We have carried out calculations towards the goal of reducing the inaccuracy of the Sr optical atomic clock to $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ and below. In particular, we focused on ac polarizabilities of the
5s2 1S0 and
5s5p 3P0o clock states that are important for reducing the uncertainty of black-body radiation-induced frequency shifts for the $^{1}S_{0}\text{\ensuremath{-}}^{3}P_{0}^{o}$ clock transition. Four low-lying even-parity states have been identified, whose total contribution to the static polarizability of the
3P0o clock state is at the level of 90%. We show that if the contribution of these states is experimentally known with 0.1% accuracy, the same accuracy can be achieved for the total polarizability of the
3P0o state. The corresponding uncertainty for the blackbody shift at a fixed room temperature will be below $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$. The calculations are confirmed by a number of experimental measurements on various Sr properties.
After reviewing parity-measurement-based interferometry with twin Fock states, which allows for supersensitivity (Heisenberg limited) and super-resolution, we consider interferometry with two different superpositions of twin Fock states, namely, two-mode squeezed vacuum states and pair coherent states. This study is motivated by the experimental challenge of producing twin Fock states on opposite sides of a beam splitter. We find that input two-mode squeezed states, while allowing for Heisenberg-limited sensitivity, do not yield super-resolutions, whereas both are possible with input pair coherent states.
Classically, the resolution of optical measurements is limited by the Rayleigh limit and their sensitivity by the shot noise limit. However, non-classical measurements can surpass these limits. Measuring the photon number parity using a photon-number resolving detector, super resolved phase measurements up to 144 better than the Rayleigh limit are presented, with coherent states of up to 4,200 photons on average. An additional measurement that can be implemented with standard single-photon detectors is proposed and demonstrated. With this scheme, super resolution at the shot noise limit is demonstrated with coherent states of up to 200 photons on average.