Abstract
We describe how to design a large class of always on spin-1 interactions between polar molecules trapped in an optical lattice. The spin degrees of freedom correspond to the hyperfine levels of a ro-vibrational ground state molecule. Interactions are induced using a microwave field to mix ground states in one hyperfine manifold with the spin entangled dipole–dipole coupled excited states. Using multiple fields, anistropic models in one, two, or three dimensions can be built with tunable spatial range. An illustrative example in one-dimension is the generalized Haldane model, which at a specific parameter has a gapped valence bond solid ground state. The interaction strengths are large compared to decoherence rates and should allow for probing the rich phase structure of strongly correlated systems, including dimerized and gapped phases.
Highlights
Spin lattices are regular arrays of quantum mechanical spins with interactions involving small sets or neighborhoods of particles
It is meant that the propagator on an n spin system can be computed with a number of resources that grows as a polynomial in n provided the propagation time is no longer than polylogarithmic in n [5]
Building on previous work on designing spin lattice Hamiltonians with spin−1/2 polar molecules we have shown how to build spin−1 models using the same mechanism
Summary
Spin lattices are regular arrays of quantum mechanical spins with interactions involving small sets or neighborhoods of particles. There are some highly correlated ground states of spin lattice Hamiltonians that serve as resources for quantum information processing [6] For these reasons, it would be advantageous to be able to build a physical quantum mechanical simulation of the Hamiltonian. The spectroscopy of the molecules is much richer than for single atoms allowing the simultaneous trapping on optical transition frequencies and coherent control at microwave frequencies with weak decoherence due to spontaneous emission These features make these systems experimentally relevant candidates for quantum simulators. Nature provides us with the state space isomorphic to interger spin by encoding in ground electronic hyperfine levels of molecules with half integer nuclear spin, of which there are many species. It is a straightforward matter to adapt the following analysis to derive effective spin models with larger integer or half integer spins
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