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.