Everything you always wanted to know about quantum tunneling and photon propagation but were afraid to ask

Aephraim M. Steinberg
Professor of Physics, Centre for Quantum Information and Quantum Control
Department of Physics, University of Toronto

cqiqc.physics.utoronto.ca

Abstract

If there are two problems you would think quantum mechanicists and quantum opticians had beaten to death, they might be quantum tunneling and the propagation of photons through a cloud of atoms.

And yet when you look more deeply – and ask "where are the atoms while they’re tunneling through the forbidden region, and how much time do they spend there?" or "how do photons get slowed down, and where is the energy spending its time?" – the answers are not so simple.

This is related to a simple reality: one of the most famous tidbits of received wisdom about quantum mechanics is that one "cannot ask" how a particle got to where it was finally observed, e.g., which path of an interferometer a photon took before it reached the screen. What, then, do present observations tell us about the state of the world in the past? I will describe two experiments looking into aspects of this “quantum retrodiction.” In the first, we measure how long Bose-condensed atoms spend inside a potential barrier (created by a far-detuned laser beam focused to 1 micron) before being transmitted; I will also talk about some predictions regarding what insidious effects actually observing a particle in the barrier could have. In the second, we measure the amount of time atoms spend in the excited state when a resonant photon is not absorbed by those atoms, but propagates clear through. We find, surprisingly, that the answer need not even be a positive number. I will connect this to better-known aspects of optical propagation.

Some References

[1] Measuring the time a tunnelling atom spends in the barrier, Ramón Ramos, David Spierings, Isabelle Racicot, & Aephraim M. Steinberg, Nature 583, 529 (2020).
[2] Observation of the decrease of Larmor tunneling times with lower incident energy, David C. Spierings, & Aephraim M. Steinberg, Phys. Rev. Lett. 127, 133001 (2021).
[3] Spin Rotations in a Bose-Einstein Condensate Driven by Counterflow and Spin-independent Interactions, David C. Spierings, Joseph H. Thywissen, & Aephraim M. Steinberg, cond-mat/2308.16069 (2023)
[3] Measuring the time atoms spend in the excited state due to a photon they do not absorb, Josiah Sinclair, Daniela Angulo, Kyle Thompson, Kent Bonsma-Fisher, Aharon Brodutch, & Aephraim M. Steinberg, PRX Quantum 3, 010314 (2022).
[4] How much time does a resonant photon spend as an atomic excitation before being transmitted?, Kyle Thompson, Kehui Li, Daniela Angulo, Vida-Michelle Nixon, Josiah Sinclair, Amal Vijayalekshmi Sivakumar, Howard M. Wiseman, & Aephraim M. Steinberg, quant-ph/2310.00432 (2023)