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arXiv:1109.4602 · Physical Review A

Few-body bound-state stability of dipolar molecules in two dimensions

Artem G. Volosniev, D. V. Fedorov, A. S. Jensen, Nikolaj Thomas Zinner

Published Feb 8, 2012• 27 citations
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Abstract

Bound structures among dipolar molecules in multilayers are a topic of great interest in the light of recent experiments that have demonstrated the feasibility of the setup. While it is known that two molecules in two adjacent layers will always bind, larger complexes have only been scarcely addressed thus far. Here we prove rigorously that three- and four-body states will never be bound when the dipoles are oriented perpendicular to the layers. The technique employed is general and can be used for more molecules or layers and other geometries. Our analytical findings are supported by numerical calculations for both fermionic and bosonic molecules. Furthermore, we calculate the reduction in intralayer repulsion necessary to bind large complexes and estimate the influence of bound complexes in systems with many layers.

DOI
10.1103/physreva.85.023609

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Bound structures among dipolar molecules in multilayers are a topic of great interest in the light of recent experiments that have demonstrated the feasibility of the setup. While it is known that two molecules in two adjacent layers will always bind, larger complexes have only been scarcely addressed thus far. Here we prove rigorously that three- and four-body states will never be bound when the dipoles are oriented perpendicular to the layers. The technique employed is general and can be used for more molecules or layers and other geometries. Our analytical findings are supported by numerical calculations for both fermionic and bosonic molecules. Furthermore, we calculate the reduction in intralayer repulsion necessary to bind large complexes and estimate the influence of bound complexes in systems with many layers.
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.
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.
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 presence of few-body bound states is an important issue in the study of interacting bosonic systems due to the instability it introduces into the condensation. The problem is more interesting in two dimensions because the system can host only a finite number of bound states, in contrast to the Efimov effect in three dimensions. The authors considered a two-component bosonic system in two dimensions, with repulsive intra- and attractive inter-species interactions. They found that there is only one three-particle bound state and the binding energies for various scattering lengths fall on an universal curve, where the microscopic details are of no relevance. Their conclusion is pertinent for various systems such as excitons in quantum well structures and bosonic dipoles in bilayer geometries. They developed an efficient renormalization group type method, capable of handling both short- and long- range physics and free of numerical instabilities. This method also makes use of the Hopf coordinates and running basis to reduce the proliferation of hyperspherical harmonics appearing in alternative approaches, yielding significant saving in numerical implementations.