Unidirectional Inter-Axial Coupling and Spontaneous Cooling in a Non-Hermitian Dynamics of a Levitated Particle

Non-Hermitian dynamics in open systems can give rise to a variety of fascinating non-equilibrium phenomena, ranging from symmetry-breaking transitions to directional energy flow. Parity-time (PT) symmetry breaking determines the occurrence of dynamical instabilities, while non-reciprocal interactions enable asymmetric energy transfer between modes. Here, we present a versatile optomechanical platform based on a vacuum-levitated nanoparticle that allows full control over the coupling of its mechanical modes, including non-reciprocal and non-conservative interactions. By engineering the spatial ellipticity and polarization of the trapping beam, we continuously tune the system from a reciprocal to a strongly non-reciprocal regime. This allows us to observe PT-symmetry phase transitions and to isolate a unidirectional regime in which one mode remains effectively decoupled while driving the other. We demonstrate that elliptical polarisation of the trapping beam spanning unidirectional and reciprocal regimes induces asymmetric intermodal energy transfer. This results in the spontaneous cooling of one mechanical mode without external feedback. Both modes share identical mass, size, charge, and optical environment, providing a clean and robust setting for exploring non-Hermitian dynamics, exceptional-point physics, and energy redistribution in minimal systems. Combined with recent advances in ground-state cooling, our results provide a direct route to realising non-Hermitian phenomena in the quantum regime.