Journal of NanophotonicsArising of the entangled photon in the one-dimensional high-finesse nanocavity
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Nonperturbative theoretical analysis of the temporal evolution of a spontaneous photon with atomic frequency &ohgr;a, emitted by a motionless two-level atom in a one-dimensional high-finesse nanocavity into a single resonance decaying mode, is presented. The explicit solution of the Schrödinger equation was found in an interaction picture with use of the Green functions technique. It has been assumed that emission leaks out of the empty cavity by exponential law at rate &Ggr;, which is a function of coupling constant g, distance between the mirrors, penetrability coefficient of the left mirror, and the velocity of light. The stationary superpositional co-phased structure of two photons with the same profiles and average frequencies 1/2(&ohgr;a ± g), quenched with continuum of final photonics states, has been revealed. The profile of this structure has been found to have the form &Ggr;t exp(-&Ggr;t/4) with maximum attained for &Ggr;/4g = 0.05 and average photon cavity lifetime equal to 4ln&Ggr;/&Ggr;.