Polariton condensates are macroscopic quantum states formed by half-matter half-light quasiparticles, thus connecting the phenomena of atomic Bose-Einstein condensation, superfluidity, and photon lasing. Here we report the spontaneous formation of such condensates in programmable potential landscapes generated by two concentric circles of light. The imposed geometry supports the emergence of annular states that extend up to 100 μm, yet are fully coherent and exhibit a spatial structure that remains stable for minutes at a time. These states exhibit a petal-like intensity distribution arising due to the interaction of two superfluids counterpropagating in the circular waveguide defined by the optical potential. In stark contrast to annular modes in conventional lasing systems, the resulting standing wave patterns exhibit only minimal overlap with the pump laser itself. We theoretically describe the system using a complex Ginzburg-Landau equation, which indicates why the condensate wants to rotate. Experimentally, we demonstrate the ability to precisely control the structure of the petal condensates both by carefully modifying the excitation geometry as well as perturbing the system on ultrafast timescales to reveal unexpected superfluid dynamics.interferometer | rings | BEC | SQUID C ircular loops are a key geometry for superfluid and superconducting devices because rotation around a closed ring is coupled to the phase of a quantum wavefunction; so far, however, they have not been optically accessible, although this would enable a new class of quantum devices, particularly if room temperature condensate operation is achieved.In lasing systems with an imposed circular symmetry, an annulus of lasing spots can sometimes form along the perimeter of the structure (1-6). Such transverse modes are often referred to as "petal states" (1) or "daisy modes" (2) and are interpreted as annular standing waves (3), whispering gallery modes (4), or coherent superpositions of Laguerre-Gauss (LG) modes with zero radial index (5, 6). Their circular symmetry makes them interesting for numerous applications such as free space communication or fiber coupling (7), and their LG-type structure suggests implementations using the orbital angular momentum of light (8), such as optical trapping (9) or quantum information processing (10). Petal states have been reported for various conventional lasing systems, including electrically and optically pumped vertical cavity surface-emitting lasers (VCSELs) (2, 4), as well as microchip (6) and rod lasers (1).A fundamentally different type of lasing system is the polariton laser (11,12). Polaritons are bosonic quasiparticles, resulting from the strong coupling between microcavity photons and semiconductor excitons (11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21). Their small effective mass (bestowed by their photonic component) and strong interactions (arising from their excitonic component) favor Bose-stimulated condensation into a single quantum state, called a polariton condensate (14,15). These full...