Model independence in two dimensions and polarized cold dipolar molecules

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.

4.1 pages, 3 figures, published version

References in corpus (4)

• Quantum phases of a Two-Dimensional Dipolar Fermi Gas
• Potential Energy Landscape for hot electrons in periodically nanostructured graphene
• Two-dimensional scattering and bound states of polar molecules in bilayers
• Spontaneous inhomogeneous phases in ultracold dipolar Fermi gases

Cited by in corpus (8)

• Comparing and contrasting nuclei and cold atomic gases
• Mass-imbalanced Three-Body Systems in Two Dimensions
• Bound states of Dipolar Bosons in One-dimensional Systems
• Two-dimensional Bose gas of tilted dipoles: roton instability and condensate depletion
• Virial expansion coefficients in the harmonic approximation
• Many-particle Systems in One Dimension in the Harmonic Approximation
• Wigner-localized states in spin-orbit-coupled bosonic ultracold atoms with dipolar interaction
• Two- and three- dimensional few-body systems in the universal regime