Observe novel tricritical phenomena in self-organized Fermi gas induced by higher order Fermi surface nesting

TL;DR

This work investigates self-organized fermionic superradiance in strongly pumped optical lattices, emphasizing the role of higher-order Fermi surface nesting in generating tricritical behavior. Using zero-temperature perturbation theory and Landau-type expansions, it shows that 1D systems host a tricritical point due to infrared divergences in the fourth-order term, whereas 2D systems do not because these divergences are mitigated. Finite-temperature analysis extends the picture to a tricritical curve in the (T, k_F) plane and reveals an optimal temperature for observing superradiance, along with multistability and hysteresis in dissipative cavities. Overall, the study clarifies how quantum and classical critical phenomena interrelate in cavity-mediated Fermi gases and provides guidance for experimental detection of these transitions.

Abstract

Cold atom systems in optical lattices have long been recognized as an ideal platform for bridging condense matter physics and quantum optics. Here, we investigate the 1D fermionic superradiance in an optical lattice, and observe novel tricritical phenomena and multistability in finite-temperature cases. As a starting point, which can be analytically calculated, we compare the 1D and 2D Fermi gases in zero-temperature limit. It turns out that the tricritical point originates from the higher-order Fermi surface nesting (FSN), and the infrared divergence in 1D systems is absent in 2D cases. When extending to finite-temperature cases, our numerical results reveal that both quantum- and classical-type trcritical phenomena can be observed simultaneously. Moreover, there exists an optimal temperature for observing superradiance. This work provides a new approach to understanding the relation between quantum and classical phase transitions.

Figures (9)

• Figure 1: (a) The experimental schematic. The contribution of (b) the first order FSN with single-photon processes, and (c) the second order FSN where two-photon processes are considered. The blue and blank parts stand for the filled and unfilled regions in momentum space. The pink arrow represents the momentum transition after single photon scattering. (d)(e) The phase diagrams for the 1D fermion gas. The white dashed curves represent the disappearance of the susceptibility $\chi$, the red solid curve is the critical boundary, and the blue solid line on left panel is the renormalized fourth-order coefficients.We set $A=1$ here and in the following text.
• Figure 2: (a)The critical scaling behavior for $k_F=0.918$(orange dots) and $k_F=k_F^t=0.9425$ (blue square dots), respectively. The red and green solid lines stand for the linear fitting for the ramping rate $1/2$ and $1$. (b)The critical scaling for fixed $B/A\approx0.376$, and the ramping rate is around $1$. The average free energy $f$ curve changes against the order parameter $\psi/\sqrt{N}$ with $k_F=0.918$, and $B/A=0.35,0.5$ in subfigure (c); $k_F=0.982$, $B/A=0.5$ in subfigure (d), and $B/A=0.41,0.414,0.418$ in the inset.
• Figure 3: (a) The stable-state phase diagram in the limit $\kappa\to 0$. The grey, orange and brown regions support $1$, $2$ and $3$ stable states, respectively, labeled by the digits. (b) The quench dynamic evolution of the order parameter with the forward and backward three-step pulse, marked by red and blue lines. The filling factor is fixed as $k_F=0.98$.
• Figure 4: The numerical equilibrium phase diagram at finite temperatures with fixed filling factors $k_F=0.2$ (a) and $k_F=0.8$ (b), and the corresponding analytical colormaps of $k_F(\tilde{\omega}+4\chi)/E_r$ are shown in (c) and (d), respectively. The grey dashed lines are the tangents lines at $T=0$.
• Figure 5: The phase diagram at finite temperatures with fixed filling factors $k_F=0.938$ (a), $k_F=0.982$ (b). The colorbar represents the order parameter, and the red stars stand for the tricritical points, corresponding to the zero points of $\eta'$ (blue line on left panel). (c) The analytical fourth order coefficients $Nk_F\eta'/(4B^2E_r)$ colormap with black line referring to the zero contour line. (d) The 3D phase diagram where three slices with fixed temperature $T=0,0.1,0.2$ are displayed. The red dashed curve is connected through all the tricritical points in every slices between $T=0$ and $T=0.2$, whose projection is shown with black dashed line in the $T$-$k_F$ plane.