Probing the quantum coherence of a nanomechanical resonator using a superconducting qubit: I. Echo scheme

TL;DR

This paper proposes a method to probe the quantum coherence of a nanomechanical resonator using a superconducting qubit, employing an echo scheme to detect decoherence effects through qubit measurements.

Contribution

It introduces a novel echo-based scheme to measure mechanical decoherence via a superconducting qubit, leveraging dispersive coupling and control pulses.

Findings

Decoherence of the resonator can be inferred from qubit measurements.

The scheme is feasible with current device technology.

Reversibility of dynamics is limited by environmental interactions.

Abstract

We propose a scheme in which the quantum coherence of a nanomechanical resonator can be probed using a superconducting qubit. We consider a mechanical resonator coupled capacitively to a Cooper-pair box and assume that the superconducting qubit is tuned to the degeneracy point so that its coherence time is maximised and the electro-mechanical coupling can be approximated by a dispersive Hamiltonian. When the qubit is prepared in a superposition of states this drives the mechanical resonator progressively into a superposition which in turn leads to apparent decoherence of the qubit. Applying a suitable control pulse to the qubit allows its population to be inverted resulting in a reversal of the resonator dynamics. However, the resonator's interactions with its environment mean that the dynamics is not completely reversible. We show that this irreversibility is largely due to the decoherence of the mechanical resonator and can be inferred from appropriate measurements on the qubit alone. Using estimates for the parameters involved based on a specific realization of the system we show that it should be possible to carry out this scheme with existing device technology.