Parametric resonance and spin-charge separation in 1D fermionic systems

We show that the periodic modulation of the Hamiltonian parameters for 1D correlated fermionic systems can be used to parametrically amplify their bosonic collective modes. Treating the problem within the Luttinger liquid picture, we show how charge and spin density waves with different momenta are simultaneously amplified. We discuss the implementation of our predictions for cold atoms in 1D modulated optical lattices, showing that the fermionic momentum distribution directly provides a clear signature of spin-charge separation.