Spin-orbit interactions lead to distinctive functionalities in photonic systems. They exploit the analogy between the quantum mechanical description of a complex electronic spin-orbit system and synthetic Hamiltonians derived for the propagation of electromagnetic waves in dedicated spatial structures. We realize an artificial Rashba-Dresselhaus spin-orbit interaction in a liquid crystal–filled optical cavity. Three-dimensional tomography in energy-momentum space enabled us to directly evidence the spin-split photon mode in the presence of an artificial spin-orbit coupling. The effect is observed when two orthogonal linear polarized modes of opposite parity are brought near resonance. Engineering of spin-orbit synthetic Hamiltonians in optical cavities opens the door to photonic emulators of quantum Hamiltonians with internal degrees of freedom.

We consider a two-dimensional (2D) nonlinear Schrödinger equation with self-focusing nonlinearity and a quasi-1D double-channel potential, i.e., a straightforward 2D extension of the well-known double-well potential. The model may be realized in terms of nonlinear optics and Bose-Einstein condensates. The variational approximation (VA) predicts a bifurcation breaking the symmetry of 2D solitons trapped in the double channel, the bifurcation being of the subcritical type. The predictions of the VA are confirmed by numerical simulations. The work presents the first example of the spontaneous symmetry breaking (SSB) of 2D solitons in any dual-core system.

Bosonic condensates of exciton polaritons (light-matter quasiparticles in a semiconductor) provide a solid-state platform for studies of non-equilibrium quantum systems with a spontaneous macroscopic coherence. These driven, dissipative condensates typically coexist and interact with an incoherent reservoir, which undermines measurements of key parameters of the condensate. Here, we overcome this limitation by creating a high-density exciton-polariton condensate in an opticallyinduced box trap. In this so-called Thomas-Fermi regime, the condensate is fully separated from the reservoir and its behaviour is dominated by interparticle interactions. We use this regime to directly measure the polariton-polariton interaction strength, and reduce the existing uncertainty in its value from four orders of magnitude to within three times the theoretical prediction. The Thomas-Fermi regime has previously been demonstrated only in ultracold atomic gases in thermal equilibrium. In a non-equilibrium exciton-polariton system, this regime offers a novel opportunity to study interaction-driven effects unmasked by an incoherent reservoir.

We analyze the structure of spin-1 Bose-Einstein condensates in the presence of a homogenous magnetic field. We classify the homogenous stationary states and study their existence, bifurcations, and energy spectra. We reveal that the phase separation can occur in the ground state of polar condensates, while the spin components of the ferromagnetic condensates are always miscible and no phase separation occurs. Our theoretical model, confirmed by numerical simulations, explains that this phenomenon takes place when the energy of the lowest homogenous state is a concave function of the magnetization. In particular, we predict that phase separation can be observed in a 23 Na condensate confined in a highly elongated harmonic trap. Finally, we discuss the phenomena of dynamical instability and spin domain formation.