Optimal frequency measurements with maximally correlated states

Abstract

We show how maximally correlated states of N two-level particles can be used in spectroscopy to yield a frequency uncertainty equal to (NT${)}^{\mathrm{\ensuremath{-}}1}$, where T is the time of a single measurement. From the time-energy uncertainty relation we show that this is the best precision possible. We rephrase these results in the language of particle interferometry and obtain a state and detection operator which can be used to achieve a phase uncertainty exactly equal to the 1/N Heisenberg limit, where N is the number of particles used in the measurement.