  We report on the magnetic trapping of an ultracold ensemble of $^{87}$Rb
atoms close to a superconducting ring prepared in different states of quantized
magnetic flux. The niobium ring of 10 $\mu$m radius is prepared in a flux state
$n \Phi_0$, with $\Phi_0 = h / 2e$ the flux quantum and $n$ varies between $\pm
5$. An atomic cloud of 250 nK temperature is positioned with a harmonic
magnetic trapping potential at $\sim 18 \mu$m distance below the ring. The
inhomogeneous magnetic field of the supercurrent in the ring contributes to the
magnetic trapping potential of the cloud. The induced deformation of the
magnetic trap impacts the shape of the cloud, the number of trapped atoms as
well as the center-of-mass oscillation frequency of Bose-Einstein condensates.
When the field applied during cooldown of the chip is varied, the change of
these properties shows discrete steps that quantitatively match flux
quantization.
