Supersolidity of dipolar Bose-Einstein condensates induced by coupling to fermions

We study a mixture of cold dipolar condensate and degenerate Fermi gas in quasi-one-dimensional geometries. We demonstrate that the presence of fermionic atoms may drastically change the behavior of a quasi-one-dimensional dipolar condensate. For strong enough boson-fermion attraction a roton elementary excitation appears in the spectrum and a roton softening mechanism leads to instability. As shown by numerically solving the coupled set of extended Gross-Pitaevskii and Hartree-Fock equations for bosons and fermions, respectively, a roton instability leads to formation of supersolid phase in a Bose-Einstein condensate. Fermionic component enforces the supersolid phase in a trapped quasi-one-dimensional dysprosium atoms and allows for observation of such phase in less magnetic atoms like chromium or even rubidium.