  This article describes the recent progress of optical lattice clocks with
neutral strontium ($^{87}$Sr), ytterbium ($^{171}$Yb) and mercury ($^{199}$Hg)
atoms. In particular, we present frequency comparison between the clocks
locally via an optical frequency comb and between two Sr clocks at remote sites
using a phase-stabilized fibre link. We first review cryogenic Sr optical
lattice clocks that reduce the room-temperature blackbody radiation shift by
two orders of magnitude and serve as a reference in the following clock
comparisons. Similar physical properties of Sr and Yb atoms, such as transition
wavelengths and vapour pressure, have allowed our development of a compatible
clock for both species. A cryogenic Yb clock is evaluated by referencing a Sr
clock. We also report on a Hg clock, which shows one order of magnitude less
sensitivity to blackbody radiation, while its large nuclear charge makes the
clock sensitive to the variation of fine-structure constant. Connecting all
three types of clocks by an optical frequency comb, the ratios of the clock
frequencies are determined with uncertainties smaller than possible through
absolute frequency measurements. Finally, we describe a synchronous frequency
comparison between two Sr-based remote clocks over a distance of 15 km between
RIKEN and the University of Tokyo, as a step towards relativistic geodesy.
