Interaction-induced hopping phase and tristability
We recently demonstrated how to control the phase that a photon picks when hopping between cavities. We accomplished this using photon-photon interactions in a photonic molecule.
Nature Commun. 7, 11887 (2016). pdf
Inspired by the success of Bose-Hubbard model (BHM) simulators with atoms in optical lattices, proposals for implementing the non-equilibrium BHM with photons have emerged. Coupled nonlinear microcavities embedded with excitonic materials are promising systems in this context. Photons in a cavity can couple strongly to excitons, giving rise to composite light-matter quasi-particles known as polaritons. Polaritons can be confined and coupled via the photonic part of their wavefunction, while polariton-polariton interactions are mediated by the excitonic part. Thus, coupled polaritons exhibit rich nonlinear dynamics, and a number of instabilities, as driving, hopping, interactions, and decay compete in setting a stationary state.
Photonic Bose-Hubbard dimer
Recently we investigated the minimal system described by the BHM, i.e. a dimer, under selective driving of one site. We observed three distinct density profiles at a given driving condition, i.e. spatial tristability. Moreover, we demonstrated that the intracavity field phase difference between the coupled microcavities can be controlled by means of effective polariton-polariton interactions.
These results demonstrate how interference can be controlled by interactions in a photonic system. When extended to multicavity systems, this mechanism could enable the realization of non-Hermitian Hamiltonians with density-dependent gauge fields. The proposed extension relates to the seminal work by Aharanov & Bohm, and Berry, who realized that a nonzero phase acquired by a particle in a closed-loop trajectory implies the existence of a nonzero vector potential A. Thus, synthethic magnetism and topological features could be engineered in multicavity photonic systems by means of interactions.