Creation of two distant entangled qutrits via interference of polarized photons: With and without rotating wave approximation

A proposal has been given in Feng et al. (2003) for generating the entangled states of two distant λ-type qutrits (three-level atoms) utilizing the interference of polarized photons under rotating wave approximation (RWA). In the present work, we first motivated to investigate the same scenario, however, using V-type atoms. Interestingly, we observed that the maximum probability of achieving the purpose (of entangling atoms) increases from 0.2 for Λ- to 0.34 for V-type atoms. Meanwhile, our detailed results show that, in both of the above model interactions, the best results are obtained when the atom–field couplings are enough large, particularly in the symmetric couplings. In this way, one enters the strong coupling constant regime, wherein the RWA is no longer valid. Accordingly, in order to study the effect of counter-rotating terms on the maximum accessible entanglement via this method, we motivated to reconsider the approach either with Λ- or V-type atoms, however, now without RWA. In this respect, for the λ-type atoms, our results interestingly show that the maximum probability 0.43 may be achieved, which is more than two times of the maximum reported value in the above-mentioned Ref. wherein the RWA is considered. Moreover, for V-type atoms, beyond RWA, we obtained the probability 0.4, which is a little more than the case with RWA, but still twice the case with RWA for Λ-type atom. Therefore, generally counter rotating terms have constructive effect on the probability of detection of entangled states for Λ- and V-type atoms.