Abstract
Non-Hermitian dynamics, as observed in photonic, atomic, electrical and optomechanical platforms, holds great potential for sensing applications and signal processing. Recently, fully tuneable non-reciprocal optical interaction has been demonstrated between levitated nanoparticles. Here we use this tunability to investigate the collective non-Hermitian dynamics of two non-reciprocally and nonlinearly interacting nanoparticles. We observe parity-time symmetry breaking and, for sufficiently strong coupling, a collective mechanical lasing transition in which the particles move along stable limit cycles. This work opens up a research avenue of non-equilibrium multi-particle collective effects, tailored by the dynamic control of individual sites in a tweezer array.