Detection of nonlocal atomic entanglement assisted by single photons

We present an efficient way for measuring the entanglement of atoms. The concurrence of atomic entanglement can be obtained according to the probability of picking up the singlet states of the atoms. In this protocol, we require the phenomenon of optical Faraday rotation, but the entangled atoms do not need to be in contact with each other and the atomic entanglement can be distributed nonlocally. Moreover, our way of measuring the concurrence for atoms can also be suitable for other solid systems, such as quantum dots inside microcavities and the nitrogen-vacancy (N-V) defect centers in diamonds, which can also induce the optical Faraday rotation. All these advantages provide important applications in future distributed quantum computations.

Figure 1

The relevant atomic structure subjected to a low-Q cavity field. It has an excited state $|e\rangle$ and two degenerate ground states $|g_L\rangle$ and $|g_R\rangle$.

Figure 2

A schematic drawing of the principle of detection of nonlocal atomic entanglement. Two input polarized photons are in the same state $\frac{1}{\sqrt{2}}\left(\right|L\rangle +|R\rangle )$. The polarization beam splitter can transmit the photon in the $|+\rangle$ polarization and reflect the photon in the $|-\rangle$ polarization. Here $|\pm \rangle =\frac{1}{\sqrt{2}}\left(\right|L\rangle \pm |R\rangle )$. ${\mathrm{D}}_1,{\mathrm{D}}_2,{\mathrm{D}}_3$, and ${\mathrm{D}}_4$ are four single-photon detectors.

Figure 3

The probability of error is altered with $\theta$. We let $\theta \in (0,2\pi )$.