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Physical Review A

Detecting the Fermi surface nesting effect for the fermionic Dicke transition by trap-induced localization

Shi Chen, Yu Chen

Published Jul 12, 2024• 3 citations
Publisher

Abstract

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 ${N}_{\mathrm{at}}$ 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 $1/3$ (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.

DOI
10.1103/physreva.110.013312

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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 Nat\ensuremath−1.33{N}_{\mathrm{at}}^{\ensuremath{-}1.33}Nat\ensuremath−1.33​ and Nat\ensuremath−0.67{N}_{\mathrm{at}}^{\ensuremath{-}0.67}Nat\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 Nat\ensuremath→\ensuremath∞{N}_{\mathrm{at}}\ensuremath{\rightarrow}\ensuremath{\infty}Nat​\ensuremath→\ensuremath∞ 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 ER/\ensuremathωz{E}_{R}/{\ensuremath{\omega}}_{z}ER​/\ensuremathωz​. 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.
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.
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.
Pairing lies at the heart of superfluidity in fermionic systems. Motivated by recent experiments in mesoscopic Fermi gases, we study up to six fermionic atoms with equal masses and equal populations in two different spin states, confined in a quasi-two-dimensional harmonic trap. We couple a stochastic variational approach with the use of an explicitly correlated Gaussian basis set, which enables us to obtain highly accurate energies and structural properties. Utilising two-dimensional two-body scattering theory with a finite-range Gaussian interaction potential, we tune the effective range to model realistic quasi-two-dimensional scattering. We calculate the excitation spectrum, pair correlation function, and number of pairs as a function of increasing attractive interaction strength. For up to six fermions in the ground state, we find that opposite spin and momentum pairing is maximised well below the Fermi surface in momentum space. By contrast, corresponding experiments on twelve fermions have found that pairing is maximal at the Fermi surface and strongly suppressed beneath [M. Holten et al., Nature 606, 287-291 (2022)]. This suggests that the Fermi sea — which acts to suppress pairing at low momenta via Pauli blocking — emerges in the transition from six to twelve particles.
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.
Pauli blocking of spontaneous emission by a single excited-state atom has been predicted to be dramatic at low temperature when the Fermi energy E F exceeds the recoil energy E R . The photon scattering rate of a ground-state Fermi gas can also be suppressed by occupation of the final states accessible to a recoiling atom; however, suppression is diminished by scattering events near the Fermi edge. We analyse two new approaches to improve the visibility of Pauli blocking in a trapped Fermi gas. Focusing the incident light to excite preferentially the high-density region of the cloud can increase the blocking signature by 14%, and is most effective at intermediate temperature. Spontaneous Raman scattering between imbalanced internal states can be strongly suppressed at low temperature, and is completely blocked for a final state E F > 4 E R in the high imbalance limit.