Formation of fermion pairs: Role in superconductivity

Scientists have divided all elementary particles into two categories based on the value of their spin, which is similar to classical rotation. The behavior of these particles varies greatly depending on whether their spin is an integer or half-integer value. Particles with an integer spin are known as bosons, whereas those with a half-integer spin are called fermions. Examples of fermions include electrons, protons, and neutrons, which make up ordinary matter, while bosons include photons, particles that mediate weak, strong, and gravitational interactions, and the Higgs boson, which gives mass to all elementary particles.

Fermions tend to stay away from each other, especially when they are identical, such as two electrons. However, under certain conditions, such as at ultralow temperatures or ultrahigh densities, they tend to form bound pairs. This phenomenon is crucial in nuclear and neutron star physics, as well as in superconductivity. When electrons form paired states, known as Cooper pairs, they can move through a superconducting material without resistance, unlike individual electrons, which can lose energy and turn into heat as they collide with each other and the crystal lattice. Therefore, studying the process of fermion pair formation is essential.

To investigate this phenomenon, a group of American physicists from the MIT-Harvard Center for Ultracold Atoms and Research Laboratory of Electronics at MIT conducted an experiment. They observed the direct formation of fermion pairs by studying the behavior of much heavier fermions than electrons, namely potassium atoms. Although these atoms are not elementary particles, they have a half-integer spin that makes their behavior similar to that of electrons.

The team cooled a dilute gas of about 1,000 potassium atoms to nanokelvins, which slowed down their movement significantly. To keep the atoms together, the scientists employed an optical trap, which consisted of a grid of laser beams that restricted the atoms’ movement but allowed them to jump from one grid cell to another, as permitted by quantum mechanics.

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To determine whether the atoms had formed fermion pairs, the team studied the gas’s response to a magnetic field. This is because fermion pairs react to magnetic fields much weaker than free electrons. After taking multiple measurements, the researchers found that many gas atoms had formed bound pairs inside the cells of the grid. However, studying the formation of electron pairs remains impossible because these particles are too light and fast to observe the formation of their bound states.

“Fermion pairing is at the basis of superconductivity and many phenomena in nuclear physics,” explained Martin Zwierlein, the Thomas A. Frank Professor of Physics at MIT and one of the authors of the study. “But no one had seen this pairing in situ. So it was just breathtaking to then finally see these images onscreen, faithfully.”

Since the experiment required a very high accuracy of measurements and a huge number of these; the authors had to take thousands of snapshots of the atomic cloud using their measurement technique to get the final picture of pair formation. “It was bloody difficult to get to a point where we could actually take these images,” Zwierlein says. “You can imagine at first getting big fat holes in your imaging, your atoms running away, nothing is working. We’ve had terribly complicated problems to solve in the lab through the years, and the students had great stamina, and finally, to be able to see these images was absolutely elating.”

Physicists have confirmed the accuracy of the Hubbard model, which is utilized to theoretically describe the conduct of fermion pairs. The researchers also found pairs of atoms forming at a considerable distance apart, which is consistent with the predictions of this model. Another projected but never seen occurrence, the arrangement of fermion pairs diagonally to create a checkerboard pattern, was also observed. Despite the fact that the physicists worked with potassium atoms at extremely low temperatures, they believe that the picture of fermion pair formation they observed and the confirmation of the Hubbard model will lead to a better comprehension of superconductivity, and possibly even allow for its achievement at room temperature in the future.

“If you normalize our gas of atoms to the density of electrons in a metal, we think this pairing behavior should occur far above room temperature,” concluded Zwierlein. “That gives a lot of hope and confidence that such pairing phenomena can in principle occur at elevated temperatures, and there’s no a priori limit to why there shouldn’t be a room-temperature superconductor one day.”

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References:
1. Thomas Hartke et al. ,Direct observation of nonlocal fermion pairing in an attractive Fermi-Hubbard gas.Science381,82-86(2023).DOI:10.1126/science.ade4245
2. M. Inguscio, W. Ketterle, C. Salomon, Ultracold Fermi Gases (IOS Press, 2008).
3. W. Zwerger, Ed., The BCS-BEC Crossover and the Unitary Fermi Gas (Springer, 2012).
4. M. Randeria, E. Taylor, Crossover from Bardeen-Cooper-Schrieffer to Bose-Einstein Condensation and the Unitary Fermi Gas. Annu. Rev. Condens. Matter Phys.5, 209–232 (2014).
5. R. A. Fontenele, N. C. Costa, R. R. dos Santos, T. Paiva, Two-dimensional attractive Hubbard model and the BCS-BEC crossover. Phys. Rev. B105, 184502 (2022).

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