22 May 2013 Creation of entangled photons by two level atom trapped in one-dimensional nanocavity with weakly decaying resonance mode
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Abstract
The entangled photons components are found to be created in the lossless nanocavity with resonance mode. The smallness of Γ ( 0 ≤ Γ<< g- coupling constant for electro-dipolar interaction) was revealed playing the crucial part in their production. It’s known that Г determines limits (ωc ± Γ) of photon frequency deflection from the mode frequency ωc, when photon passes through empty cavity. When Γ = 0 and ωac , the Hamiltonian is time independent and has two eigenstates with eigenvalies (ωa ± g). Each state is superposition of the upper and lower atomic states, taken with signs plus and minus respectively. These states are stationary and form a time-depended superposition. Matrix elements of the interaction Hamiltonian, taken between that superposition and atomic unperturbed states, contain two anti-phases components of entangled photons. Since Γ = 0, their emission out of cavity is forbidden so they interfere, producing beatings of the resonance mode by sin (g•t). When 0 < Γ<< g those beatings become quasi-stationary, and with probability proportional to Γ/4g they go out through the partly transparent mirror and disintegrate into two photons, each of them taking its own spectral place outside the cavity. This process is illustrated by 3D-plots in the (ω, t)-space.
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Vladislav Cheltsov, Vladislav Cheltsov, } "Creation of entangled photons by two level atom trapped in one-dimensional nanocavity with weakly decaying resonance mode", Proc. SPIE 8766, Nanotechnology VI, 87660U (22 May 2013); doi: 10.1117/12.2014218; https://doi.org/10.1117/12.2014218
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