Phonon-number resolution of voltage-biased mechanical oscillators with weakly-anharmonic superconducting circuits

TL;DR

This paper investigates how to achieve phonon-number resolution in a system where a low-frequency mechanical oscillator is coupled to a high-frequency superconducting transmon circuit, aiming to observe quantum phenomena in macroscopic objects.

Contribution

It analyzes the challenges and requirements for resolving phonon numbers in a weakly-anharmonic superconducting circuit coupled to a mechanical oscillator.

Findings

Identifies the frequency gap challenge between mechanical and superconducting systems.

Proposes conditions for reaching phonon-number resolution.

Explores the coupling dynamics in the resonant regime.

Abstract

Observing quantum phenomena in macroscopic objects, and the potential discovery of a fundamental limit in the applicability of quantum mechanics, has been a central topic of modern experimental physics. Highly coherent and heavy micro-mechanical oscillators controlled by superconducting circuits are a promising system for this task. Here, we focus in particular on the electrostatic coupling of motion to a weakly anharmonic circuit, namely the transmon qubit. In the case of a megahertz mechanical oscillator coupled to a gigahertz transmon, we explain the difficulties in bridging the large electro-mechanical frequency gap. To remedy this issue, we explore the requirements to reach phonon-number resolution in the resonant coupling of a megahertz transmon and a mechanical oscillator.