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

We present a quantum optics scheme of generating large-amplitude Schrödinger 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.

Figure 1

(Color online) (a) The coupled system. The SCPB is made of two Josephson junctions and biased by the gate voltage $V_g$. The phase ${\varphi }_x$ controls the Josephsen energy of the SCPB. The resonator is biased at the voltage $V_x$. (b) The evolution of the resonator starting from $x=0$ and ∣↓⟩. The parabolic curves are the qubit-dependent harmonic potentials $U_{\uparrow ,\downarrow }\left(x\right)$. The solid circles indicate the position and energy of the resonator with the qubit state labeled as ↑,↓. The dotted arrows describe the displacement and the increase in energy of the resonator.

Figure 2

(Color online) Main plot: the fidelity of the amplification versus ${ϵ}_{\perp }$. The curves from top to bottom are for $n=4,8,12$ pulses. Inset: the probability $p_{-}$ after the detection pulses versus ${ϵ}_d$ at ${ϵ}_z=4.0{\omega }_0$ (solid line) and ${ϵ}_z=3.2{\omega }_0$ (dotted line). The axes of ${ϵ}_{\perp ,d}$ are in units of ${\omega }_0$.