Ghost Exchange: Ferromagnetic-antiferromagnetic Phase Transition in Linear Optics of Non-magnetic Dielectrics

While many photonic equivalents exist for the physics originally associated with electronic systems, from Anderson localization to Berezenskii-Kosterlitz-Thouless transition, none of them operating in the linear regime offers the possibility of sign reversal of the exchange interaction inherent to strongly correlated fermionic systems. As a result, many exchange-mediated phenomena of condensed matter physics are currently beyond the reach of a linear photonic platform. Here we break through this obstacle by mapping the effective Hamiltonian for the electronic exchange interaction to that of coupled optical modes, using the oscillatory properties of the recently discovered ghost coupling (Opt. Lett. 46, 1708-1711 (2021)). The resulting "ghost exchange" offers full control of the exchange dynamics and can lead to a photonic analog of the ferromagnetic–antiferromagnetic phase transition.