Effect of atomic interactions on tunneling time measurements

A Larmor clock uses the spin degree of freedom of tunneling particles to time the duration of the interaction between the particles and the barrier. It is well known that in the absence of inter-particle interactions, a Larmor clock measures the 'dwell time' (i.e. the expectation value of a projector onto the barrier region) of the wavepacket conditioned on transmission or reflection. Recently we observed that Larmor times for weakly interacting ultra-cold atoms tunneling through an optical barrier show good agreement with theory for conditional dwell times given by weak values. For these transmitted particles, atomic interactions do not significantly disturb the measurement of time but simply modify the momentum distribution of the incident wavepacket prior to collision with the barrier. For the reflected particles, however, the disturbance caused by atomic interactions is much more serious. We observe evidence of negative dwell times for a portion of the reflected wavepacket, perhaps indicative of interference between particles reflected from the barrier and those reflected from the wavepacket itself. Here, we discuss the implications for measurements of time in experiments on barrier penetration.