Entanglement of Two Qubits Mediated by One-Dimensional Plasmonic Waveguides

We investigate qubit-qubit entanglement mediated by plasmons supported by one-dimensional waveguides. We explore both the situation of spontaneous formation of entanglement from an unentangled state and the emergence of driven steady-state entanglement under continuous pumping. In both cases, we show that large values for the concurrence are attainable for qubit-qubit distances larger than the operating wavelength by using plasmonic waveguides that are currently available.

Figure 1

(a) Two qubits interacting with a plasmonic waveguide, in this case a channel waveguide. (b) Scheme of levels, couplings, and decays in the particular case where ${\omega }_1={\omega }_2={\omega }_0$ and ${\gamma }_{11}={\gamma }_{22}=\gamma$.

Figure 2

(a) Dispersion relation (red curve) of a CPP mode supported by a $V$ groove of angle $20°$ and height 140 nm. For comparison we show the dispersion of a surface plasmon mode of an infinite 2D silver surface (black dotted line). The inset displays the wavelength dependence of the propagation length $L$. (b) $\beta$ factor versus wavelength $\lambda$ and vertical distance $h$ associated with the CPP mode.

Figure 3

Concurrence as a function of time when just one of the two qubits is initially excited. The continuous black line corresponds to two qubits entangled by means of a channel PW with $\overline{\beta }=0.9$, $k_{\mathrm{pl}}d=2\pi$. The dashed red line is for two qubits in a cavity with a detuning such that it produces $g_{12}/\gamma =5$ and ${\gamma }_{12}=0$. The dotted blue line is for the ideal case of both PW and CQED (see the text). The inset shows the time evolution of $C$ and the populations of states $|+⟩$ and $|-⟩$ for the nonideal PW case.

Figure 4

Panel (a) shows the steady-state concurrence as a function of the separation between two equal qubits for $\beta =0.94$, $L=2\mu \mathrm{m}$, and three different laser configurations: ${\Omega }_1=0.15\gamma$ and ${\Omega }_2=0$ (solid black curve), ${\Omega }_1={\Omega }_2=0.1\gamma$ (dotted blue line), and ${\Omega }_1=-{\Omega }_2=0.1\gamma$ (dashed red line). Insets (b) and (c) correspond to the first type of pumping ${\Omega }_1=0.15\gamma$ and ${\Omega }_2=0$. Panel (b) shows the concurrence time evolution for a system with $\overline{\beta }=0.99$, while the $\beta$ dependence of the steady-state concurrence evaluated at $d={\lambda }_{\mathrm{pl}}$ is rendered in panel (c).