Spin–orbit interaction of light induced by transverse spin angular momentum engineering. Tunable topological charge vortex microlaser. 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. 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. Here we demonstrate a hyperdimensional, spin–orbit microlaser for chip-scale flexible generation and manipulation of arbitrary four-level states. Even with extensive efforts dedicated to recently emerged vector lasers and microcavities for the expansion of dimensionalities 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, it still remains a challenge to actively tune the diversified, high-dimensional superposition states of light on demand. 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. 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.
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