# Quantum Adiabatic Doping with Incommensurate Optical Lattices

## TL;DR

This paper proposes a method for doping Fermi-Hubbard models in optical lattices via adiabatic evolution, addressing localization challenges and suggesting interaction-induced delocalization to improve efficiency in low-temperature quantum simulations.

## Contribution

It introduces a theoretical protocol for adiabatic doping in incommensurate optical lattices, overcoming localization issues with many-body delocalization techniques.

## Key findings

- Localization hinders adiabatic doping in strong lattice regimes.
- Interaction-induced delocalization can mitigate slowing down in 1D.
- The protocol is potentially effective in 2D where localization is less stable.

## Abstract

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. Here we propose to achieve the low temperature phase of the doped Fermi-Hubbard model using incommensurate optical lattices through adiabatic quantum evolution. In this theoretical proposal, we find that one major problem about the adiabatic doping that shows up is atomic localization in the incommensurate lattice, potentially causing exponential slowing down of the adiabatic procedure. We study both one- and two-dimensional incommensurate optical lattices, and find that the localization prevents efficient adiabatic doping in the strong lattice regime for both cases. With density matrix renormalization group calculation, we further show that the slowing down problem in one dimension can be circumvented by considering interaction induced many-body delocalization, which is experimentally feasible using Feshbach resonance techniques. This protocol is expected to be efficient as well in two dimensions where the localization phenomenon is less stable.