Nanoscale quantum dots in microwave cavities can be used as a laboratory for
exploring electron-electron interactions and their spin in the presence of
quantized light and a magnetic field. We show how a simple theoretical model of
this interplay at resonance predicts complex but measurable effects. New
polariton states emerge that combine spin, relative modes, and radiation. These
states have intricate spin-space correlations and undergo polariton transitions
controlled by the microwave cavity field. We uncover novel topological effects
involving highly correlated spin and charge density, that display
singlet-triplet and inhomogeneous Bell-state distributions. Signatures of these
transitions are imprinted in the photon distribution, which will allow for
optical read out protocols in future experiments and nanoscale quantum
technologies.Comment: 28 pages, 7 figures, supplementary material is located after the
bibliograph