Entanglement between charge qubit states and coherent states of nanomechanical resonator generated by AC Josephson effect

TL;DR

This paper demonstrates how a nanoelectromechanical system with a Cooper-pair box can generate entangled states between charge qubits and resonator coherent states through the AC Josephson effect, controllable by bias voltage.

Contribution

It introduces a method to generate and control entanglement between charge qubits and mechanical resonator states using bias voltage in a nanoelectromechanical system.

Findings

Bias voltage induces entanglement between qubit and resonator.

Formation of cat-states can be controlled via bias voltage.

Entanglement characterized by entropy and Wigner function analysis.

Abstract

We considered a nanoelectromechanical system consisting of a movable Cooper-pair box qubit which is subject to an electrostatic field, and coupled to the two bulk superconductors via tunneling processes. We suggest that qubit dynamics is related to the one of a quantum oscillator and demonstrate that a bias voltage applied between superconductors generates states represented by the entanglement of qubit states and coherent states of the oscillator if certain resonant conditions are fulfilled. It is shown that a structure of this entanglement may be controlled by the bias voltage in a way that gives rise to the entanglement incorporating so-called cat-states - the superposition of coherent states. We characterize the formation and development of such states analyzing the entropy of entanglement and corresponding Wigner function. The experimentally feasible detection of the effect by measuring the average current is also considered.