Supersensitive measurement of angular displacements using entangled photons

Abstract

We show that the use of path-entangled states of photons, having nonzero orbital angular momentum (OAM), increases the resolution and sensitivity of angular-displacement measurements performed using an interferometer. In the ideal case of maximally path-entangled states, the resolution of angular-displacement measurements increases by a factor of $\mathit{Nl}$, while the uncertainty in the measurement of angular displacements scales as $1/\mathit{Nl}$, where $N$ is the number of entangled photons, half of which carry, on average, an OAM of $+l\ensuremath{\hbar}$ per photon and the other half carry an OAM of $\ensuremath{-}l\ensuremath{\hbar}$ per photon. We analyze measurement schemes for two- and four-photon entangled states produced by parametric down-conversion and, by employing a 4$\ifmmode\times\else\texttimes\fi{}$4 matrix formalism to study the propagation of entangled OAM modes, obtain explicit expressions for the resolution and sensitivity in these schemes. These results constitute an improvement over what could be obtained with $N$ nonentangled photons carrying an orbital angular momentum of $|l|\ensuremath{\hbar}$ per photon.