Very cool (literary) experiment! While simple in principle and complicated in practice, they can tease apart the effects both experimentally and theoretically. The measurement is weak, so they have to integrate out the result - the ground state of the tunneling require simulation over an imaginary time axis - and they get that "about 40% of the measured time for the lowest incident energy comes from the time spent in the classically forbidden region."
And of course there is the traversal time estimate: "At the lowest incident velocity (4.1 mm s^−1), we observe a transmission probability of 3%. Given the energy dependence of the transmission, we calculate that the transmitted atoms have a velocity distribution with a peak at 4.8 mm s^−1, corresponding to κd ≈ 3. About three-quarters of this distribution cor-responds to energies below the barrier height. The measured traversal time τ_y is 0.61(7) ms."
It would be interesting to know the exit velocity from the barrier. This might indicate whether the tunneling changed the momentum of the particle reversibly or irreversibly inside the barrier. Or otherwise stated, does the particle return to its original entrance velocity or not as it exits the barrier.
Unfortunately the measurement is complicated and the particle behavior also depends on a measurement backaction.
"Considering incident particles polarized in the x direction and a magnetic field along z, one would expect the spin to precess by an angle θ = ω_Lτ, where ω_L is the Larmor frequency and τ is the time spent in the barrier. By working in the limit of a weak magnetic field (ω_L →0), this time can be measured without substantially perturbing the tunnelling [sic] particle. Büttiker15 noted that even in this limit, measurement backaction cannot be neglected, and it results in preferential transmission of atoms aligned with the magnetic field. This leads to two spin rotation angles: a precession in the plane orthogonal to the applied magnetic field, θ_y, as well as an alignment along the direction of the field, θ_z. He defined times associated with the spin projections: τ_z, τ_y and τ_x=sqrt(t_y^2+t_s^2); the latter is often known as the ‘Büttiker time’. It turns out that combinations of two such quantities appear in other theoretical treatments as a single complex number33,34, but researchers were hesitant to accept complex-valued times without a clear interpretation. Later, further studies11,12 associated τ_y and τ_z with the real and imaginary parts of the ‘weak value’13 of a dwell-time operator, thereby providing them with distinct interpretations as the inherent tunnelling time and the measurement backaction, respectively."
"We investigate the two Larmor times by performing full-spin tomography of the transmitted spin-½ particles. Rotations after the scattering event enable us to measure the spin components along the x, y and z axes of the Bloch sphere (Fig. 4b). From the different projections, we find the traversal time τ_y and the time τ_z associated with the backaction of the measurement (Fig. 4c). At the lowest incident velocity (4.1 mm s^−1), we observe a transmission probability of 3%. Given the energy dependence of the transmission, we calculate that the transmitted atoms have a velocity distribution with a peak at 4.8 mm s^−1, corresponding to κd ≈ 3. About three-quarters of this distribution corresponds to energies below the barrier height. The measured traversal time τy is 0.61(7) ms."
"The total duration of the simulations is set such that all the atoms have finished interacting with the barrier. By setting the scattering lengths to zero, we go from the Gross–Pitaevskii equation, also known as the nonlinear Schrödinger equation, to the Schrödinger equation. We find no major differences between the interacting and the non-interacting cases (see Extended Data Fig. 2)."
The passing of the barrier is a complicated situation, especially in this setup.
Where *exactly* was the atom during that 0.27 msec? I'm guessing it was in superposition, on both sides of the barrier simultaneously.
Good question!
It is easier to think of the elementary particles as particles of their quantum fields at first. The field penetrates the barrier but there is no probability current inside the barrier, there is no observable particle inside the volume [
https://en.wikipedia.org/wiki/Probability_current ] but it is its wave function (describing the particle probability amplitude) that has been delocalized over the barrier [
https://en.wikipedia.org/wiki/Quantum_tunnelling ].
Pulling that back to the atom, if it tunnels as a coherent system - as we can see it does - I doubt you can say it existed - was observable - in the common sense definition during the tunneling time. Quantum fields are funny things, they answer the classical question "particle and/or wave", but not always in the way we would think.