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arXiv:1106.1644 · Physical Review Letters

Tunable Superfluidity and Quantum Magnetism with Ultracold Polar Molecules

Alexey Vyacheslavovich Gorshkov, Salvatore R. Manmana, Gang Chen, Jun Ye, Eugene Demler, Mikhail D. Lukin, Ana María Rey

Published Sep 8, 2011• 324 citations
arXivHTMLPDF

Abstract

By selecting two dressed rotational states of ultracold polar molecules in an optical lattice, we obtain a highly tunable generalization of the $t\mathrm{\text{\ensuremath{-}}}J$ model, which we refer to as the $t\mathrm{\text{\ensuremath{-}}}J\mathrm{\text{\ensuremath{-}}}V\mathrm{\text{\ensuremath{-}}}W$ model. In addition to $XXZ$ spin exchange, the model features density-density interactions and density-spin interactions; all interactions are dipolar. We show that full control of all interaction parameters in both magnitude and sign can be achieved independently of each other and of the tunneling. As a first step towards demonstrating the potential of the system, we apply the density matrix renormalization group method to obtain the 1D phase diagram of the simplest experimentally realizable case. Specifically, we show that the tunability and the long-range nature of the interactions in the $t\mathrm{\text{\ensuremath{-}}}J\mathrm{\text{\ensuremath{-}}}V\mathrm{\text{\ensuremath{-}}}W$ model enable enhanced superfluidity. Finally, we show that Bloch oscillations in a tilted lattice can be used to probe the phase diagram experimentally.

DOI
10.1103/physrevlett.107.115301

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By selecting two dressed rotational states of ultracold polar molecules in an optical lattice, we obtain a highly tunable generalization of the t\ensuremath-Jt\mathrm{\text{\ensuremath{-}}}Jt\ensuremath-J model, which we refer to as the t\ensuremath-J\ensuremath-V\ensuremath-Wt\mathrm{\text{\ensuremath{-}}}J\mathrm{\text{\ensuremath{-}}}V\mathrm{\text{\ensuremath{-}}}Wt\ensuremath-J\ensuremath-V\ensuremath-W model. In addition to XXZXXZXXZ spin exchange, the model features density-density interactions and density-spin interactions; all interactions are dipolar. We show that full control of all interaction parameters in both magnitude and sign can be achieved independently of each other and of the tunneling. As a first step towards demonstrating the potential of the system, we apply the density matrix renormalization group method to obtain the 1D phase diagram of the simplest experimentally realizable case. Specifically, we show that the tunability and the long-range nature of the interactions in the t\ensuremath-J\ensuremath-V\ensuremath-Wt\mathrm{\text{\ensuremath{-}}}J\mathrm{\text{\ensuremath{-}}}V\mathrm{\text{\ensuremath{-}}}Wt\ensuremath-J\ensuremath-V\ensuremath-W model enable enhanced superfluidity. Finally, we show that Bloch oscillations in a tilted lattice can be used to probe the phase diagram experimentally.
We show that dipolar interactions between ultracold polar alkali-metal dimers in optical lattices can be used to realize a highly tunable generalization of the ttt-JJJ model, which we refer to as the ttt-JJJ-VVV-WWW model. The model features long-range spin-spin interactions Jz{J}_{z}Jz​ and ${J}_{\ensuremath{\perp}}$ of XXZXXZXXZ type, long-range density-density interaction VVV, and long-range density-spin interaction WWW, all of which can be controlled in both magnitude and sign independently of each other and of the tunneling ttt. The ``spin'' is encoded in the rotational degree of freedom of the molecules, while the interactions are controlled by applied static electric and continuous-wave microwave fields. Furthermore, we show that nuclear spins of the molecules can be used to implement an additional (orbital) degree of freedom that is coupled to the original rotational degree of freedom in a tunable way. The presented system is expected to exhibit exotic physics and to provide insights into strongly correlated phenomena in condensed-matter systems. Realistic experimental imperfections are discussed.
Recent work on ultracold polar molecules, governed by a generalization of the ttt-JJJ Hamiltonian, suggests that molecules may be better suited than atoms for studying ddd-wave superfluidity due to stronger interactions and larger tunability of the system. We compute the phase diagram for polar molecules in a checkerboard lattice consisting of weakly coupled square plaquettes. In the simplest experimentally realizable case where there is only tunneling and an XXXXXX-type spin-spin interaction, we identify the parameter regime where ddd-wave superfluidity occurs. We also find that the inclusion of a density-density interaction destroys the superfluid phase and that the inclusion of a spin-density or an Ising-type spin-spin interaction can enhance the superfluid phase. We also propose schemes for experimentally realizing the perturbative calculations exhibiting enhanced ddd-wave superfluidity.
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.
Abstract : With the production of polar molecules in the quantum regime, long-range dipolar interactions are expected to facilitate understanding of strongly interacting many-body quantum systems and to realize lattice spin models for exploring quantum magnetism. In ordinary atomic systems, where contact interactions require wavefunction overlap, effective spin interactions on a lattice can be mediated by tunnelling, through a process referred to as superexchange; however, the coupling is relatively weak and is limited to nearest-neighbour interactions. In contrast, dipolar interactions exist even in the absence of tunnelling and extend beyond nearest neighbours. This allows coherent spin dynamics to persist even for gases with relatively high entropy and low lattice filling. Measured effects of dipolar interactions in ultracold molecular gases have been limited to the modification of inelastic collisions and chemical reactions. Here we use dipolar interactions of polar molecules pinned in a three-dimensional optical lattice to realize a lattice spin model. Spin is encoded in rotational states of molecules that are prepared and probed by microwaves. Resonant exchange of rotational angular momentum between two molecules realizes a spin-exchange interaction. The dipolar interactions are apparent in the evolution of the spin coherence, which shows oscillations in addition to an overall decay of the coherence. The frequency of these oscillations, the strong dependence of the spin coherence time on the lattice filling factor and the effect of a multipulse sequence designed to reverse dynamics due to two-body exchange interactions all provide evidence of dipolar interactions. Furthermore, we demonstrate the suppression of loss in weak lattices due to a continuous quantum Zeno mechanism. Measurements of these tunnelling-induced losses allow us to determine the lattice filling factor independently.
We compute physical properties across the phase diagram of the $t\ensuremath{-}{J}_{\ensuremath{\perp}}$ chain with long-range dipolar interactions, which describe ultracold polar molecules on optical lattices. Our results obtained by the density-matrix renormalization group indicate that superconductivity is enhanced when the Ising component Jz{J}_{z}Jz​ of the spin-spin interaction and the charge component VVV are tuned to zero and even further by the long-range dipolar interactions. At low densities, a substantially larger spin gap is obtained. We provide evidence that long-range interactions lead to algebraically decaying correlation functions despite the presence of a gap. Although this has recently been observed in other long-range interacting spin and fermion models, the correlations in our case have the peculiar property of having a small and continuously varying exponent. We construct simple analytic models and arguments to understand the most salient features.
We propose encoding a pseudo-spin-1/21/21/2 system in the ground (v=0v=0v=0) and first excited (v=1v=1v=1) vibrational states of polar molecules. Double microwave shielding simultaneously shields molecules in both states, suppressing two-body losses by orders of magnitude while strictly avoiding three-body recombination. The microwave dressing is state-dependent and results in highly tunable, long-range dipolar Ising exchange (JzJ_zJz​), density-density (VVV), and spin-density (WWW) interactions. These interaction length scales readily exceed the typical interparticle spacing, pushing the molecules deep into the strongly interacting regime. In bulk gases, this enables the exploration of itinerant quantum magnetism and quantum droplets with novel anisotropic spin textures; in optical lattices, it naturally realizes extended Hubbard and ttt-JzJ_zJz​ models, opening new directions in quantum simulation.