Goldstino spectrum in an ultracold Bose-Fermi mixture with explicitly broken supersymmetry

Abstract

We theoretically investigate a supersymmetric collective mode called the Goldstino in a Bose-Fermi mixture. The explicit supersymmetry breaking, which is unavoidable in cold-atom experiments, is considered. We derive the Gell-Mann-Oakes-Renner (GOR) relation for the Goldstino, which gives the relation between the energy gap at zero momentum and the explicit breaking term. We also numerically evaluate the gap of the Goldstino above the Bose-Einstein condensation temperature within the random phase approximation (RPA). While the gap obtained from the GOR relation coincides with that in the RPA for the mass-balanced system, there is a deviation from the GOR relation in the mass-imbalanced system. We point out that the deviation becomes large when the Goldstino pole is close to the branch point, although it is parametrically a higher order with respect to the mass-imbalanced parameter. To examine the existence of the Goldstino pole in realistic cold atomic systems, we show how the mass-imbalance effect appears in Li6-Li7, K40-K41, and Yb173-Yb174 mixtures. Furthermore, we analyze the Goldstino spectral weight in a Yb173-Yb174 mixture with realistic interactions and show a clear peak due to the Goldstino pole. As a possibility to observe the Goldstino spectrum in cold-atom experiments, we discuss the effects of the Goldstino pole on fermionic single-particle excitation as well as the relationship between the GOR relation and Tan's contact.