Abstract

In this paper the nonlinear optical effects arising under very large density of photons and their long lifetime in the damped microcavity with one and two ultra-cold two-level atoms trapped inside the latter have been investigated nonperturbatively by means of the Green functions technique in the Heitler-Ma’s form modified by the present author [1]. It has been assumed that a single resonance mode with its frequency tuned to the atomic one decay in the empty cavity at the rate Γ .The analysis has been done by solving the Schroedinger equation with the proper Hamiltonian. The cooperative emission from the compound interacting system “atoms + decaying mode field + atomic vibrations in the trap’s potential well (in the case of one atom)” has been investigated as a function of photon escaping rate, vibrational frequency and photon frequencies. As predicted in [1] in the case of one motionless initially excited atom the spectrum has been shown to be a triplet with a weak central maximum and two sidebands when Γ < 4g (g is a coupling constant). For Γ ≥ 4g the triplet turns to singlet. For the combinational spectrum, i.e., the Stokes component the optical analog of the Moessbauer effect has been discovered in the limit Γ → 0. The physical mechanism of this effect in its nature is basically resonance and its features look as follows. Under resonance condition when thr Rabi frequency becomes equal to the frequency of vibrations of atom in the well and Γ → 0 strong photon-phonon interaction leads to rearrangement of energy levels of the whole interacting system. The energy levels assemble into a very narrow packet centered at the energy of the noninteracting system. Further the Stokes component shifts to the atomic frequency, turning into a very narrow, high and sharp “Moessbauer” peak (see Figure on the left, where x-dimensionless photon frequency, y-dimensionless photon escaping rate).

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