  A large polaron is a quasiparticle that consists of a nearly free electron
interacting with the phonons of a material, whose lattice parameters are much
smaller than the polaron scale. The electron-phonon interaction also leads to
an attractive interaction between electrons, which can allow two polarons to
pair up and form a bipolaron. It has been shown that large bipolarons can form
in theory due to strong 1-electron-1-phonon coupling, but they have not been
seen in real materials because the critical value of the required
electron-phonon interaction is too large. Here, we investigate the effect of
1-electron-2-phonon coupling on the large bipolaron problem.
  Starting from a generalization of the Fr\"ohlich Hamiltonian that includes
both the standard 1-electron-1-phonon interaction as well as an anharmonic
1-electron-2-phonon interaction, we use the path integral method to find a
semi-analytical upper bound for the bipolaron energy that is valid at all
values of the Fr\"ohlich coupling strength $\alpha$. We find the bipolaron
phase diagram and conditions for the bipolaron stability by comparing the
bipolaron energy to the energy of two free polarons. The critical value of the
Fr\"ohlich coupling strength $\alpha_{\text{crit}}$ is calculated as a function
of the strength of the 1-electron-2-phonon interaction. The results suggest
that large bipolaron formation is more likely in materials with significant
1-electron-2-phonon interaction as well as strong 1-electron-1-phonon
interaction, such as strontium titanate.
