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We report on Kerr nonlinearity and dispersive optical bistability of aFabry-Perot optical resonator due to the displacement of ultracold atomstrapped within. In the driven resonator, such collective motion is induced byoptical forces acting upon up to $10^5$ $^{87}$Rb atoms prepared in the lowestband of a one-dimensional intracavity optical lattice. The longevity of atomicmotional coherence allows for strongly nonlinear optics at extremely low cavityphoton numbers, as demonstrated by the observation of both branches of opticalbistability at photon numbers below unity.

Cavity Nonlinear Optics at Low Photon Numbers from Collective Atomic Motion