  We study the quantum tunneling of two one-dimensional quasi-condensates made
of alkali-metal atoms, considering two different tunneling configurations:
side-by-side and head-to-tail. After deriving the quasiparticle excitation
spectrum, we discuss the dynamics of the relative phase following a sudden
coupling of the independent subsystems. In particular, we calculate the
coherence factor of the system, which, due to the nonzero tunneling amplitude,
it exhibits dephasing-rephasing oscillations instead of pure dephasing. These
oscillations are enhanced by a higher tunneling energy, and by higher system
densities. Our predictions provide a benchmark for future experiments at
temperatures below $T \lesssim 5 \, \mbox{nK}$.
