Optical lattice emulators

Abstract

Abstract The equilibrium thermodynamics of bosons and fermions in optical lattices are considered in the single-band Hubbard regime, with an emphasis on interesting magnetic, superfluid, and spin liquid ground states. The parameters of the Hubbard model—the tunneling and interaction parameters—can be obtained quantitatively in terms of the strength and periodicity of the optical lattice potential, tuned by the laser intensity and wavelength. This direct link between the parameters of a theoretical model and the actual experimental optical lattice gives rise to the phase diagram of the Bose–Hubbard model. The definition of the order parameter as an expectation value of the annihilation operator in a coherent state is discussed. This phase-coherent superfluid state is contrasted with the phase-incoherent Mott state naturally defined in terms of number states. Following the repulsive Bose–Hubbard model, the phase diagram of the Fermi–Hubbard model is considered with both attractive and repulsive interactions.