction (blue line) and the radius of death (red dashed line) are represented by Bz′ and rD, respectively. (b) The trap of depth (blue line) and the variation of the minimum of magnetic field (red dashed line) are represented by UD and δB, respectively.