Classical St\"uckelberg interferometry of a nanomechanical two-mode system at room temperature

TL;DR

This paper demonstrates classical St"uckelberg interferometry using a nanomechanical two-mode system at room temperature, highlighting the analogy to quantum systems and providing a theoretical framework for classical-quantum comparisons.

Contribution

It presents the first experimental realization of classical St"uckelberg interferometry in a nanomechanical system and offers an exact theoretical solution for the classical double passage problem.

Findings

Successful demonstration of classical St"uckelberg interferometry in nanomechanics

Theoretical analysis showing the analogy between classical and quantum return probabilities

Establishment of classical two-mode systems as testbeds for quantum interferometry

Abstract

The transition from classical to quantum mechanics has intrigued scientists in the past and remains one of the most fundamental conceptual challenges in state-of-the-art physics. Beyond the quantum mechanical correspondence principle, quantum-classical analogies have attracted considerable interest. In this work, we present classical two-mode interference for a nanomechanical two-mode system, realizing classical St\"uckelberg interferometry. In the past, St\"uckelberg interferometry has been investigated exclusively in quantum mechanical two-level systems. Here, we experimentally demonstrate a classical analog of St\"uckelberg interferometry taking advantage of coherent energy exchange between two-strongly coupled, high quality factor nanomechanical resonator modes. Furthermore, we provide an exact theoretical solution for the double passage St\"uckelberg problem 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 as a testbed for quantum mechanical interferometry.