The question of the time a particle takes to tunnel through a classically forbidden region has a long history, complicated by the fact that the simplest predictions for the arrival time of a wave packet peak may be smaller than the barrier thickness divided by the speed of light. By now it is well understood that this result is not paradoxical, but it leaves open the question of how long a particle interacts with the barrier, and of whether it is sensible to distinguish between interaction times for transmitted and reflected particles.
By preparing ultracold Rubidium atoms in an atom waveguide and cooling them to approximately 1 nK, we are able to study tunneling across a 1-μm barrier formed by a blue-detuned laser beam. Using Raman coupling to generate a fictitious magnetic field, we let the spin of each atom act as a “clock” to record how long it spends in the barrier region. I will present our first results characterizing the tunneling time in this way. We analyze them in terms of the weak-measurement formalism, which makes it possible for one to discuss different “histories” for particles which end up in different final states. I will spend some time discussing this formalism more broadly, including problems it resolves and puzzles it raises.