We report a method to determine propagation delays of optical 10 Gb/s data traveling through a 75 km long amplified fiber link with an uncertainty of 4 ps. The one-way propagation delay is determined by two-way exchange and cross correlation of short
(< 1 ms) bursts of 10 Gb/s data, with a single-shot time resolution better than 2.5 ps. We thus achieve a novel optical communications link suited for both long-haul high-capacity data transfer and time transfer with picosecond-range uncertainty. This opens up the perspective of synchronized optical telecommunication networks allowing picosecond-range time distribution and millimeter-range positioning.
A calculation of dynamic polarizabilities of rovibrational states with vibrational quantum number $v=0-7$ and rotational quantum number $J=0,1$ in the 1s$sigma_g$ ground-state potential of HD$^+$ is presented. Polarizability contributions by transiti
ons involving other 1s$sigma_g$ rovibrational states are explicitly calculated, whereas contributions by electronic transitions are treated quasi-statically and partially derived from existing data [R.E. Moss and L. Valenzano, textit{Molec. Phys.}, 2002, textbf{100}, 1527]. Our model is valid for wavelengths $>4~mu$m and is used to to assess level shifts due to the blackbody radiation (BBR) electric field encountered in experimental high-resolution laser spectroscopy of trapped HD$^+$ ions. Polarizabilities of 1s$sigma_g$ rovibrational states obtained here agree with available existing accurate textit{ab initio} results. It is shown that the Stark effect due to BBR is dynamic and cannot be treated quasi-statically, as is often done in the case of atomic ions. Furthermore it is pointed out that the dynamic Stark shifts have tensorial character and depend strongly on the polarization state of the electric field. Numerical results of BBR-induced Stark shifts are presented, showing that Lamb-Dicke spectroscopy of narrow vibrational optical lines ($sim 10$ Hz natural linewidth) in HD$^+$ will become affected by BBR shifts only at the $10^{-16}$ level.
