Tunneling through an Eternal Traversable Wormhole

The Maldancena-Qi model describes two copies of the Sachdev-Ye-Kitaev model coupled with an additional coupling, and is dual to the Jackiw-Teitelboim gravity which exhibits eternal traversable wormhole in the low-temperature limit. In this work, we study the experimental consequence of the existence of the traversable wormhole by considering the tunneling spectroscopy for the Maldancena-Qi model. Comparing to the high-temperature black hole phase where the bulk geometry is disconnected, we find both the tunneling probability and the differential conductance in the low-temperature wormhole phase show non-trivial oscillation, which directly provides an unambiguous signature of the underlying $SL(2)$ symmetry of the bulk geometry. We also perform bulk calculations in both high and low-temperature phases, which match the results from the boundary quantum theory.