We demonstrate the possibility of creating and controlling an ideal and \textit{trimerized} optical Kagom\'e lattice, and study the low temperature physics of various atomic gases in such lattices. In the trimerized Kagom\'e lattice, a Bose gas exhibits a Mott transition with fractional filling factors, whereas a spinless interacting Fermi gas at 2/3 filling behaves as a quantum magnet on a triangular lattice. Finally, a Fermi-Fermi mixture at half filling for both components represents a frustrated quantum antiferromagnet with a resonating-valence-bond ground state and quantum spin liquid behavior dominated by continuous spectrum of singlet and triplet excitations. We discuss the method of preparing and observing such quantum spin liquid employing molecular Bose condensates.
@article{arxiv.cond-mat/0401502,
title = {Atomic quantum gases in Kagom\'e lattices},
author = {L. Santos and M. A. Baranov and J. I. Cirac and H. -U. Everts and H. Fehrmann and M. Lewenstein},
journal= {arXiv preprint arXiv:cond-mat/0401502},
year = {2009}
}