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arXiv:1110.0071 · Physical Review A

Long-range and frustrated spin-spin interactions in crystals of cold polar molecules

Yan‐Li Zhou, Michael Ortner, Peter Rabl

Published Nov 29, 2011• 24 citations
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Abstract

We describe a simple scheme for the implementation and control of effective spin-spin interactions in self-assembled crystals of cold polar molecules. In our scheme, spin states are encoded in two long-lived rotational states of the molecules and coupled via state-dependent dipole-dipole forces to the lattice vibrations. We show that, by choosing an appropriate time-dependent modulation of the induced dipole moments, the resulting phonon-mediated interactions compete with the direct dipole-dipole coupling and lead to long-range and tunable spin-spin interaction patterns. We illustrate how this technique can be used for the generation of multiparticle entangled spin states and the implementation of spin models with long-range and frustrated interactions, which exhibit nontrivial phases of magnetic ordering.

DOI
10.1103/physreva.84.052332

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We describe a simple scheme for the implementation and control of effective spin-spin interactions in self-assembled crystals of cold polar molecules. In our scheme, spin states are encoded in two long-lived rotational states of the molecules and coupled via state-dependent dipole-dipole forces to the lattice vibrations. We show that, by choosing an appropriate time-dependent modulation of the induced dipole moments, the resulting phonon-mediated interactions compete with the direct dipole-dipole coupling and lead to long-range and tunable spin-spin interaction patterns. We illustrate how this technique can be used for the generation of multiparticle entangled spin states and the implementation of spin models with long-range and frustrated interactions, which exhibit nontrivial phases of magnetic ordering.
We show that indirect spin-spin interactions between effective spin-1/2 systems can be realized in two parallel one-dimensional optical lattices loaded with polar molecules and/or Rydberg atoms. The effective spin can be encoded into low-energy rotational states of polar molecules or long-lived states of Rydberg atoms, tightly trapped in a deep optical lattice. The spin-spin interactions can be mediated by Rydberg atoms, placed in a parallel shallow optical lattice, interacting with the effective spins by charge-dipole (for polar molecules) or dipole-dipole (for Rydberg atoms) interaction. Indirect XXXXXX, Ising, and XXZXXZXXZ interactions with interaction coefficients ${J}^{\ensuremath{\perp}}$ and Jzz{J}^{zz}Jzz sign varying with interspin distance can be realized, in particular, the ${J}_{1}\ensuremath{-}{J}_{2} XXZ$ model with frustrated ferro-(antiferro-)magnetic nearest (next-nearest) neighbor interactions.
We discuss techniques to tune and shape the long-range part of the interaction potentials in quantum gases of bosonic polar molecules by dressing rotational excitations with static and microwave fields. This provides a novel tool towards engineering strongly correlated quantum phases in combination with low-dimensional trapping geometries. As an illustration, we discuss the 2D superfluid-crystal quantum phase transition for polar molecules interacting via an electric-field-induced dipole-dipole potential.
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.
We show how to use polar molecules in an optical lattice to engineer quantum spin models with arbitrary spin $S\ensuremath{\ge}1/2$ and with interactions featuring a direction-dependent spin anisotropy. This is achieved by encoding the effective spin degrees of freedom in microwave-dressed rotational states of the molecules and by coupling the spins through dipolar interactions. We demonstrate how one of the experimentally most accessible anisotropies stabilizes symmetry protected topological phases in spin ladders. Using the numerically exact density matrix renormalization group method, we find that these interacting phases---previously studied only in the nearest-neighbor case---survive in the presence of long-range dipolar interactions. We also show how to use our approach to realize the bilinear-biquadratic spin-1 and the Kitaev honeycomb models. Experimental detection schemes and imperfections are discussed.
We present a technique for engineering quantum magnets via ultracold polar molecules in optical lattices and explore exotic interplay between its spin superfluidity and solidity. The molecular ground and first excited rotational states are resonantly coupled by a linearly polarized microwave field. The spin-up (spin-down) states are presented by molecular rotational states of electric dipole moment along (against) the coupling field. By controlling the angle between the lattice direction and the coupling field, the inter-site interaction can be tuned from antiferromagnetic to ferromagnetic. Furthermore, the dipole-dipole interaction induces an exotic interplay between spin superfluidity and solidity, and spin supersolid phases may appear in mediate regions.