One-dimensional Fermi polaron in a combined harmonic and periodic potential

We study an impurity in a one-dimensional potential consisting of a harmonic and a periodic part using both the time-evolving block decimation (TEBD) algorithm and a variational ansatz. Attractive and repulsive contact interactions with a sea of fermions are considered. We find excellent agreement between TEBD and variational results and use the variational ansatz to investigate higher lattice bands. We conclude that the lowest band approximation fails at sufficiently strong interactions and develop a new method for computing the Tan contact parameter.