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arXiv:0709.1825 · Physical Review Letters

Cold Atoms and Molecules in Self-Assembled Dipolar Lattices

Guido Pupillo, Andreas Griessner, Andrea Micheli, Michael Ortner, Daw-Wei Wang, P. Zoller

Published Feb 5, 2008• 109 citations
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Abstract

We study the realization of lattice models, where cold atoms and molecules move as extra particles in a dipolar crystal of trapped polar molecules. The crystal is a self-assembled floating mesoscopic lattice structure with quantum dynamics given by phonons. We show that within an experimentally accessible parameter regime extended Hubbard models with tunable long-range phonon-mediated interactions describe the effective dynamics of dressed particles.

DOI
10.1103/physrevlett.100.050402

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•Jan 1, 2013•1 citation
We study the realization of lattice models, where cold atoms and molecules move as extra particles in a dipolar crystal of trapped polar molecules. The crystal is a self-assembled floating mesoscopic lattice structure with quantum dynamics given by phonons. We show that within an experimentally accessible parameter regime extended Hubbard models with tunable long-range phonon-mediated interactions describe the effective dynamics of dressed particles.
In this paper we study the realization of lattice models in mixtures of atomic and dipolar molecular quantum gases. We consider a situation where polar molecules form a self-assembled dipolar lattice, in which atoms or molecules of a second species can move and scatter. We describe the system dynamics in a master equation approach in the Brownian motion limit of slow particles and fast phonons, which we find appropriate for our system. In a wide regime of parameters, the reduced dynamics of the particles leads to physical realizations of extended Hubbard models with tuneable long-range interactions mediated by crystal phonons. This extends the notion of quantum simulation of strongly correlated systems with cold atoms and molecules to include phonon-dynamics, where all coupling parameters can be controlled by external fields.
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.
Point defects in self-assembled crystals, such as vacancies and interstitials, attract each other and form stable clusters. This leads to a phase separation between perfect crystalline structures and defect conglomerates at low temperatures. We propose a method that allows one to tune the effective interactions between point defects from attractive to repulsive by means of external periodic fields. In the quantum regime, this allows one to engineer strongly correlated many-body phases. We exemplify the microscopic mechanism by considering dipolar quantum gases of ground-state polar molecules and weakly bound molecules of strongly magnetic atoms trapped in a weak optical lattice in a two-dimensional configuration. By tuning the lattice depth, defect interactions turn repulsive, which allows us to deterministically design a novel supersolid phase in the continuum limit.
We discuss the realization of mesoscopic phases of dipolar gases relevant to current experiments with cold polar molecules and Rydberg atoms confined to two dimensions. We predict the existence of superfluid clusters, mesoscopic supersolids, and crystals for a small number of trapped particles, with no counterpart in the homogeneous situation. For certain strengths of the dipole-dipole interactions, the stabilization of purely {\it non-classical crystals} by quantum fluctuations is possible. We propose a magnification scheme to detect the spatial structure of these crystalline phases.
The ground state of a two-dimensional, harmonically confined mesoscopic assembly of up to 30 polar molecules is studied by computer simulations. As the strength of the confining trap is increased, clusters evolve from superfluid, to supersolid, to insulating crystals. For strong confinement, the crystalline structure can be predicted based on classical energetics. However, clusters of specific numbers of particles (i.e., N=12N=12N=12 and N=19N=19N=19) display a nonclassical crystalline structure, stabilized by quantum effects, in an intermediate range of confinement strength. In these cases, coexistence of quantum and classical crystalline configurations is observed at finite temperature.
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.