Nonlinear atomic Fabry-Perot interferometer: From the mean-field theory to theatom blockadeeffect

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Abstract
We have investigated nonlinear atom optical effects which arise from atom-atom collisional interactions in a single-mode atomic Fabry-Perot cavity driven by a coherent cw atom laser beam. When the nonlinear interaction energy per single atom is small, the exact numerical solution of the master equation is well reproduced by a mean-field treatment in which quantum fluctuations are included linearizing the stochastic equations of the Positive-P representation. On the other hand, when the damping of the cavity mode is very weak and its wave-function is tightly confined in space, a regime of strong nonlinearity can be achieved. For the specific case of an incident atom laser frequency at resonance with the empty cavity, the numerical calculations predict a sort of atom blockade effect, which is a sort of atom optical analog of the well-known Coulomb blockade effect of electronic transport through microscopic structures: only one atom can occupy the cavity mode at a time and the statistical properties of the transmitted beam, being very similar to the resonance fluorescence from a single two-level system, show definitely nonclassical behaviors such as antibunching. Only at very large incident intensities, more than one atom can be simultaneously forced inside the cavity mode: in this regime, the results of the numerical calculations can be successfully interpreted using a dressed cavity model. From the formal analogy between atomic matter waves and optical light waves in nonlinear media, it follows that the same results hold for photonic systems.