Tuning Density and Spin Ordering of Degenerate Fermi Gases in an Optical Cavity

This paper investigates how the internal spin degrees of freedom of a degenerate Fermi gas, when coupled to an optical cavity, influence the superradiant self-organization phase transition. Specifically, the authors explore how tuning the relative polarization angle between the transverse pump and the cavity field allows for the manipulation of scalar and vectorial light-matter couplings, and how this competition interacts with Fermi statistics and spin-population imbalances.

Using a mean-field theoretical framework, the authors derive the effective Hamiltonian for a spin-dependent Fermi gas in a high-finesse cavity. They analyze the system's susceptibility—which is heavily influenced by Pauli blocking and Fermi surface nesting—to determine the threshold for the superradiant phase transition. The study extends this model to a two-component Fermi gas with opposite spins, using numerical steady-state analysis to map out phase diagrams and investigate real-space phase separation as a function of the polarization angle and spin-population ratio.

The researchers find that the superradiant threshold is synergistically determined by the weight of the scalar-vectorial coupling and the density-dependent susceptibility of the Fermi gas. A key result is that the relative polarization angle acts as a control knob for the phase transition: it can enhance or suppress superradiance depending on the ratio of atomic polarizabilities. In two-component systems, the authors identify that real-space phase separation occurs at a specific critical polarization angle. Furthermore, they demonstrate that the nature of this transition (continuous vs. discontinuous) depends on the population imbalance between the two spin components, with a crossover occurring at a specific population ratio.

This work provides a theoretical roadmap for experimentalists to manipulate many-body phases in hybrid light-matter systems. By demonstrating that polarization control can tune phase transitions and induce real-space separation in Fermi gases, the study offers new ways to probe quantum magnetism and nonequilibrium phase transitions in ultracold atomic platforms. These insights are also applicable to bosonic systems, broadening the potential impact of the findings.