Model independence in two dimensions and polarized cold dipolar molecules

TL;DR

This paper derives universal analytic expressions for two particles in two dimensions with anisotropic interactions, demonstrating how universality emerges in cold dipolar molecules and validating results with numerical methods.

Contribution

It provides the first rigorous analytic framework for understanding universality in anisotropic two-dimensional systems with cold dipolar molecules.

Findings

Universal behavior is approached in weak coupling limit.

Monopole component of anisotropic potentials is key to universality.

Analytic results agree with stochastic variational method simulations.

Abstract

We calculate the energy and wave functions of two particles confined to two spatial dimensions interacting via arbitrary anisotropic potentials with negative or zero net volume. The general rigorous analytic expressions are given in the weak coupling limit where universality or model independence are approached. The monopole part of anisotropic potentials is crucial in the universal limit. We illustrate the universality with a system of two arbitrarily polarized cold dipolar molecules in a bilayer. We discuss the transition to universality as function of polarization and binding energy, and compare analytic and numerical results obtained by the stochastic variational method. The universal limit is essentially reached for experimentally accessible strengths.