Collective ferromagnetism in two-component Fermi-degenerate gas trapped in finite potential

TL;DR

This paper investigates the conditions under which collective ferromagnetism can occur in two-component Fermi gases trapped in finite potentials, identifying stable ferromagnetic states and their properties through analytical solutions.

Contribution

It formulates Thomas-Fermi equations for the system and classifies three types of ground states, providing analytical density profiles and critical atom numbers for ferromagnetic states.

Findings

Stable ferromagnetic states are energetically favorable at large particle numbers.

Density profiles show spin asymmetry occurs in the central region of the trap.

Analytical expressions for critical atom numbers and state classifications are derived.

Abstract

Spin asymmetry of the ground states is studied for the trapped spin-degenerate (two-component) gases of the fermionic atoms with the repulsive interaction between different components, and, for large particle number, the asymmetric (collective ferromagnetic) states are shown to be stable because it can be energetically favorable to increase the fermi energy of one component rather than the increase of the interaction energy between up-down components. We formulate the Thomas-Fermi equations and show the algebraic methods to solve them. From the Thomas-Fermi solutions, we find three kinds of ground states in finite system: 1) paramagnetic (spin-symmetric), 2) ferromagnetic (equilibrium) and 3) ferromagnetic (nonequilibrium) states. We show the density profiles and the critical atom numbers for these states obtained analytically, and, in ferromagnetic states, the spin-asymmetries are shown to occur in the central regions of the trapped gas, and grows up with increasing particle number. Based on the obtained results, we discuss the experimental conditions and current difficulties to realize the ferromagnetic states of the trapped atom gas, which should be overcome.