Demonstration of a Tunable, Non-Hermitian, Nonlinear Microwave Dimer

Harmonic oscillators are ubiquitous in physics. However, interactions between oscillators are typically symmetric and can be described by Hermitian Hamiltonians. Here, we introduce a novel, tunable, non-Hermitian, nonlinear microwave dimer, enabling non-reciprocal energy transfer between distantly coupled harmonic oscillators. Using a simple configuration of 3D microwave cavities, unidirectional amplifiers, digital attenuators, and phase shifters, our setup provides a versatile platform for precisely manipulating signal amplitude and phase in each unidirectional propagation path. This configuration allows for an in-depth study of gain, loss, and non-reciprocity effects, especially in regimes where gain balances and exceeds inherent losses in the system. We explore the system's dynamics under various operational conditions through systematic analysis, emphasizing phenomena such as undriven limit cycles, synchronization effects, and weak-drive transmission spectra. Our findings open new avenues in applications ranging from neuromorphic computing and synthetic photonic materials to quantum information science, while offering fundamental insights into the underlying physics of non-Hermitian and nonlinear systems.