Synthetic crystal lattices provide ideal environments for simulating and exploring the band structure of solid-state materials in clean and controlled experimental settings. Physical realisations have, so far, dominantly focused on implementing irreversible patterning of the system, or interference techniques such as optical lattices of cold atoms. Here, we realise reprogrammable synthetic band-structure engineering in an all optical exciton-polariton lattice. We demonstrate polariton condensation into excited states of linear one-dimensional lattices, periodic rings, dimerised non-trivial topological phases, and defect modes utilising malleable optically imprinted non-Hermitian potential landscapes. The stable excited nature of the condensate lattice with strong interactions between sites results in an actively tuneable non-Hermitian analogue of the Su-Schrieffer-Heeger system.

We investigate the spin behaviour of the first excited state of a polariton condensate in an optical trap by means of polarisation resolved spectroscopy. The interplay between the repulsive polariton interactions and the gain saturation results in a non-trivial spontaneous switching between the two quasi-degenerate spatial modes of the polariton condensate. As a result the polarisation pattern of the emitted light dramatically changes. Successful harnessing of this effect can lead to a spindemultiplexing device for polariton based optical integrated circuits.

Interferometric measurements of an optically trapped exciton-polariton condensate reveal a regime where the condensate pseudo-spin precesses persistently within the driving optical pulse. For a single 20 µs optical pulse the condensate pseudo-spin undergoes over 10 5 full precessions with striking frequency stability. The emergence of the precession is traced to polariton non-linear interactions, that give rise to a self-induced out-of-plane magnetic field, which in turn drives the system spin dynamics. The Larmor precession frequency and trajectory is directly influenced by the condensate density, enabling the control of this effect with optical means. Our results accentuate the system's potential for the realization of magnetometry devices and can lead to the emergence of spin-squeezed polariton condensates.

We demonstrate spin polarized jets in extended systems of ballistic exciton-polariton condensates in semiconductor microcavities using optical non-resonant excitation geometries. The structure of the spin jets is determined by the digitally reprogrammable, spatially non-uniform, degree of circular polarization of the excitation laser. The presence of the laser excitation, strong particle interactions, and spin-relaxation leads to a tunable spin-dependent potential landscape for polaritons, with the appearance of intricate polarization patterns due to coherent matter-wave interference. Our work realizes polarization-structured coherent light sources in the absence of gauge fields.

First order coherence measurements of a polariton condensate, reveal a regime where the condensate pseudo-spin precesses persistently within the driving optical pulse. Within a single 20 µs optical pulse the condensate pseudo-spin performs over 10 5 precessions with striking frequency stability. The condensate maintains its phase coherence even after a complete precession of the spin vector, making the observed state by a definition a spin coherent state. The emergence of the precession is traced to the polariton interactions that give rise to a self-induced out-of-plane magnetic field that in turn drives the spin dynamics. We find that the Larmor oscillation frequency scales with the condensate density, enabling external tuning of this effect by optical means. The stability of the system allows for the realization of integrated optical magnetometry devices with the use of materials with enhanced exciton g-factor and can facilitate spin squeezing effects and active coherent control on the Bloch sphere in polariton condensates.