Generation and purification of maximally entangled atomic states in optical cavities

We present a probabilistic scheme for generating and purifying maximally entangled states of two atoms inside an optical cavity via no-photon detection at the cavity output, where ideal detectors are not required. The intermediate mixed states can be continuously purified so as to violate Bell inequalities in a parametrized manner. The scheme relies on an additional strong-driving field that realizes, atypically, simultaneous Jaynes-Cummings and anti-Jaynes-Cummings interactions.

Figure 1

(a) Two three-level atoms inside an optical cavity, (b) scheme of the atomic energy levels and the exciting fields for each three-level atom. $\Delta$ and ${\Delta }^{\prime }$ are frequency detunings and $g$, $\Omega$, ${\Omega }_1^{\prime }$, and ${\Omega }_2^{\prime }$ the respective coupling strengths.

Figure 2

Violation of the Bell inequality.