Abstract
We establish that two-dimensional dipolar quantum gases admit a universal description, i.e., their thermodynamic properties are independent of details of the interaction at short distances. The only relevant parameters are the dipole length as well as the scattering length of the combined short-range plus dipolar interaction potential. We derive adiabatic relations that link the change in the thermodynamic potentials with respect to the scattering length and the dipole length to a generalized Tan contact parameter and a new dipolar contact, which involves an integral of a short-distance regularized pair distribution function. These two quantities determine the scale anomaly in the difference between pressure and energy density and also the internal energy in the presence of a harmonic confinement. For a weak transverse confinement, configurations with attractive interactions appear, which lead to a density-wave instability beyond a critical strength of the dipolar interaction. We show that this instability essentially coincides with the onset of a roton minimum in the excitation spectrum and may be understood in terms of a quantum analog of the Hansen-Verlet criterion for freezing of a classical fluid.
Highlights
Interactions in ultracold gases are usually described in terms of the two-body scattering length a as a single parameter, which characterizes the complicated and in detail unknown microscopic interaction
We establish that two-dimensional dipolar quantum gases admit a universal description, i.e., their thermodynamic properties are independent of details of the interaction at short distances
We derive adiabatic relations that link the change in the thermodynamic potentials with respect to the scattering length and the dipole length to a generalized Tan contact parameter and a new dipolar contact, which involves an integral of a short-distance regularized pair distribution function
Summary
Interactions in ultracold gases are usually described in terms of the two-body scattering length a as a single parameter, which characterizes the complicated and in detail unknown microscopic interaction. Unlike the case of isotropic short-range interactions with a van der Waals tail, the s-wave scattering length is not sufficient to describe the two-body interaction of dipolar gases at low energies in three dimensions and no universal description of the thermodynamics and short-distance correlation functions exists. III C, we derive exact results for the behavior of the static structure factor at large wave vectors They allow to distinguish the transition to a supersolid phase that is caused by partially attractive interactions from the transition of a homogeneous superfluid to a commensurate, nonsuperfluid crystal, which appears both in strictly two-dimensional dipolar gases and in 4He at high pressure due to purely or dominantly repulsive interactions. There are three appendices that discuss an example potential that gives rise to universal dipolar scattering, derive the adiabatic relations, and generalize the universal relations in two dimensions to general repulsive power-law interactions
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