Strongly Interacting p-wave Fermi Gas in Two-Dimensions: Universal Relations and Breathing Mode

TL;DR

This paper extends the concept of p-wave contact to two-dimensional strongly interacting Fermi gases, deriving universal relations, calculating contacts at high temperature, and linking them to breathing mode shifts, with implications for experiments.

Contribution

It generalizes p-wave contacts to 2D systems, deriving universal relations and connecting them to observable breathing mode shifts, which was previously limited to 3D systems.

Findings

Derived universal relations for 2D p-wave Fermi gases.

Explicit calculation of p-wave contacts at high temperature.

Established connection between breathing mode frequency shift and p-wave contacts.

Abstract

The contact is an important concept that characterizes the universal properties of a strongly interacting quantum gas. It appears in both thermodynamic (energy, pressure, etc.) and dynamic quantities (radio-frequency and Bragg spectroscopies, etc.) of the system. Very recently, the concept of contact has been extended to higher partial waves, in particular, the p-wave contacts have been experimentally probed in recent experiment. So far discussions on p-wave contacts have been limited to three-dimensions. In this paper, we generalize the p-wave contacts to two-dimensions and derive a series of universal relations, including the adiabatic relations, high momentum distribution, virial theorem and pressure relation. At high temperature and low density limit, we calculated the p-wave contacts explicitly using virial expansion. A formula which directly connects the shift of the breathing mode frequency and the p-wave contacts are given in a harmonically trapped system. Finally, we also derive the relationships between interaction parameters in three and two dimensional Fermi gas and discuss possible experimental realization of two dimensional Fermi gas with p-wave interactions.