  Resonant tunneling through identical potential barriers is a textbook problem
in quantum mechanics. Its solution yields total transparency (100% tunneling)
at discrete energies. This dramatic phenomenon results from coherent
interference among many trajectories, and it is the basis of transport through
periodic structures. Resonant tunneling of electrons is commonly seen in
semiconducting 'quantum dots'. Here we demonstrate that detecting
(distinguishing) electron trajectories in a quantum dot (QD) renders the QD
nearly insulating. We couple trajectories in the QD to a 'detector' by
employing edge channels in the integer quantum Hall regime. That is, we couple
electrons tunneling through an inner channel to electrons in the neighboring
outer, 'detector' channel. A small bias applied to the detector channel
suffices to dephase (quench) the resonant tunneling completely. We derive a
formula for dephasing that agrees well with our data and implies that just a
few electrons passing through the detector channel suffice to dephase the QD
completely. This basic experiment shows how path detection in a QD induces a
transition from delocalization (due to coherent tunneling) to localization
(sequential tunneling).
