New theory of one-dimensional anyons on an optical lattice.

Physicists at the Technical University of Kaiserslautern and the University of Hamburg were able to demonstrate theoretical and experimentally accessible properties of anyons in one-dimensional optical lattices. These are in no way inferior to two-dimensional models. The scientists published their results in the journal Physical Review Letters.

Quantum mechanical particles do not have an exact location or momentum. There are only residence probabilities, which are described by so-called wave functions. When indistinguishable particles are considered, many-particle wave functions must be found that do not change their properties when two or more particles are interchanged. This led to the division into particles with symmetric wave functions, the bosons, and particles with antisymmetric wave functions, the fermions, as already proved in the 1940s.

This proof is valid in three or more space dimensions and allows in low space dimensions the existence of particles which are neither bosons nor fermions.
These so-called anyons were assumed to exist exclusively in two space dimensions. In one-dimensional space, no statistic can be defined without taking into account the interactions of the system, since particles must collide to be interchanged. In 1999, Indian physicist Anjan Kundu described a model of such one-dimensional anyons. However, Kundu's model earned criticism and was dismissed by other researchers as unrealistic and an academic gimmick. Reasons were mathematically not well defined interactions, as well as the lack of periodicity in the statistical parameter defining the phase of the wave function under permutation. Thus, the existence of such one-dimensional anyons in real continuous systems remained unresolved until today.

The scientists from Kaiserslautern and Hamburg now found that one-dimensional anyons on an optical lattice can elegantly circumvent these two problems. In theory, the researchers were able to show that the mathematically not well-defined interactions that occurred at Kundu can be fixed by the optical lattice, and thus are in principle realizable in ultracold gases. "We are particularly pleased that Kundu's model is included in our theory as a special case," says Martin Bonkhoff, first author of the paper from the University of Kaiserslautern. "We are thus posthumously upgrading his model from an academic gimmick to an experimentally accessible theory."
"We now hope to be able to implement these findings in new quantum technologies," adds Dr. Thore Posske, co-author from the University of Hamburg.

Original publication
Bosonic Continuum Theory of One-Dimensional Lattice Anyons,
M. Bonkhoff, K. Jägering, S. Eggert, A. Pelster, M. Thorwart, and T. Posske,
Phys. Rev. Lett. 126, 163201 (2021).
DOI: https://doi.org/10.1103/PhysRevLett.126.163201

Questions answered:
Prof. Dr. Sebastian Eggert
Fundamentals of Solids and Many-Particle Systems
Tel.: 0631 205-2375
E-Mail: eggert(at)physik.uni-kl.de