Layers of Cold Dipolar Molecules in the Harmonic Approximation

TL;DR

This paper models layered cold dipolar molecules using a harmonic approximation, analyzing their bound states, normal modes, and instabilities, with implications for experimental observation of such structures.

Contribution

It introduces a harmonic approximation framework for layered dipolar molecules, incorporating adjustable intra-layer repulsion and analyzing normal modes and stability.

Findings

Identification of chain and layer vibrational modes as acoustic and optical phonons.

Instabilities arise at high intra-layer repulsion, causing diverging molecular amplitudes.

Potential for experimental observation of layered dipolar structures.

Abstract

We consider the N-body problem in a layered geometry containing cold polar molecules with dipole moments that are polarized perpendicular to the layers. A harmonic approximation is used to simplify the hamiltonian and bound state properties of the two-body inter-layer dipolar potential are used to adjust this effective interaction. To model the intra-layer repulsion of the polar molecules, we introduce a repulsive inter-molecule potential that can be parametrically varied. Single chains containing one molecule in each layer, as well as multi-chain structures in many layers are discussed and their energies and radii determined. We extract the normal modes of the various systems as measures of their volatility and eventually of instability, and compare our findings to the excitations in crystals. We find modes that can be classified as either chains vibrating in phase or as layers vibrating against each other. The former correspond to acoustic and the latter to optical phonons. Instabilities can occur for large intra-layer repulsion and produce diverging amplitudes of molecules in the outer layers. Lastly, we consider experimentally relevant regimes to observe the structures.