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It is well known that the result of any phase measurement on an optical modemade using linear optics has an introduced uncertainty in addition to theintrinsic quantum phase uncertainty of the state of the mode. The bestpreviously published technique [H. M. Wiseman and R.B. Killip, Phys. Rev. A 57,2169 (1998)] is an adaptive technique that introduces a phase variance thatscales as n^{-1.5}, where n is the mean photon number of the state. This is farabove the minimum intrinsic quantum phase variance of the state, which scalesas n^{-2}. It has been shown that a lower limit to the phase variance that isintroduced scales as ln(n)/n^2. Here we introduce an adaptive technique thatattains this theoretical lower limit.Comment: 9 pages, 5 figures, updated with better feedback schem

Phase measurements at the theoretical limit