Classical Stückelberg interferometry of a nanomechanical two-mode system

Abstract

St\"uckelberg interferometry is a phenomenon that has been well established for quantum-mechanical two-level systems. Here, we present classical two-mode interference of a nanomechanical two-mode system, realizing a classical analog of St\"uckelberg interferometry. Our experiment relies on the coherent energy exchange between two strongly coupled, high-quality factor nanomechanical resonator modes. Furthermore, we discuss an exact theoretical solution for the double-passage St\"uckelberg problem by expanding the established finite-time Landau-Zener single-passage solution. For the parameter regime explored in the experiment, we find that the St\"uckelberg return probability in the classical version of the problem formally coincides with the quantum case, which reveals the analogy of the return probabilities in the quantum-mechanical and the classical version of the problem. This result qualifies classical two-mode systems at large to simulate quantum-mechanical interferometry.