Deterministic cavity-QED source of polarization-entangled photon pairs

We present two cavity quantum electrodynamics proposals that, sharing the same basic elements, allow for the deterministic generation of entangled photon pairs by means of a three-level atom successively coupled to two single longitudinal mode high-$Q$ optical resonators presenting polarization degeneracy. In the faster proposal, the three-level atom yields a polarization-entangled photon pair via two truncated Rabi oscillations, whereas in the adiabatic proposal, a counterintuitive stimulated Raman adiabatic passage process is considered. Although slower than the former process, this second method is very efficient and robust under fluctuations of the experimental parameters and, particularly interesting, almost completely insensitive to atomic decay.

Figure 1

(a) $\mathsf{V}$-type three-level atomic configuration under investigation. (b) Proposed setup for the deterministic generation of polarization entangled photon pairs. $\mid \Omega {⟩}_i$ is the two-mode vacuum state of cavity $i$. The two proposed configurations based, respectively, on two truncated ROs and STIRAP are simultaneously shown. Also shown are the basic optical elements needed for the Bell analysis of the entangled states (QWP, quarter-wave plate; HWP, rotating half-wave plate; PBS, polarization beam splitter; $D_i$, single-photon detector).

Figure 2

(a) Manifold of states coupled to $\mid I⟩=a_{1+}^{†}{a}_{1-}^{†}\mid \Omega ⟩$ and the corresponding relative energies and coupling strengths (in the interaction picture). (b) The same manifold in terms of the basis states given in Eqs. (4, 5, 6, 7, 8) under the two-photon resonance condition.

Figure 3

Evolution of the system toward the entangled state $\mid E^{+}⟩$ through two truncated ROs (a) and via STIRAP (b,c). $\Gamma =0.05g$ and $\kappa =0.005g$ for (a) and (b); $\Gamma =0.08g$ and $\kappa =0.053g$ for (c). In all cases, ${\Delta }_{+}={\Delta }_{-}=0$. $g$ is the vacuum Rabi frequency at the cavity center that we assume to be the same for both cavities. Realistic parameter values have been chosen for the Gaussian transverse profiles of the cavity modes. For STIRAP, appropriate overlapping between the transverse modes of the two cavities has been considered. (d) Probabilities for the different processes involving photon emission through the cavity mirrors and their eventual photodetection, for the RO as well as for the STIRAP scheme. Parameters are as in (c). Note that in (a)–(c), the height of column (i), i.e., the success probability $P$, corresponds to the maximum of the dotted line.

Figure 4

The CHSH parameter $S$ [(a) and (b), see text] and the success probability $P$ and fidelity $F$ [(c) and (d)] as a function of the atomic decay for RO (a,c) and the STIRAP process (b,d). The parameters are $\Delta =0$ and $\kappa =0.053g$.

Figure 5

Contour plots of the success probabilities for the RO scheme (a,c) and via STIRAP (b,d). Parameters are ${\Delta }_{+}={\Delta }_{-}=0$ for (a,b) and $\kappa =\Gamma =0$ for (c,d). $({\Delta }_{+}+{\Delta }_{-})∕2g$ and $({\Delta }_{+}-{\Delta }_{-})∕2g$ measure the deviation from the single- and the two-photon resonance condition, respectively.