29 July 2015 Strong Interactions in Quantum Systems

Strong coupling between pendulums

A study published in Science Advances proposes a powerful Ansatz capable of describing strong coupling between particles in a Fermi gas. One-dimensional quantum systems are often used as a model for understanding the effects of interactions between particles, since there are few physical scenarios that may be solved exactly in this case. However, if the interacting particles are trapped or confined, as occurs in most real-life systems, no exact solutions are generally known, and the complete calculation rapidly becomes impossible as the number of particles increases. Moreover, many materials with potentially important technological applications are poorly understood because they feature particles (electrons) with strong interactions. Therefore, this appears a major unsolved problem in physics.

In the recent study “Strong-coupling Ansatz for the one-dimensional Fermi gas in a harmonic potential” published in Science Advances, a team of researchers including Dr. Pietro Massignan, from the Quantum Optics Theory group led by ICREA Prof. Maciej Lewenstein at ICFO, has presented a theoretical model that provides an incredibly accurate description for a fundamental quantum problem that cannot be solved exactly, the behavior of many particles that strongly interact with one another in a one dimensional harmonic trap.

In the setup considered, the one-dimensional quantum particles behave as a collection of overlapping pendulums. In absence of interactions, the particles just swing back and forth independently. Now, if one of these is different — an impurity — and it is made to interact with the others, it will bounce away from them, modifying both its own motion and that of the “background” particles in some complex manner. What the researchers showed is that if you take interactions as strong as allowed by quantum mechanics and a very large number of background pendulums, then the position of the impurity is almost completely unaffected by the background, it just behaves as if it were a bit lighter. For a strongly interacting quantum system, this is a very surprising collective phenomenon.

Another intriguing result obtained in this study is that the probability of finding the impurity at a specific position relative to the background particles is to great accuracy described by the square of the classical Pascal’s triangle (divided by the sum of the squares in the corresponding row). Such results were derived taking into consideration that the “background” pendulums needed to behave as quantum mechanical identical particles known as fermions. However, since roughly half of the atoms in the periodic table are fermions, this is no great restriction.

The results obtained in this study pave a feasible and exciting pathway towards scenarios where near-exact solutions can be found for systems that are currently considered “too complicated to solve”.