Robust Creation of Entanglement between Ions in Spatially Separate Cavities

We present a protocol that allows the generation of a maximally entangled state between individual atoms held in spatially separate cavities. Assuming perfect detectors and neglecting spontaneous emission from the atoms, the resulting idealized scheme is deterministic. Under more realistic conditions, when the atom-cavity interaction departs from the strong coupling regime, and considering imperfect detectors, we show that the scheme is robust against experimental inefficiencies and yields probabilistic entanglement of very high fidelity.

Figure 1

We consider a setup in which individual ions are trapped inside two spatially separated optical cavities $A$ and $B$. Photons can leak out of the cavities and are then mixed on a beam splitter BS and subsequently detected by photodetectors $D_1$ and $D_2$.

Figure 2

Internal level scheme of the ions. A stable entangled state can be created when quantum information is encoded in the lower two levels $|1⟩$ and $|2⟩$. These two levels are coupled via the upper level $|3⟩$, employing two fields that have the same large detuning $\Delta$ on their respective transitions to the upper level $|3⟩$. The $|1⟩\leftrightarrow |3⟩$ transition couples to the cavity mode while the $|2⟩\leftrightarrow |3⟩$ transition is driven by a strong classical field. There may be spontaneous decay from $|3⟩$ to levels $|1⟩$ and $|2⟩$ at rates $2{\gamma }_{31}$ and $2{\gamma }_{32}$, respectively.

Figure 3

The success probability (solid line) and the deviation from unit fidelity are plotted versus the detector efficiency for $\Omega =g$, $\kappa =10g$, ${\gamma }_{31}={\gamma }_{32}=0.1g$, and $\Delta =20g$ and a waiting time of $T=100/g$. The plot has been obtained from a quantum jump simulation of the exact dynamics given by Eq. (4). Each point is the result of an average over ${10}^6$ runs of the scheme.