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arXiv:quant-ph/0412185 · Physical Review B

Entanglement from a nanomechanical resonator weakly coupled to a single Cooper-pair box

Lin Tian

Published Nov 10, 2005• 64 citations
arXivHTMLPDF

Abstract

We present a quantum optics scheme of generating large-amplitude Schr\"odinger cat states and entanglement in a weakly coupled nanomechanical resonator and single Cooper-pair box system. We show that the entanglement in this system can be detected by a spectroscopic method and can be generated at finite temperature and in the presence of environmental fluctuations.

DOI
10.1103/physrevb.72.195411

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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 upon 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.
A scheme for generating the Schrödinger cat state based on geometric operations by a nanomechanical resonator coupled to a superconducting charge qubit is proposed. The charge qubit, driven by two strong classical fields, interacts with a high‐frequency phonon mode of the nanomechanical resonator. During the operation, the charge qubit undergoes no real transitions, while the phonon mode of the nanomechanical resonator is displaced along different paths in the phase space, dependent on the states of the charge qubit. This generates the entangled cat state between the NAMR and charge qubit, and the NAMR cat state can be achieved after some operations applied on this entangled cat state. The robustness of the scheme is justified by considering noise from environment, and the feasibility of the scheme is discussed.
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 that 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.
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