Making use of self-assembly techniques, we realize nanoscopic semiconductor quantum rings in which the electronic states are in the true quantum limit. We employ two complementary spectroscopic techniques to investigate both the ground states and the excitations of these rings. Applying a magnetic field perpendicular to the plane of the rings, we find that, when approximately one flux quantum threads the interior of each ring, a change in the ground state from angular momentum ᐉ 0 to ᐉ 21 takes place. This ground state transition is revealed both by a drastic modification of the excitation spectrum and by a change in the magnetic-field dispersion of the single-electron charging energy. PACS numbers: 73.20.Dx, 03.65.Bz, 78.66.Fd The fascination of ringlike atomic and quantum structures dates back to Kekulé's famous proposal of the structure of benzene [1]. Particularly interesting are the magnetic properties of such nonsimply connected quantum systems, which are related to the possibility of trapping magnetic flux in their interior. Trapping of a single flux quantum in a small molecule such as benzene is impossible with the magnetic fields available in today's laboratories. In recent years, however, the availability of submicron solid-state ring structures has triggered a strong interest in the magnetic properties of rings, especially in view of the fact that, even in the presence of scattering, the many-particle ground state becomes chiral in a magnetic field, which leads to so-called "persistent currents" [2]. The large body of theoretical work on the properties of quantum rings [3] is accompanied by a number of ground breaking experimental investigations of the magnetic and transport properties of rings [4]. These studies have been carried out in the mesoscopic range, where scattering still influences the phase coherent transport, and a large number of quantum states are filled. To the best of our knowledge, no spectroscopic data is available on rings in the scatter-free, few-electron quantum limit. Furthermore, despite a strong theoretical interest [5,6], the only data available on the excitations of rings were taken on macroscopic structures [7].Here, we report on the spectroscopy of the ground states and excitations of self-assembled, nanoscopic InGaAs quantum rings, occupied with one or two electrons each, and subjected to magnetic fields 0 # B # 12 T, corresponding to 0-1.5 flux quanta threading the interior of the ring. In both ground state and excitation spectroscopies we observe characteristic changes at about B 8 T which are attributed to the development of a magneticfield-induced chiral ground state.The quantum rings are fabricated by solid-source molecular-beam epitaxy, using the Stranski-Krastanov growth mode, which has now become a well-established technique for the fabrication of high-quality, selfassembled semiconductor nanostructures [8]. Recently, we reported on a remarkable change in morphology when InAs self-assembled dots, grown on GaAs, are covered with a thin layer of GaAs and annealed...