Superposition states photon correlations

As we have shown in Sec. III. A, the second-order correlation function of the fluorescence field depends on correlation functions of the atomic dipole moments (S+(f)S+(f + x)Sy(t)Sj (t)), which correspond to different processes including photon emissions from a superposition of the excited levels. Therefore, we write the correlation functions G (R, t) and G (R, t R, t + x) in terms of the symmetric and antisymmetric superposition states as... 

Quantum-beat lasers are a particular form of correlated spontaneous emission lasers (CEL s) [43-49]. Quantum-beat is formed by creating coherence between near degenerate atomic states, either excited states or ground states. In particular, a beam of three-level atoms in Vee configuration emit photons into two modes. The atomic upper levels are initially prepared in a coherent superposition or are coupled by a coherent field [13-17]. The fluetuations of the relative phase and the relative amplitude drop to the vacuum levels. In addition to this, as a different form, correlated spontaneous emission can be formed by creating eoherenee between a pair of states between which lasing transitions occm. One such example is a two-photon CEL [13-17] with a beam of three-level atoms in cascade configuration. The top and bottom states are initially prepared in a coherent superposition state. It was predicted that the phase noise is reduced by 50% below the vacuum noise level. 

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