Even localized particles very gradually interact

Alex Lukin in a postdoc in atomic and molecular physics at Harvard and a member of the Greiner Lab. I sat across from him on a Tuesday night in June and tried to get an angle on a paper of his that I had come across in Science. The paper by him and eight other authors seemed fascinating, but it deals in quantum physics, and my background is in plasma physics.

Their paper has to do with the unusual dynamics of quantum systems. In other words, particle motions. If we can even say that, because particles are also waves, and therefore particle motion is not a fully cogent concept. Yet physicists are human and often have to think in particle terms.

This specific paper discusses the dynamics of particles in a controlled system. The key method of experimentation in this controlled system is the introduction of disorder.

Order and disorder, then.

To create the order, the authors start out with a regular grid of high intensity light beams, spaced with atomic precision. Drop ultracold rubidium atoms into the grid and they settle into the low energy wells that lie between the light beams.

In the authors’ experiment, each well starts out with one single atom. Then they reduce the intensity of the light, and hence the depth of the wells, so that the atoms start moving — tunneling — between the well walls.

But very quickly, into this regular system of atoms, the authors introduce a disorder. Disorder in this case consists in firing light into the wells with an incongruous pattern such that the energy of particles in certain areas is enhanced.

This was a point that I at first completely mistook. Alex and I spent a few minutes addressing and redressing the same point. He explained in both pictures and math. In his own words, he is both an experimentalist and a theorist.

The secondary light shined into the wells that introduces disorder does not change the shape of the wells, even though those wells are themselves created by an optical beam system. This is because the disordering light is of a low enough intensity that it only changes the particle energy.

If the particles are there. In a disordered system, the particles do not move all about. The heightened energy of certain regions excludes them, forcing the particles to become localized in a well-known process called Anderson localization.

Yet when Lukin et. al. introduce disorder, the particles are not only localized, but forced to lie within the fixed set of wells. Hypothetically, the particles can pile up in the same wells and interact. This chance of interacting — which is essentially negligible, and only a chance because particles fundamentally spread out like waves — leads to an exotic phenomenon called many-body-localization.

The dynamics of this process are not easy to study. But when particles can even virtually pile up and interact, there is a slow growth in entropy that evolves over a long time scale, which the authors measure for the first time. Though the authors cannot measure the entropy directly, they invent a new correlation function that scales with the entropy.

Measurements of this function show how the particles very gradually interact and entangle without ever actually moving. In Lukin’s own words:

“Although we see that the particles are completely stuck, with no transport through the system, and naively nothing can develop anymore, we see that in a many-body way these subsystems can get entangled through virtual processes where particles are interacting with one another.”

References:

Probing entanglement in a many-body–localized system. Alexander Lukin, Matthew Rispoli, Robert Schittko, M. Eric Tai, Adam M. Kaufman, Soonwon Choi, Vedika Khemani, Julian Léonard, Markus Greiner. Science, 19 Apr 2019: Vol. 364, Issue 6437, pp. 256–260. DOI: 10.1126/science.aau0818

In the phenomenon of many-body-localization (MBL), isolated particles gradually interact and entangle. Image credit: Greiner Lab

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