Quantum Dynamics of Polaron Formation

We calculate the real space and time formation of a polaron quasiparticle from a bare electron. The time-dependent Schr\"odinger equation for the Holstein model of electron-phonon coupling is numerically integrated in a large Hilbert space to obtain the time evolution of the electron and phonon densities and the electron-phonon (el-ph) correlation functions. The quantum dynamical nature of the phonons is preserved. As the el-ph coupling increases, qualitative changes in polaron formation occur when the one-phonon polaron bound state forms. A potential barrier between the quasifree and heavy polaron states exists in dimensions $D\ensuremath{\geqslant}2$, consistent with earlier adiabatic theory. We compare to recent experiments.