From sub-atomic particles, to atoms, to molecules, our physical universe emerges from interacting elementary particles. For systems that approach a mesoscopic size the details of their shared wavefunction depend on the nature of their coupling. For the most part, a coupled phase-amplitude oscillator model is illustrative of the two possible mechanisms: quantum systems will either synchronise in phase or open spectral gaps and initiate dynamical oscillation when in proximity with each other. These two fundamentally different mechanisms are responsible, on the one hand, for various synchronisation and ballistic transport phenomena and, on the other hand, for the emergence of band structures in tight binding models and super- and sub-radiance in arrays of quantum emitters. Continuous tuning between the nature of the coupling between these two regimes likely requires a hyperbolic dispersion, which naturally arises in systems with mixed periodic and continuous translation symmetry, a situation which can be engineered in artificial systems. Here, we demonstrate how this is possible in a photonic crystal exciton-polariton waveguide, where the continuous symmetry stems from the planar geometry of the waveguide and the discrete one from the inscribed unidirectional grating.

Exciton-polaritons (polaritons from here on) are bosonic light-matter quasiparticles that form under the strong coupling of confined photons and quantum well excitons. They possess a small effective mass (stemming from the photonic component) and exhibit dipole-dipole interactions (driven by the excitonic component). These two properties, when combined with high-quality photonic modes, enable their nonequilibrium condensation at elevated temperatures across a wide range of materials. The coupling between neighbouring polariton condensates is defined by their engineered potential landscape, excitation technique, on-site energy and separation distance which gives access to a variety of distinct polariton Hamiltonians. As such, considerable effort has been dedicated towards controlling the environment and potential landscape and, consequently, the coupling between polariton condensates through intricate sample fabrication and patterning and all-optical techniques.

To date, mode hybridisation and population oscillations of deeply confined evanescently-coupled polariton condensates have been confirmed between accidental sample defects or in pre-designed photonic micropillar molecules. There, the usual tight-binding approach, supplemented with non-Hermitian terms, captures the essential physics between coupled polariton condensates. In contrast to deeply confined condensates, there are ballistic polariton condensates which are defined by strong radial polariton outflow and stringent phase matching conditions between neighbours that defines their synchronisation. These ballistic condensates appear when pumped with a tightly focused beam, which leads to spatially localised blueshift and gain and strong out-of-equilibrium polariton behaviour.

It is important to notice that these two coupling mechanisms cannot be straightforwardly described as purely Hermitian or anti-Hermitian. Consequently, they differ fundamentally from the well-studied dissipative and dispersive couplings. This is because both mechanisms affect the real but also the imaginary components of the polariton condensates. The more pronounced difference is observed in the ballistic coupling. Although it may initially appear to be predominantly dissipative, it actually involves a direct exchange of population leading to eigenvalues with a small but significant real gap and no indication of an imaginary gap.

Here, we propose a system of reduced symmetry, in contrast to cylindrically symmetric planar microcavities, to access a new geometric tuning parameter for the inter-condensate coupling mechanism. Our system is a subwavelength grated waveguiding slab with multiple embedded quantum wells [see schematic Fig. 1] that supports optically reconfigurable bound-in-the-continuum (BiC) polariton condensates. The properties of BiC polaritons are notably different from conventional cavity polariton platforms. They exhibit extremely low radiative decay rates, which substantially decreases their condensation threshold as compared to ballistically coupled condensates. Additionally, the low radiative decay enables the attainment of high densities suitable for the study of highly nonlinear quantum hydrodynamics that requires long spatio-temporal coherence scales. When dimerised, in this highly anisotropic photonic crystal, the angle of the axis connecting two condensates, with respect to the grating direction, plays a pivotal role in determining whether the coupling mechanism can be interpreted as evanescent or ballistic in origin, or a mixture of the two. The ability to continuously tune between the two natures of inter-condensate coupling introduces a new paradigm in polaritonic lattice systems, which until now have remained limited to either fully ballistic or fully evanescent coupling mechanisms. In the following, we connect the coexistence of these two coupling mechanisms with the geometrical properties of a repulsive polariton condensate lying on a hyperbolic dispersion. We directly visualise the effects of the self-confining mechanism and investigate its phenomenology and pronounced directionality. Here, we propose a system of reduced symmetry, in contrast to cylindrically symmetric planar microcavities, to access a new geometric tuning parameter for the inter-condensate coupling mechanism. Our system is a subwavelength grated waveguiding slab with multiple embedded quantum wells [see schematic Fig. 1] that supports optically reconfigurable bound-in-the-continuum (BiC) polariton condensates. The properties of BiC polaritons are notably different from conventional cavity polariton platforms. They exhibit extremely low radiative decay rates, which substantially decreases their condensation threshold as compared to ballistically coupled condensates. Additionally, the low radiative decay enables the attainment of high densities suitable for the study of highly nonlinear quantum hydrodynamics that requires long spatio-temporal coherence scales. When dimerised, in this highly anisotropic photonic crystal, the angle of the axis connecting two condensates, with respect to the grating direction, plays a pivotal role in determining whether the coupling mechanism can be interpreted as evanescent or ballistic in origin, or a mixture of the two. The ability to continuously tune between the two natures of inter-condensate coupling introduces a new paradigm in polaritonic lattice systems, which until now have remained limited to either fully ballistic or fully evanescent coupling mechanisms. In the following, we connect the coexistence of these two coupling mechanisms with the geometrical properties of a repulsive polariton condensate lying on a hyperbolic dispersion. We directly visualise the effects of the self-confining mechanism and investigate its phenomenology and pronounced directionality. Here, we propose a system of reduced symmetry, in contrast to cylindrically symmetric planar microcavities, to access a new geometric tuning parameter for the inter-condensate coupling mechanism. Our system is a subwavelength grated waveguiding slab with multiple embedded quantum wells [see schematic Fig. 1] that supports optically reconfigurable bound-in-the-continuum (BiC) polariton condensates. The properties of BiC polaritons are notably different from conventional cavity polariton platforms. They exhibit extremely low radiative decay rates, which substantially decreases their condensation threshold as compared to ballistically coupled condensates. Additionally, the low radiative decay enables the attainment of high densities suitable for the study of highly nonlinear quantum hydrodynamics that requires long spatio-temporal coherence scales. When dimerised, in this highly anisotropic photonic crystal, the angle of the axis connecting two condensates, with respect to the grating direction, plays a pivotal role in determining whether the coupling mechanism can be interpreted as evanescent or ballistic in origin, or a mixture of the two. The ability to continuously tune between the two natures of inter-condensate coupling introduces a new paradigm in polaritonic lattice systems, which until now have remained limited to either fully ballistic or fully evanescent coupling mechanisms. In the following, we connect the coexistence of these two coupling mechanisms with the geometrical properties of a repulsive polariton condensate lying on a hyperbolic dispersion. We directly visualise the effects of the self-confining mechanism and investigate its phenomenology and pronounced directionality.