Spin-orbit microlaser emitting in a four-dimensional Hilbert space.

A step towards the next generation of high-capacity, noise-resilient communication and computing technologies is a substantial increase in the dimensionality of information space and the synthesis of superposition states on an N-dimensional (N > 2) Hilbert space featuring exotic group symmetries. Despite the rapid development of photonic devices and systems, on-chip information technologies are mostly limited to two-level systems owing to the lack of sufficient reconfigurability to satisfy the stringent requirement for 2(N - 1) degrees of freedom, intrinsically associated with the increase of synthetic dimensionalities. Even with extensive efforts dedicated to recently emerged vector lasers and microcavities for the expansion of dimensionalities1-10, it still remains a challenge to actively tune the diversified, high-dimensional superposition states of light on demand. Here we demonstrate a hyperdimensional, spin-orbit microlaser for chip-scale flexible generation and manipulation of arbitrary four-level states. Two microcavities coupled through a non-Hermitian synthetic gauge field are designed to emit spin-orbit-coupled states of light with six degrees of freedom. The vectorial state of the emitted laser beam in free space can be mapped on a Bloch hypersphere defining an SU(4) symmetry, demonstrating dynamical generation and reconfiguration of high-dimensional superposition states with high fidelity.