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arXiv:2511.10802 · Physical Review A

Paramagnetic phases of strongly correlated ultracold fermions coupled to an optical cavity

Renan da Silva Souza, Youjiang Xu, Walter Hofstetter

Published Feb 24, 2026• 0 citations
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Abstract

We numerically study a gas of two-component fermions coupled to a transversely pumped optical cavity and confined to a two-dimensional static square optical lattice. In the dispersive regime, the steady state of the system is described by an extended Hubbard Hamiltonian with cavity-mediated long-range interactions. Using real-space dynamical mean-field theory (RDMFT), we investigate the formation of the (superradiant) checkerboard density-wave phase. Our analysis focuses on paramagnetic phases both at quarter and half filling. At quarter filling, we find a reentrant homogeneous Fermi liquid to density wave phase transition with increasing temperature, which is due to the higher entropy of the ordered phase. At half filling, in addition to the Fermi liquid to Mott insulator phase transition, marked by a vanishing quasiparticle residue at the Fermi level, we identify the transition into a density-wave phase. Due to perfect Fermi surface nesting at half filling, we find that arbitrarily small long-range interactions destabilize the system towards the density-wave phase in the absence of short-range interactions. By varying short- and long-range interactions at a fixed low temperature, we obtain the full phase diagram and identify a region of coexistence between the homogeneous Fermi liquid and Mott insulating phase with the density-wave phase. In this region, we determine the thermodynamic phase transition by comparing the energies of the different RDMFT solutions.

DOI
10.1103/1b7p-z928

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We show that cavity-field fluctuations can induce interesting magnetic phases and phase transitions in an atom-cavity coupled system. Adopting a numerical density-matrix-renormalization-group method, we study the steady state of a two-component Fermi gas subject to cavity-assisted Raman coupling in a one-dimensional lattice at half filling. The cavity-enhanced atom-photon coupling introduces a dynamic long-range interaction in the atoms, which competes with the short-range on-site interactions and leads to a rich phase diagram with a variety of magnetic orders. Importantly, as all the phase transitions take place outside the superradiant regime, the magnetic orders are associated with cavity-field fluctuations with a vanishing number of photons on the mean-field level.
We investigate properties of an ultracold, two-component bosonic gas in a square optical lattice at unit filling. In addition to density-density interactions, the atoms are subject to coherent light-matter interactions that couple different internal states. We examine the influence of this coherent coupling on the system and its quantum phases by using Gutzwiller mean-field theory as well as bosonic dynamical mean-field theory. We find that the interplay of strong interspecies repulsion and coherent coupling affects the Mott insulator to superfluid transition and shifts the tip of the Mott lobe toward higher values of the tunneling amplitude. In the strongly interacting Mott regime, the resulting Bose-Hubbard model can be mapped onto an effective spin Hamiltonian that offers additional insights into the observed phenomena.
Based on a generalized one-band Hubbard model, we study magnetic properties of Mott insulating states for ultracold spin-32\frac{3}{2}23​ fermionic atoms in optical lattices. When the sss-wave scattering lengths for the total spin S=2,0S=2,0S=2,0 satisfy conditions a2>a0>0{a}_{2}>{a}_{0}>0a2​>a0​>0, we apply a functional integral approach to the half filled case, where the spin-quadrupole fluctuations dominate. On a two-dimensional square lattice, the saddle-point solution yields a staggered spin-quadrupole ordering at zero temperature with symmetry breaking from SO(5) to SO(4). Both spin and spin-quadrupole static structure factors are calculated, displaying highly anisotropic spin antiferromagnetic fluctuations and antiferroquadrupole long-range correlations, respectively. When Gaussian fluctuations around the saddle point are taken into account, spin-quadrupole density waves with a linear dispersion are derived. Compared with the spin-density waves in the half filled spin-12\frac{1}{2}21​ Hubbard model, the quadrupole density wave velocity is saturated in the strong-coupling limit, and there are no transverse spin-quadrupole mode couplings, as required by the SO(4) invariance of the effective action. Finally, in the strong-coupling limit of the model Hamiltonian, we derive the effective hyperfine spin-exchange interactions for the Mott insulating phases in the quarter filled and half filled cases, respectively.
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Coupling Bose-Einstein condensates to optical cavities has enabled the study of many-body states with long-range interactions. However, equivalent experiments with ultracold Fermi gases have remained largely unexplored. Here, we report an experimental realization of a superradiant quantum phase transition of a degenerate Fermi gas in a transversely pumped optical cavity. The self-ordering checkerboard density pattern of Fermi gases and superradiant transitions of the cavity field spontaneously emerge by increasing the pumping intensity above a threshold value. The effects of Fermi statistics are manifested by an inverse square root scaling of the threshold with atom number and the slow dynamics of low–atomic momentum states. Our work provides an ideal platform for studying nonequilibirium dynamics of many-body states for long-range interacting Fermi gases.