Cold atoms in an optical lattice with a synthetic extra dimension could be used to see the 4D version of the quantum Hall effect.
Oded Zilberberg /ETH
The quantum Hall effect (QHE) is now sufficiently “standard” that it’s the basis for a unit of measure (the ohm). But more exotic offshoots of this famously 2D phenomenon have yet to be explored, such as a 4D version predicted in 2001. This hyperdimensional “topological” material is predicted to host relativistic-like particles that carry electric current along its 3D surfaces, an effect that’s difficult to isolate in a regular solid. A way to observe the 4DQHE in a cold atomic system has now been proposed by a team of theorists from the Bose-Einstein Condensate Center in Trento, Italy, the Swiss Federal Institute of Technology (ETH) in Zurich, and the Université libre de Bruxelles, Belgium.
The 4DQHE can emerge in a 4D lattice when magnetic fields pierce two orthogonal lattice planes. To engineer an analogous situation in an atomic system, the authors imagine trapping atoms in a 3D optical lattice and then stretching it into a synthetic fourth dimension. This is possible thanks to a relatively new approach that involves using a laser to couple the internal states of an atom in such a way as to simulate the presence of an extra spatial dimension. Finally, the researchers would harness established atom-manipulation techniques based on lasers to generate “artificial” magnetic fields.
If experimentalists implement this idea, they’ll need a measurable signature of the 4DQHE in a 4D lattice. The authors suggest detecting the speed with which an atom cloud drifts through the lattice, as its value should be characteristic of the 4DQHE topology.
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