Itinerant ferromagnetism of two-dimensional repulsive fermions with Rabi coupling

Abstract

We study a two-dimensional fermionic cloud of repulsive alkali-metal atoms characterized by two hyperfine states which are Rabi coupled. Within a variational Hartree-Fock scheme, we calculate analytically the ground-state energy of the system. Then we determine the conditions under which there is a quantum phase transition with spontaneous symmetry breaking from a spin-balanced configuration to a spin-polarized one, an effect known as itinerant ferromagnetism. Interestingly, we find that the transition appears when the interaction energy per particle exceedes both the kinetic energy per particle and the Rabi coupling energy. The itinerant ferromagnetism of the polarized phase is analyzed, obtaining the population imbalance as a function of interaction strength, Rabi coupling, and number density. Finally, the inclusion of a external harmonic confinement is investigated by adopting the local density approximation. We predict that a single atomic cloud can display population imbalance near the center of the trap and a fully balanced configuration at the periphery.

Probing ferromagnetic order in few-fermion correlated spin-flip dynamics

“…However, upon increasing g | |, (in particular for g 0.5 4 < < | | ) TDHF predicts no loss of P S 1 ( ) in contrast to the MB case (compare figures 1(a) and (c)), while a similar spin-correlation dynamics is observed compare figures 1(b) and 1(d). This behaviour of the TDHF can be interpreted in terms of the Stoner model [4,30], see figure 2(a). Indeed, within HF the interaction energy of contact interacting spin-1/2 fermions is proportional to the density overlap between the two spin-components [4,30].…”

“…This behaviour of the TDHF can be interpreted in terms of the Stoner model [4,30], see figure 2(a). Indeed, within HF the interaction energy of contact interacting spin-1/2 fermions is proportional to the density overlap between the two spin-components [4,30]. Therefore, for large enough g the system initialized in a spin-polarized state characterized by zero interaction energy, cannot access states with a single (or more) spin-flips due to their large interaction energy.…”

“…This coupling scheme introduces a spatially dependent spin-flip transition amplitude and thus probes the stability of the initial state by breaking the spinsymmetries of the unperturbed system (see below). An argumentation based on the Hartree-Fock (HF) framework of the Stoner model testified within the time-dependent Hartree-Fock (TDHF) [29] showed that the spin-polarization of the Fermi gas is stable for interparticle repulsions that exceed the kinetic and spin-flip contributions [30,31]. Inspecting the correlated spin-flip dynamics within the latter interaction regime (where TDHF predicts stable ferromagnetism) we reveal that the many-body (MB) spin-spin correlator exhibits ferromagnetic spin-spin correlations throughout the dynamics.…”

Polarization in a three-dimensional Fermi gas with Rabi coupling

“…In our approach (see also [34]), we first write E as function of n and ζ and then we find the value of ζ which minimizes the energy density E at fixed total number density n. The procedure is repeated for different values of interaction strength g and Rabi frequency Ω. As suggested by equations (5), (14) and (16), we define the characteristic energy scales…”

“…polarization [28]. In this 2D theoretical study the density of states is quite simple and the obtained phase diagram is fully analytical [34].…”