Effect of imaginary gauge on wave transport in driven-dissipative systems

Wave transport in disordered media is a fundamental problem with direct implications in condensed matter, materials science, optics, atomic physics, and even biology. The majority of these studies focuses on disorder-induced localization in Hermitian systems. However, recent studies of non-Hermitian disordered media have revealed unique behaviors, with a universal principle emerging that links the eigenvalue spectrum of the disordered Hamiltonian and its statistics with its transport properties. In this work we show that the situation can be very different in driven-dissipative lattices of cavities, where a uniform gain applied equally to all the components of the system can act as a knob for controlling the wave transport properties without altering the eigenvalue statistics of the underlying Hamiltonian. Our results provide deeper insight into the transport properties of disordered media and will aid in the development of new devices. Our work, which is presented in the context of optics, generalizes to any physical platforms where gain can be implemented. These include acoustics, electronics, and coupled quantum oscillators such as atoms, diamond centers, and superconducting qubits.