Fermionizing the ideal Bose gas via topological pumping

We investigate the coherence and correlations of many-body states appearing in topological pumping in a one-dimensional Bose gas. By analyzing the system at zero and infinite interaction strengths, we reveal a rescaling of momentum distributions accompanied by a self-similar behavior in first- and second-order correlation functions. In the excited states of noninteracting bosons, the momentum distribution shows a comblike structure similar to that of noninteracting fermions but at a higher density. This is mirrored by Friedel oscillations in the one-body density matrix. At the same time, the density-density correlations still exhibit a bosonic enhancement. Our work illustrates how topological pumping induces a nontrivial mapping between bosonic and fermionic correlations.