Fermions in Optical Lattices across Feshbach Resonance

TL;DR

This paper analyzes fermions in optical lattices across Feshbach resonance, deriving effective Hamiltonians, energy expressions, and explaining band population dynamics during adiabatic sweeps, with implications for condensed matter physics.

Contribution

It provides a theoretical framework for understanding fermionic behavior in optical lattices across Feshbach resonance, including energy calculations and entanglement evolution.

Findings

Derived effective Hamiltonian for fermions in optical lattices.

Explained selective band population after adiabatic sweep.

Showed increasing quantum entanglement during the process.

Abstract

We point out that the recent experiments at ETH \cite{Esslinger} on fermions in optical lattices, where a band insulator evolves continuously into states occupying many bands as the system is swept adiabatically across Feshbach resonance, have implications on a wide range of fundamental issues in condensed matter. We derive the effective Hamiltonian of these systems, obtain expressions for their energies and band populations, and point out the increasing quantum entanglement of the ground state during the adiabatic sweep. Our results also explains why only specific regions in $k$-space can be populated after the sweep as found in ref. \cite{Esslinger}.