Concept of contact spectrum and its applications in atomic quantum Hall states

TL;DR

This paper introduces the concept of a contact spectrum for arbitrary partial-wave scattering in ultracold atoms, revealing universal thermodynamic relations and connections to entanglement spectra in quantum Hall states.

Contribution

It generalizes the contact concept beyond s-wave scattering to all partial waves, establishing new universal relations and linking to entanglement spectra in atomic quantum Hall states.

Findings

Contact spectrum extends universal relations to all partial waves.

Connection established between contact spectrum and entanglement spectrum.

Provides a method to probe highly correlated quantum Hall states.

Abstract

A unique feature of ultracold atoms is the separation of length scales, $r_0\ll k_F^{-1}$, where $k_F$ and $r_0$ are the Fermi momentum characterizing the average particle distance and the range of interaction between atoms respectively. For $s$-wave scattering, Shina Tan discovered that such diluteness leads to universal relations, all of which are governed by contact, among a wide range of thermodynamic quantities. Here, we show that the concept of contact can be generalized to an arbitrary partial-wave scattering. Contact of all partial-wave scatterings form a contact spectrum, which establishes universal thermodynamic relations with notable differences from those in the presence of $s$-wave scattering alone. Moreover, such a contact spectrum has an interesting connection with a special bipartite entanglement spectrum of atomic quantum Hall states, and enables an intrinsic probe of these highly correlated states using two-body short-ranged correlations.