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Engineering spin-orbit synthetic Hamiltonians in liquid-crystal optical cavities

Inducing optical spin-orbit coupling The coupling of the spin-orbit interactions in solid-state systems can give rise to a wide range of exotic electronic transport effects. But solid-state systems tend to be somewhat limited in their flexibility because the spin-orbit coupling is fixed. By contrast, optical systems have recently been shown to mimic complex solid-state systems, with flexibility in design providing the ability to control and manipulate the system properties. Using a liquid crystal–filled photonic cavity, Rechcińska et al. emulated an artificial Rashba-Dresselhaus spin-orbit coupling in a photonic system and showed control of an artificial Zeeman splitting. The results illustrate a powerful approach of engineering synthetic Hamiltonians with photons for the simulation of nontrivial condensed matter and quantum phenomena. Science, this issue p. 727 Complex Hamiltonians are engineered optically using liquid crystals embedded in a cavity. 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.