Simulating the Wess-Zumino Supersymmetry Model in Optical Lattices

We study a cold atom-molecule mixture in two-dimensional optical lattices. We show that, by fine-tuning the atomic and molecular interactions, the Wess-Zumino supersymmetry (SUSY) model in $2+1$ dimensions emerges in the low-energy limit and can be simulated in such mixtures. At zero temperature, SUSY is not spontaneously broken, which implies identical relativistic dispersions of the atom and its superpartner, a bosonic diatom molecule. This defining signature of SUSY can be probed by single-particle spectroscopies. Thermal breaking of SUSY at a finite temperature is accompanied by a thermal Goldstone fermion, i.e., phonino excitation. This and other signatures of broken SUSY can also be probed experimentally.

Figure 1

(a) Josephson tunneling between the atom-molecule mixture (lower lattice plane) and the dimolecule Bose-Einstein condensate nearby (upper plane). The orange dots are molecules in the mixture, and red dots are dimolecules. Fermionic atoms are in the lattice sites. (b) The square lattice where 1, 2, 3, and 4 denote the next nearest neighbor sites.