This paper proposes new ways to tell whether the mobile carriers in a strongly correlated quantum system behave like electrons or like holes. The authors show that measurements of nonlinear responses and non-Gaussian fluctuations in cold-atom quantum simulators can reveal the sign of the quasiparticle charge. These approaches avoid the usual route of measuring the Hall effect with a synthetic magnetic field, which in cold atoms typically causes heating and experimental complications.

The core idea is to use two kinds of probes. The first is a second-order response of the density or current to a spatially modulated perturbation. In plain terms, if you push the system with a pattern that varies in space and time, you get a small response at the drive frequency and a second-harmonic response at twice that frequency. Because this second-harmonic response depends on an odd power of the carrier charge, its sign tells you whether carriers are electron-like or hole-like. The second approach uses equilibrium statistics: repeated single-site measurements give the full distribution of particle number in a region, and the third cumulant (skewness) of that distribution changes sign depending on the carrier type.

The authors test the ideas with concrete calculations. For a multi-leg ladder version of the Fermi–Hubbard model, numerical simulations show a crossover from hole-like to electron-like carriers when the system is hole-doped away from half-filling. That crossover matches the sign change seen in the Hall coefficient in these simulations. They also analyze a hard-core boson ladder and find that the second-harmonic density response reveals the carrier sign there as well. In the bosonic case, the nonlinear signal can be much stronger if the drive is tuned near a nonlinear collective mode, which could help experiments detect the effect.