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The Pancharatnam–Berry phase is a geometric phase acquired over a cycle of parameters in the Hamiltonian governing the evolution of the system. Here, we report on the observation of the Pancharatnam–Berry phase in a condensate of indirect excitons (IXs) in a GaAs-coupled quantum well structure. The Pancharatnam–Berry phase is directly measured by detecting phase shifts of interference fringes in IX interference patterns. Correlations are found between the phase shifts, polarization pattern of IX emission, and onset of IX spontaneous coherence. The evolving Pancharatnam–Berry phase is acquired due to coherent spin precession in IX condensate and is observed with no decay over lengths exceeding 10 μm indicating long-range coherent spin transport.

Collective electronic modes or lattice vibrations usually prohibit propagation of electromagnetic radiation through the bulk of common materials over a frequency range associated with these oscillations. However, this textbook tenet does not necessarily apply to layered crystals. Highly anisotropic materials often display nonintuitive optical properties and can permit propagation of subdiffractional waveguide modes, with hyperbolic dispersion, throughout their bulk. Here, we report on the observation of optically induced electronic hyperbolicity in the layered transition metal dichalcogenide tungsten diselenide (WSe₂). We used photoexcitation to inject electron-hole pairs in WSe₂and then visualized, by transient nanoimaging, the hyperbolic rays that traveled along conical trajectories inside of the crystal. We establish here the signatures of programmable hyperbolic electrodynamics and assess the role of quantum transitions of excitons within the Rydberg series in the observed polaritonic response.