Quantum Measurement of a Coupled Nanomechanical Resonator -- Cooper-Pair Box System

TL;DR

This paper investigates how second-order corrections in a coupled nanomechanical resonator and Cooper-pair box system lead to state-dependent spectral shifts, enabling quantum measurement and state preparation of the resonator.

Contribution

It introduces a novel analysis of second-order spectral effects that facilitate quantum non-demolition measurements and state control in a coupled nanomechanical and superconducting qubit system.

Findings

Spectrum of the Cooper-pair box depends on the resonator's Fock state.

Resonator frequency shifts depend on the Cooper-pair box state.

Potential for quantum non-demolition measurement of the resonator.

Abstract

We show two effects as a result of considering the second-order correction to the spectrum of a nanomechanical resonator electrostatically coupled to a Cooper-pair box. The spectrum of the Cooper-pair box is modified in a way which depends on the Fock state of the resonator. Similarly, the frequency of the resonator becomes dependent on the state of the Cooper-pair box. We consider whether these frequency shifts could be utilized to prepare the nanomechanical resonator in a Fock state, to perform a quantum non-demolition measurement of the resonator Fock state, and to distinguish the phase states of the Cooper-pair box.