  Suitably patterned single crystals made of the cuprate superconductor
Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ (BSCCO), intrinsically forming a stack of
Josephson junctions, can generate electromagnetic radiation in the lower
terahertz regime. Due to Joule heating the emission power of single stacks
seems to be limited to values below 100 $\mu$W. To increase the radiation
power, mutually synchronized arrays situated on the same BSCCO base crystal
have been studied. Mutual electromagnetic interactions via a connecting BSCCO
base crystal have been considered essential for synchronization, but the
approach still suffers from Joule heating, preventing the synchronization of
more than three stacks. In the present paper we show, on the basis of two
emitting stacks, that mutual synchronization can also be achieved by
stand-alone stacks contacted by gold layers and sharing only a common gold
layer. Compared to BSCCO base crystals, the gold layers have a much higher
thermal conductivity and their patterning is not very problematic. We analyze
our results in detail, showing that the two oscillators exhibit phase
correlations over a range of $\pm$0.4 GHz relative to their center frequencies,
which we mainly studied between 745 GHz and 765 GHz. However, we also find that
strong phase gradients in the beams radiated from both the mutually locked
stacks and the unlocked ones play an important role and, presumably, diminish
the detected emission power due to destructive interference. We speculate that
the effect arises from higher-order cavity modes which are excited in the
individual stacks. Our main message is that the mutual interaction provided by
a common gold layer may open new possibilities for relaxing the
Joule-heating-problem, allowing the synchronization of a higher number of
stacks. Our findings may boost attempts to substantially increase the output
power levels of the BSCCO terahertz oscillators.
