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arXiv:2303.00965

Detecting Fermi Surface Nesting Effect for Fermionic Dicke Transition by Trap Induced Localization

Shi Chen, Yu Chen

Published Mar 2, 2023• 0 citations
arXivHTMLPDF

Abstract

Recently, the statistical effect of fermionic superradiance is approved by series of experiments both in free space and in a cavity. The Pauli blocking effect can be visualized by a 1/2 scaling of Dicke transition critical pumping strength against particle number Nat for fermions in a trap. However, the Fermi surface nesting effect, which manifests the enhancement of superradiance by Fermi statistics is still very hard to be identified. Here we studied the influence of localized fermions on the trap edge when both pumping optical lattice and the trap are presented. We find due to localization, the statistical effect in superradiant transition is enhanced. Two new scalings of critical pumping strength are observed as 4/3, and 2/3 for mediate particle number, and the Pauli blocking scaling 1/3 (2d case) in large particle number limit is unaffected. Further, we find the 4/3 scaling is subject to a power law increasing with rising ratio between recoil energy and trap frequency in pumping laser direction. The divergence of this scaling of critical pumping strength against $N_{\rm at}$ in $E_R/ω_x\rightarrow+\infty$ limit can be identified as the Fermi surface nesting effect. Thus we find a practical experimental scheme for visualizing the long-desired Fermi surface nesting effect with the help of trap induced localization in a two-dimensional Fermi gas in a cavity.

DOI
10.48550/arxiv.2303.00965

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Recently, the statistical effect of fermionic superradiance is approved by series of experiments both in free space and in a cavity. The Pauli blocking effect can be visualized by a 1/2 scaling of Dicke transition critical pumping strength against particle number Nat for fermions in a trap. However, the Fermi surface nesting effect, which manifests the enhancement of superradiance by Fermi statistics is still very hard to be identified. Here we studied the influence of localized fermions on the trap edge when both pumping optical lattice and the trap are presented. We find due to localization, the statistical effect in superradiant transition is enhanced. Two new scalings of critical pumping strength are observed as 4/3, and 2/3 for mediate particle number, and the Pauli blocking scaling 1/3 (2d case) in large particle number limit is unaffected. Further, we find the 4/3 scaling is subject to a power law increasing with rising ratio between recoil energy and trap frequency in pumping laser direction. The divergence of this scaling of critical pumping strength against NatN_{\rm at}Nat​ in ER/ωx→+∞E_R/ω_x\rightarrow+\inftyER​/ωx​→+∞ limit can be identified as the Fermi surface nesting effect. Thus we find a practical experimental scheme for visualizing the long-desired Fermi surface nesting effect with the help of trap induced localization in a two-dimensional Fermi gas in a cavity.
Recently, the statistical effect of fermionic superradiance has been verified by a series of experiments both in free space and in a cavity. The Pauli blocking effect can be visualized by a 1/2 scaling of the Dicke transition critical pumping strength against the particle number Nat{N}_{\mathrm{at}}Nat​ for fermions in a trap. However, the evidence for the Fermi surface (FS) nesting effect, which manifests the enhancement of superradiance by Fermi statistics, is still missing. Here we report a scheme for detecting FS nesting with the help of the trap-induced localization on the trap edge. We find two scalings of the critical pumping strength as ${N}_{\mathrm{at}}^{\ensuremath{-}1.33}$ and ${N}_{\mathrm{at}}^{\ensuremath{-}0.67}$ for a moderate particle number when localization enters and the Pauli blocking scaling 1/31/31/3 (two-dimensional case) in the ${N}_{\mathrm{at}}\ensuremath{\rightarrow}\ensuremath{\infty}$ limit is unaffected. Further, we find the scaling of the critical pumping strength against the particle number increases with the ratio between the recoil energy and the trap frequency in the direction orthogonal to the pumping direction ${E}_{R}/{\ensuremath{\omega}}_{z}$. The scaling larger than 1 can be identified as a result of the Fermi surface nesting effect. Thus, we find a practical experimental scheme for visualizing the long-desired Fermi surface nesting effect with the help of trap-induced localization in a two-dimensional Fermi gas in a cavity.
In this Letter we consider spinless Fermi gases placed inside a cavity and study the critical strength of a pumping field for driving a superradiance transition. We emphasize that the Fermi surface nesting effect can strongly enhance the superradiance tendency. Around certain fillings, when the Fermi surface is nearly nested with a relevant nesting momentum, the susceptibility of the system toward a checkboard density-wave ordered state is greatly enhanced in comparison with a Bose gas with the same density, because of which a much smaller (sometime even vanishingly small) critical pumping field strength can give rise to superradiance. This effect leads to interesting reentrance behavior and a topologically distinct structure in the phase diagram. Away from these fillings, the Pauli exclusion principle brings about the dominant effect for which the critical pumping strength is lowered in the low-density regime and increased in the high-density regime. These results open the prospect of studying the rich phenomena of degenerate Fermi gases in a cavity.
The superradiant phase transitions of one-dimensional correlated Fermi gases in a transversely driven optical cavity, under the umklapp condition that the cavity wave number is equal to two times the Fermi wave number, are studied with bosonization and renormalization group techniques. The bosonization of Fermi fields gives rise to an all-to-all sine-Gordon (SG) model due to the cavity-assisted nonlocal interactions, where the Bose fields at any two spatial points are coupled. The superradiant phase transition is then mapped to the Kosterlitz-Thouless phase transition of the all-to-all SG model. The nesting effect, in which the superradiant phase transition can be triggered by an infinitely small atom-cavity coupling strength, is shown to be preserved for any nonattractive local interactions. For attractive local interactions, the phase transition occurs at a finite critical coupling strength. Nevertheless, the analysis of the scaling dimension indicates that the perturbation of the nonlocal cosine term is indeed relevant (irrelevant) when the scaling dimension is lower (higher) than the critical dimension, similar to the case of an ordinary local SG model. Our work provides an analytical framework for understanding the superradiant phase transitions in low-dimensional correlated intracavity Fermi gases.
Understanding the interplay between collective optical response and disorder presents significant challenges in modern many-body physics. While there has been considerable interest and a wealth of theoretical work in recent years, the experimental investigation of the superradiant phase transition and disorder has been unexplored. Here, we report an observation of the localization-driven superradiance with a degenerate Fermi gas in an optical cavity. We show that the dynamics of Fermi gases exhibits Anderson localization in an intracavity incommensurate lattice. The exponential localization is directly observed in both spatial and momentum spaces. We observe the localization driving a nearly vanishing pump threshold in fermionic superradiance when the system is in the localized state. The underlying mechanism of the self-organization and the quantum statistic of the atoms are revealed by measuring the atom momentum distribution and characteristic growth of the superradiant field. Our work provides a platform for studying superradiant quantum phase transition and localization in photon-mediated long-range interacting Fermi gases.
Collective light-matter phenomena such as Dicke superradiance are often described as a collection of effective spins coupled homogeneously to a bosonic mode, giving rise to a collective bright mode with enhanced light-matter coupling. In fermionic systems, Pauli exclusion and Fermi-surface structure can significantly modify this picture, while randomness in the atom-light couplings raises the question of whether disorder promotes or suppresses collective behavior. Here, we study a cavity model in which fermionic particles couple to a photonic mode through a random all-to-all interaction matrix with tunable mean and variance. Combining numerical mean-field methods, analytic stability analysis and random-matrix predictions, and benchmarks against exact diagonalization, we characterize both the onset and structure of the superradiant phase. While mean coupling and disorder variance contribute in the same way to the onset, they lead to drastically different behavior within the condensed phase. Uniform coupling supports a single bright collective fermionic mode with conventional Dicke-like scaling of the cavity field. Disorder, instead, gives rise to a qualitatively different collective regime in which many grey fermionic states participate coherently, producing a parametrically enhanced scaling of the condensate with system size. Our results reveal a mechanism through which disorder can, perhaps counterintuitively, promote collective light-matter phenomena.
Following the experimental realization of Dicke superradiance in Bose gases coupled to cavity light fields, we investigate the behavior of ultracold fermions in a transversely pumped cavity. We focus on the equilibrium phase diagram of spinless fermions coupled to a single cavity mode and establish a zero temperature transition to a superradiant state. In contrast to the bosonic case, Pauli blocking leads to lattice commensuration effects that influence self-organization in the cavity light field. This includes a sequence of discontinuous transitions with increasing atomic density and tricritical superradiance. We discuss the implications for experiment.