Atomic Quantum Simulator for Lattice Gauge Theories and Ring Exchange Models

We present the design of a ring exchange interaction in cold atomic gases subjected to an optical lattice using well-understood tools for manipulating and controlling such gases. The strength of this interaction can be tuned independently and describes the correlated hopping of two bosons. We discuss a setup where this coupling term may allow for the realization and observation of exotic quantum phases, including a deconfined insulator described by the Coulomb phase of a three-dimensional U(1) lattice gauge theory.

Figure 1

(a) Two-dimensional setup: the bosons (black dots) are on the square lattice with the molecules (gray dots) in the center of each plaquette. (b) Three-dimensional setup: the bosons (black dots) are on the links of the cubic lattice. Within each face there are four bosonic sites, which establish a plaquette (dashed square). The molecules (gray dots) are in the center of each plaquette.

Figure 2

(a) Single-particle energies ${ϵ}_l$ of the states $a_{l,\square }^{†}|0⟩$ for $v_{\mathrm{a}}=30$. (b) Energy levels of the two-particle states with symmetry $B_2$ and $E$. The frequency $\omega =({ϵ}_0+{ϵ}_2+U_{02}+\nu )/2\hslash$ of the Raman transition is chosen near resonance with the molecular state $a_0^{†}{a}_2^{†}|0⟩$ and far detuned to the single-particle excitations.