Testing Spontaneous Collapse Models with Coulomb Mediated Squeezing

We show that detecting steady-state Coulomb-mediated reduction in the thermal variance of the differential motional mode of two nanospheres can bound the Continuous Spontaneous Localization (CSL) parameter ($\lambda_{{\text{CSL}}}$). For realistic experimental parameters, the resulting bounds are comparable to those obtained from X-ray emission experiments and surpass those set by bulk-heating ones. Unlike these latter experiments, our bounds are robust against plausible coloured-noise extensions of collapse models. In the short-time regime, we find that a weak Coulomb-induced entanglement-based test between two charged nanospheres initialized in ground state can provide constraints on $\lambda_{\text{CSL}}$ comparable to limits set by early X-ray experiments.