Geometric Amplification via Non-Hermitian Berry Phase
Despite their apparent simplicity, coupled oscillators exhibit surprisingly complex phenomena. Two notable examples are Berry phase (a geometric or topological aspect of the oscillators' memory) and non-Hermiticity (the often counterintuitive impact of dissipation), both of which possess rich mathematical structures. Here, we demonstrate that combining Berry phase and non-Hermiticity leads to a fundamentally new form of amplification. Specifically, we show that this combination allows a lossy oscillator system to be converted into one with gain via slow modulation of its parameters. This is distinct from other amplification mechanisms, as it results specifically from the complex-valued Berry phase that is unique to non-Hermitian systems. We show that this mechanism produces continuous, useful gain in an optomechanical system, and that similar results can be realized in a very wide range of settings.