Tunneling Time of a Bose-Einstein condensate in a 1D atomic waveguide

We report on measurements of the tunneling time of Bose-condensed Rubidium~atoms in a one-dimensional system, tunneling through a 1-micron optical barrier. By localizing a pseudo-magnetic field inside the barrier and using the spin precession of the atoms to `clock' the time it takes for the atoms to pass through the classically forbidden region, we implement a Larmor measurement, as envisioned by Baz, Rybanchenko, and Buttiker [1,2,3,4]. In the limit that this measurement is `weak' (in the sense of Aharonov, Albert, and Vaidman), we are able to disentangle the back-action of the measurement from the inherent tunneling time. We measure a tunneling time of 0.62(7) milliseconds through our barrier. Our results show good agreement with theory and shed light onto this long-standing problem. [1] Baz', A. Lifetime of Intermediate States. \textit{Sov. J. Nucl. Phys. }4, 182 (1966).\textunderscore [2] Rybachenko, V. Time of Penetration of a Particle through a Potential Barrier. \textit{Sov. J. Nucl.} \textit{Phys. }5, 635 (1967). [\textunderscore 3] B\"{u}ttiker, M. Larmor precession and the traversal time for tunneling. \textit{Phys. Rev. B }27, 6178--6188 (1983). [4] Steinberg, A. M. Time and history in quantum tunneling. \textit{Superlattices and Microstructures}, \textit{23}(3--4), 823--832. (1998). \underline {http://doi.org/10.1006/spmi.1997.0543}