  We perform a phase-space analysis of strong-field enhanced ionisation in
molecules, with emphasis on quantum-interference effects. Using Wigner
quasi-probability distributions and the quantum Liouville equation, we show
that the momentum gates reported in a previous publication [N. Takemoto and A.
Becker, Phys. Rev. A \textbf{84}, 023401 (2011)] may occur for static driving
fields, and even for no external field at all. Their primary cause is an
interference-induced bridging mechanism that occurs if both wells in the
molecule are populated. In the phase-space regions for which quantum bridges
occur, the Wigner functions perform a clockwise rotation whose period is
intrinsic to the molecule. This evolution is essentially non-classical and
non-adiabatic, as it does not follow equienergy curves or field gradients.
Quasi-probability transfer via quantum bridges is favoured if the electron's
initial state is either spatially delocalised, or situated at the upfield
molecular well. Enhanced ionisation results from the interplay of this cyclic
motion, adiabatic tunnel ionisation and population trapping. Optimal conditions
require minimising population trapping and using the bridging mechanism to feed
into ionisation pathways along the field gradient.
