Phonon Josephson Junction with Nanomechanical Resonators

TL;DR

This paper explores the dynamics of coupled nonlinear nanomechanical resonators, revealing a phonon Josephson junction with oscillation and self-trapping behaviors, and analyzes coherence loss due to interactions.

Contribution

It introduces the concept of a phonon Josephson junction in nanomechanical systems and analyzes its dynamical regimes and coherence properties.

Findings

Identification of Josephson oscillation and self-trapping regimes.

Derivation of an effective classical Hamiltonian for the system.

Observation of coherence loss due to resonator interactions.

Abstract

We study coherent phonon oscillations and tunneling between two coupled nonlinear nanomechanical resonators. We show that the coupling between two nanomechanical resonators creates an effective phonon Josephson junction which exhibits two different dynamical behaviors: Josephson oscillation (phonon-Rabi oscillation) and macroscopic self-trapping (phonon blockade). Self-trapping originates from mechanical nonlinearities, meaning that when the nonlinearity exceeds its critical value, the energy exchange between the two resonators is suppressed, and phonon-Josephson oscillations between them are completely blocked. An effective classical Hamiltonian for the phonon Josephson junction is derived and its mean-field dynamics is studied in phase space. Finally, we study the phonon-phonon coherence quantified by the mean fringe visibility, and show that the interaction between the two resonators may lead to the loss of coherence in the phononic junction.