  We propose a dissipative phase transition in a head-to-tail Bose Josephson
junction. The quantum phase transition has the same origin as the one in a
resistively shunted Josephson junction, but the intrinsic momentum coupling
between the Josephson mode and the bath modes enables us to observe the
dissipative phase transition without any synthetic dissipation. We show that
the inter-atomic interaction strength plays the role of the damping parameter.
Consequently, in contrast to a resistively shunted Josephson circuit, the Bose
Josephson junction can exhibit an insulating phase in a wider parameter region
by increasing the repulsive interaction strength, which is robust against
nonperturbative effects. We argue that tight transverse confinement of the
quasi-one-dimensional atomic gas allows us to reach the insulating phase.
