Pair Density Wave correlations in the Kondo-Heisenberg Model

We show, using density matrix renormalization group calculations complemented by field theoretic arguments, that the spin gapped phase of the one dimensional Kondo-Heisenberg model exhibits quasi-long range superconducting correlations {\it only} at a non-zero momentum. The local correlations in this phase resemble those of the pair density wave state which was recently proposed to describe the phenomenology of the striped ordered high temperature superconductor {La${}_{2-x}$Ba${}_x$% CuO${}_4$}, in which the spin, charge, and superconducting orders are strongly intertwined.