  The fabrication precision is one of the most critical challenges on the way
to the creation of practical photonic circuits composed of coupled high
Q-factor microresonators. While very accurate transient tuning of
microresonators based on local heating has been reported, the record precision
of permanent resonance positioning achieved by post-processing is still within
1-5 GHz. Here we demonstrate two coupled bottle microresonators fabricated at
the fiber surface which resonances are matched with a better than 0.16 GHz
precision. This corresponds to a better than 0.17 angstrom precision in the
effective fiber radius variation. The achieved fabrication precision is only
limited by the resolution of our optical spectrum analyzer and can be
potentially improved by an order of magnitude.
