A proposed experiment that would involve trapping atoms on a two-layered laser grid could be used to study the mechanism behind high-temperature superconductivity. Developed by physicists in Germany and France led by Henning Schlömer the new techniques could revolutionize our understanding of high-temperature superconductivity.

Superconductivity is a phenomenon characterized by an abrupt drop to zero of electric resistance when certain materials are cooled below a critical temperature. It has remained in the physics zeitgeist for over a hundred years and continues to puzzle contemporary physicists. While scientists have a good understanding of “conventional” superconductors (which tend to have low critical temperatures), the physics of high-temperature superconductors remains poorly understood.  A deeper understanding of the mechanisms responsible for high-temperature superconductivity could unveil the secrets behind macroscopic quantum phenomena in many-body systems.

Mimicking real crystalline materials

Optical lattices have emerged as a powerful tool to study such many-body quantum systems. Here, two counter-propagating laser beams overlap to create a standing wave. Extending this into two dimensions creates a grid (or lattice) of potential-energy minima where atoms can be trapped (see figure). The interactions between these trapped atoms can then be tuned to mimic real crystalline materials giving us an unprecedented ability to study their properties.

Superconductivity is characterized by the formation of long-range correlations between electron pairs. While the electronic properties of high-temperature superconductors can be studied in the lab, it can be difficult to test hypotheses because the properties of each superconductor are fixed. In contrast, correlations between atoms in an optical lattice can be tuned, allowing different models and parameters to be explored.

This could be done by trapping fermionic atoms (analogous to electrons in a superconducting material) in an optical lattice and enabling them to form pair correlations. However, this has proved to be challenging because these correlations only occur at very low temperatures that are experimentally inaccessible. Measuring these correlations presents an additional challenge of adding or removing atoms at specific sites in the lattice without disturbing the overall lattice state. But now, Schlömer and colleagues propose a new protocol to overcome these challenges.

The proposal

The researchers propose trapping fermionic atoms on a two-layered lattice. By introducing a potential-energy offset between the two layers, they ensure that the atoms can only move within a layer and there is no hopping between layers. They enable magnetic interaction between the two layers, allowing the atoms to form spin-correlations such as singlets, where atoms always have opposing spins . The dynamics of such interlayer correlations will give rise to superconducting behaviour.

This system is modelled using a “mixed-dimensional bilayer” (MBD) model. It accounts for three phenomena: the hopping of atoms between lattice sites within a layer; the magnetic (spin) interaction between the atoms of the two layers; and the magnetic interactions within the atoms of a layer.

Numerical simulations of the MBD model suggest the occurrence of superconductor-like behaviour in optical lattices at critical temperatures much higher than traditional models. These temperatures are readily accessible in experiments.

To measure the correlations, one needs to track pair formation in the lattice. One way to track pairs is to add or remove atoms from the lattice without disturbing the overall lattice state. However, this is experimentally infeasible. Instead, the researchers propose doping the energetically higher layer with holes – that is the removal of atoms to create vacant sites. The energetically lower layer is doped with doublons, which are atom pairs that occupy just one lattice site. Then the potential offset between the two layers can be tuned to enable controlled interaction between the doublons and holes. This would allow researchers to study pair formation via this interaction rather than having to add or remove atoms from specific lattice sites.

Clever mathematical trick

To study superconducting correlations in the doped system, the researchers employ a clever mathematical trick. Using a mathematical transformation, they transform the model to an equivalent model described by only “hole-type” dopants without changing the underlying physics. This allows them to map superconducting correlations to density correlations, which can be routinely accessed is existing experiments.

With their proposal, Schlömer and colleagues are able to both prepare the optical lattice in a state, where superconducting behaviour occurs at experimentally accessible temperatures and study this behaviour by measuring pair formation.

When asked about possible experimental realizations, Schlömer is optimistic: “While certain subtleties remain to be addressed, the technology is already in place – we expect it will become experimental reality in the near future”.

The research is described in PRX Quantum

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