Capacitive Coupling of Two Transmission Line Resonators Mediated by the Phonon Number of a Nanoelectromechanical Oscillator

TL;DR

This paper proposes a method for quantum non-demolition detection of phonon number in a nanoelectromechanical oscillator via capacitive coupling with transmission line resonators, enabling entanglement and superposition state generation.

Contribution

It introduces a scheme for mediating interactions between TLRs through a nano-mechanical oscillator and demonstrates how to detect phonon numbers and generate non-classical states.

Findings

Quantum non-demolition detection of phonons achieved

Tripartite entanglement generated in the system

Conditional mechanical superposition states produced

Abstract

Detection of quantum features in mechanical systems at the nanoscale constitutes a challenging task, given the weak interaction with other elements and the available technics. Here we describe how the interaction between two monomodal transmission-line resonators (TLRs) mediated by vibrations of a nano-electromechanical oscillator can be described. This scheme is then employed for quantum non-demolition detection of the number of phonons in the nano-electromechanical oscillator through a direct current measurement in the output of one of the TLRs. For that to be possible an undepleted field inside one of the TLR works as a amplifier for the interaction between the mechanical resonator and the remaining TLR. We also show how how the non-classical nature of this system can be used for generation of tripartite entanglement and conditioned mechanical coherent superposition states, which may be further explored for detection processes.