Heralded entanglement of arbitrary degree in remote qubits

Incoherent scattering of photons off two remote atoms with a $\Lambda$-level structure is used as a basic Young-type interferometer to herald long-lived entanglement of an arbitrary degree. The degree of entanglement, as measured by the concurrence, is found to be tunable by two easily accessible experimental parameters. Fixing one of them to certain values unveils an analog to the Malus’ law. An estimate of the variation in the degree of entanglement due to uncertainties in an experimental realization is given.

Figure 1

Scheme of two atoms with internal $\Lambda$-level structures using two detectors in the far field with polarization filters in front to register the photons emitted by the atoms. The inset shows the same configuration using optical fibers.

Figure 2

(Color online) The concurrence as a function of the phase ${\delta }_{21}$ (scaled in multiples of $\pi$) and the parameter ${\mathcal{V}}_{12}$. The thick orange lines mark constant ${\delta }_{21}=\left(n+1/2\right)\pi$, where the dependence of $\mathcal{C}$ on ${\mathcal{V}}_{12}$ becomes linear.