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The cooperative Lamb shift in an atomic nanolayer

We present an experimental measurement of the cooperative Lamb shift and the Lorentz shift using an atomic nanolayer with tunable thickness and atomic density. The cooperative Lamb shift arises due to the exchange of virtual photons between identical atoms. The interference between the forward and backward propagating virtual fields is confirmed by the thickness dependence of the shift which has a spatial frequency equal to $2k$, i.e. twice that of the optical field. The demonstration of cooperative interactions in an easily scalable system opens the door to a new domain for non-linear optics.