By the way, apart from experiments conducted by physicists, are there any other applications that would demand precision of measured time of up to 16 to 18 digits? 10^(-18) sec is one insanely small time interval! Just wondering!

GPS synchronization relies on atomic fountains. Except this, we need such a precision to test general relativity to its deepest details (some reference to @alexander.alexis). See fo instance the Pharao project.