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arXiv:1003.5873 · Europhysics Letters (EPL)

Bound states and universality in layers of cold polar molecules

J. R. Armstrong, Nikolaj Thomas Zinner, D. V. Fedorov, A. S. Jensen

Published Jul 1, 2010• 50 citations
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Abstract

The recent experimental realization of cold polar molecules in the rotational and vibrational ground state opens the door to the study of a wealth of phenomena involving long-range interactions. By applying an optical lattice to a gas of cold polar molecules one can create a layered system of planar traps. Due to the long-range dipole-dipole interaction one expects a rich structure of bound complexes in this geometry. We study the bilayer case and determine the two-body bound-state properties as a function of the interaction strength. The results clearly show that a least one bound state will always be present in the system. In addition, bound states at zero energy show universal behavior and extend to very large radii. These results suggest that non-trivial bound complexes of more than two particles are likely in the bilayer and in more complicated chain structures in multilayer systems.

DOI
10.1209/0295-5075/91/16001

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The recent experimental realization of cold polar molecules in the rotational and vibrational ground state opens the door to the study of a wealth of phenomena involving long-range interactions. By applying an optical lattice to a gas of cold polar molecules one can create a layered system of planar traps. Due to the long-range dipole-dipole interaction one expects a rich structure of bound complexes in this geometry. We study the bilayer case and determine the two-body bound-state properties as a function of the interaction strength. The results clearly show that a least one bound state will always be present in the system. In addition, bound states at zero energy show universal behavior and extend to very large radii. These results suggest that non-trivial bound complexes of more than two particles are likely in the bilayer and in more complicated chain structures in multilayer systems.
The exploration of cold polar molecules in different geometries is a rapidly developing experimental and theoretical pursuit. Recently, the implementation of optical lattices has enabled confinement in stacks of planes, the number of which is also controllable. Here we consider the bound state structure of two polar molecules confined in two adjacent planes as function of the polarization angle of the dipole moment of the molecules. We prove analytically and present numerical evidence for the existence of bound states for arbitrary dipole moments and polarization directions in this two-dimensional geometry. The spatial structure of the bound states is dominated by two-dimensional s- and p-waves, where the latter exceeds 40 percent over a large range of polarization angles for intermediate or strong dipole strength. Finally, we consider the influence of the dimer bound states on the potential many-body ground-state of the system.
Recent experimental progress in producing ultracold polar molecules with a net electric dipole moment opens up possibilities for realizing quantum phases governed by the long-range and anisotropic dipole-dipole interactions. In this work we predict the existence of experimentally observable broken-symmetry states with spontaneous interlayer coherence in cold polar molecule bilayers. These exotic states, which are manifestations of collective bilayer quantum entanglement, appear due to strong repulsive interlayer interactions and exhibit properties of superfluids, ferromagnets, and excitonic condensates.
The research in this dissertation is devoted to few-body bound state physics in experimentally relevant systems of trapped atoms and molecules. First, the complexes of tubes containing dipoles are considered. The tubes are assumed to have zero width such that one-dimensional treatment can be applied. For this setup few-body bound structures are found for different polarization an- gles and dipole strengths by using stochastic variational methods. After that a similar analysis is provided for two-dimensional planes filled with dipolar par- ticles. At the end of the thesis, a system of particles in one-dimensional traps is analyzed assuming that two-body interactions are of zero range. It is shown that such a system is solvable in the limit of infinitely strong repulsion between particles.
We study the two-body bound states of a model Hamiltonian that describes the interaction between two field-oriented dipole moments. This model has been used extensively in the many-body physics of ultracold polar molecules and magnetic atoms, but its few-body physics has been explored less fully. With a hard-wall short-range boundary condition, the dipole-dipole bound states are universal and exhibit a complicated pattern of avoided crossings between states of different character. For more realistic Lennard--Jones short-range interactions, we consider parameters representative of magnetic atoms and polar molecules. For magnetic atoms, the bound states are dominated by the Lennard--Jones potential, and the perturbative dipole-dipole interaction is suppressed by the special structure of van der Waals bound states. For polar molecules, we find a dense manifold of dipole-dipole bound states with many avoided crossings as a function of induced dipole or applied field, similar to those for hard-wall boundary conditions. This universal pattern of states may be observable spectroscopically for pairs of ultracold polar molecules.
Ultracold polar molecules, because of their long-range, spatially anisotropic interactions, are a new quantum system in which to study novel many-body phenomena. In our lab, we have produced the first quantum gas of 40K87Rb polar molecules. These molecules were found to undergo exothermic chemical reactions, and this led to interesting studies of chemistry near absolute zero. By creating the molecules at individual sites of a 3D optical lattice, we completely suppress these chemical reactions, and the polar molecule gas becomes stable and lives for tens of seconds. This thesis documents our efforts to explore coherent, many-body phenomena resulting from long-range dipolar interactions in the lattice. By encoding a spin-1=2 system in the rotational states of the molecules, we were able to realize spin-exchange interactions based on a spin Hamiltonian, which is one of the first steps in studying quantum magnetism with polar molecules. While this study was the first realization of such coherent dipolar interactions with polar molecules in a lattice, its full potential was limited by the low lattice filling fractions. Using our ability to exquisitely control the initial atomic gas mixture, we loaded a Mott insulator of Rb and a band insulator of K into the lattice. This quantum synthesis approach led to significantly higher molecular filling fractions and represents the first fully connected system of polar molecules in an optical lattice. This low-entropy quantum gas of polar molecules opens the door to interesting quantum simulations, which should be attainable in the next generation of the experiment.