Quantum Adiabatic Doping with Optical Lattice

Quantum simulations of Fermi-Hubbard models have been attracting considerable efforts in the optical lattice research, with the ultracold anti-ferromagnetic atomic phase reached at half filling in recent years. An unresolved issue is to dope the system while maintaining the low thermal entropy. We propose to achieve the low temperature phase of doped FermiHubbard model via converting two lattices with different spacing period. We firstly demonstrate the feasibility of this proposal using a generic irrational filling factor and simulate the adiabatic evolution of free fermions in one- and two- dimensional lattice. The incommmensurate lattice induces localization problem which prevents the adiabatic preparation. We introduce the interaction to solve the localization slowing down. The DMRG calculation show that the preparation efficiency can be strongly enhanced. We extend this proposal to a wide range of filling factors and find that the localization also exists for finite-size system with rational filling. The efficiency of the hole doping is generally much higher than the particle doping because the large tunneling reduces the localization. We also consider starting from Mott insulator state instead of band insulator which further improves the efficiency for some filling.