Creation of entangled photons by two level atom trapped in one-dimensional nanocavity with weakly decaying resonance mode

摘要

The entangled photons components are found to be created in the lossless nanocavity with resonance mode. The smallness of F( 0≤F《g- coupling constant for electro-dipolar interaction)was revealed playing the crucial part in their production. It's known that ? determines limits(ω_c ±?)of photon frequency deflection from the mode frequency ω_c, when photon passes through empty cavity. When ?= 0 and ω_a=ω_c , the Hamiltonian is time-independent and has two eigenstates with eigenvalies(ω_a ± 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 ?= 0, their emission out of cavity is forbidden so they interfere, producing beatings of the resonance mode by sin(g·t). When 0＜?《g those beatings become quasi-stationary, and with probability proportional to ?/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.