Natural and unnatural parity states of small trapped equal-mass two-component Fermi gases at unitarity and fourth-order virial coefficient

TL;DR

This paper calculates energy spectra of small two-component Fermi gases at unitarity, including parity states, and uses these to determine the fourth-order virial coefficient, providing insights into their thermodynamic properties.

Contribution

It provides detailed energy spectra for (2,2) and (3,1) systems at unitarity, including unnatural parity states, and accurately estimates the fourth-order virial coefficient for trapped gases.

Findings

Zero-range energies estimated with 0.1% uncertainty.

Calculated energies used to determine the virial coefficient.

Compared virial coefficient with predictions for homogeneous systems.

Abstract

Equal-mass two-component Fermi gases under spherically symmetric external harmonic confinement with large s-wave scattering length are considered. Using the stochastic variational approach, we determine the lowest 286 and 164 relative eigenenergies of the (2,2) and (3,1) systems at unitarity as a function of the range $r_0$ of the underlying two-body potential and extrapolate to the $r_0 \rightarrow 0$ limit. Our calculations include all states with vanishing and finite angular momentum $L$ (and natural and unnatural parity $\Pi$) with relative energy up to $10.5 \hbar \Omega$, where $\Omega$ denotes the angular trapping frequency of the external confinement. Our extrapolated zero-range energies are estimated to have uncertainties of 0.1% or smaller. The (2,2) and (3,1) energies are used to determine the fourth-order virial coefficient of the trapped unitary two-component Fermi gas in the low-temperature regime. Our results are compared with recent predictions for the fourth-order virial coefficient of the homogeneous system. We also calculate small portions of the energy spectra of the (3,2) and (4,1) systems at unitarity.