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arXiv:2604.06004

Rf spectra and pseudogap in ultracold Fermi gases across the BCS-BEC crossover from pairing fluctuation theory

Chuping Li, Lin Sun, Kaichao Zhang, Junru Wu, Yuxuan Wu, Dingli Yuan, Pengyi Chen, Qijin Chen

Published Apr 7, 2026• 0 citations
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Abstract

The pseudogap phenomenon is a hallmark of strongly interacting Fermi systems, from high-temperature superconductors to ultracold atomic gases, yet its precise origin remains debated. Here we calculate the spectral function and rf spectra of ultracold atomic gases across the BCS-BEC crossover to quantitatively investigate the pairing mechanism of the pseudogap. We advance our pairing fluctuation theory by incorporating particle-hole fluctuations, which renormalize the effective interaction in the particle-particle channel. To achieve quantitative accuracy, we employ a full numerical convolution for the pair susceptibility and self-energy, moving beyond previous analytic pseudogap approximations. This convolution approach automatically captures two critical effects: (i) the full spectral broadening of fermions due to finite pair lifetime, and (ii) the previously neglected pair-hole scattering effect, which manifests as a substantial Hartree energy. We calculate the spectral function, and use rf spectral intensity maps and energy distribution curves to determine the quasiparticle dispersion. From these, we extract the pseudogap $Δ$, Hartree energy, and chemical potential, mapping their evolution across the crossover. Our results show that the pseudogap emerges continuously as the system moves from the BCS regime toward BEC. Furthermore, the pair spectral function reveals that pairs become diffusive at energies above 2$Δ$, indicating that the pair lifetime is governed by virtual binding and unbinding processes. Our calculations achieve quantitative agreement with recent experiments across the BCS-BEC crossover, including at unitarity, providing strong support for a pairing-based origin of the pseudogap as described by our pairing fluctuation theory.

DOI
10.48550/arxiv.2604.06004

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The pseudogap phenomenon is a hallmark of strongly interacting Fermi systems, from high-temperature superconductors to ultracold atomic gases, yet its precise origin remains debated. Here we calculate the spectral function and rf spectra of ultracold atomic gases across the BCS-BEC crossover to quantitatively investigate the pairing mechanism of the pseudogap. We advance our pairing fluctuation theory by incorporating particle-hole fluctuations, which renormalize the effective interaction in the particle-particle channel. To achieve quantitative accuracy, we employ a full numerical convolution for the pair susceptibility and self-energy, moving beyond previous analytic pseudogap approximations. This convolution approach automatically captures two critical effects: (i) the full spectral broadening of fermions due to finite pair lifetime, and (ii) the previously neglected pair-hole scattering effect, which manifests as a substantial Hartree energy. We calculate the spectral function, and use rf spectral intensity maps and energy distribution curves to determine the quasiparticle dispersion. From these, we extract the pseudogap ΔΔΔ, Hartree energy, and chemical potential, mapping their evolution across the crossover. Our results show that the pseudogap emerges continuously as the system moves from the BCS regime toward BEC. Furthermore, the pair spectral function reveals that pairs become diffusive at energies above 2ΔΔΔ, indicating that the pair lifetime is governed by virtual binding and unbinding processes. Our calculations achieve quantitative agreement with recent experiments across the BCS-BEC crossover, including at unitarity, providing strong support for a pairing-based origin of the pseudogap as described by our pairing fluctuation theory.
We investigate strong-coupling effects on normal-state properties of an ultracold Fermi gas. Within the framework of TTT-matrix approximation in terms of pairing fluctuations, we calculate the single-particle density of states (DOS), as well as the spectral weight, over the entire BCS--Bose-Einstein condensate (BEC) crossover region above the superfluid phase-transition temperature Tc{T}_{\text{c}}Tc​. Starting from the weak-coupling BCS regime, we show that the so-called pseudogap develops in DOS above Tc{T}_{\text{c}}Tc​, which becomes remarkable in the crossover region. The pseudogap structure continuously changes into a fully gapped one in the strong-coupling BEC regime, where the gap energy is directly related to the binding energy of tightly bound molecules. We determine the pseudogap temperature ${T}^{\ensuremath{\ast}}$ where the dip structure in DOS vanishes. The value of ${T}^{\ensuremath{\ast}}$ is shown to be very different from another characteristic temperature ${T}^{\ensuremath{\ast}\ensuremath{\ast}}$ where a BCS-type double-peak structure disappears in the spectral weight. While one finds ${T}^{\ensuremath{\ast}}>{T}^{\ensuremath{\ast}\ensuremath{\ast}}$ in the BCS regime, ${T}^{\ensuremath{\ast}\ensuremath{\ast}}$ becomes higher than ${T}^{\ensuremath{\ast}}$ in the crossover region and BEC regime. Including this, we determine the pseudogap region in the phase diagram of ultracold Fermi gases. Our results would be useful in the search for the pseudogap region in ultracold 6Li^{6}\text{L}\text{i}6Li and 40K^{40}\text{K}40K Fermi gases.
The existence of a pseudogap in unitary Fermi gases has recently been established and measured experimentally [Li et al., Nature 626, 288 (2024)]. This lends strong support for the pairing origin as the mechanism of the pseudogap in Fermi superfluids. Here we present a spectral study of unitary Fermi gases, and show how the data can be understood quantitatively, when compared with theoretically calculated momentum-resolved rf or microwave spectra, and the pseudogap extracted from the spectra. We use an iterative treatment of the fermion self energy and hence the spectral function, beyond previous pseudogap approximation, based on a pairing fluctuation theory that incorporates both particle-particle and particle-hole T matrices, with self-consistent self energy feedback. Our results not only provide a microscopic explanation of the experimental data but also strengthen the support for both the pairing-induced pseudogap physics and the pairing fluctuation theory of Fermi superfluidity.
This article presents a comparison of two finite-temperature BCS--Bose-Einstein condensation (BEC) crossover theories above the transition temperature: Nozieres--Schmitt-Rink (NSR) theory and finite-TTT extended BCS-Leggett theory. The comparison is cast in the form of numerical studies of the behavior of the fermionic spectral function both theoretically and as constrained by (primarily) radio frequency (rf) experiments. Both theories include pair fluctuations and exhibit pseudogap effects, although the nature of this pseudogap is very different. The pseudogap in finite-TTT extended BCS-Leggett theory is found to follow a BCS-like dispersion which, in turn, is associated with a broadened BCS-like self-energy, rather more similar to what is observed in high-temperature superconductors (albeit, for a ddd-wave case). The fermionic quasiparticle dispersion is different in NSR theory and the damping is considerably larger. We argue that the two theories are appropriate in different temperature regimes with the BCS-Leggett approach being more suitable nearer to condensation. There should, in effect, be little difference at higher TTT as the pseudogap becomes weaker and where the simplifying approximations used in the BCS-Leggett approach break down. On the basis of momentum-integrated rf studies of unpolarized gases, it would be difficult to distinguish which theory is the better one. A full comparison for polarized gases is not possible since it is claimed that there are inconsistencies in the NSR approach (not found in the BCS-Leggett scheme). Future experiments along the lines of momentum-resolved experiments look to be very promising in distinguishing the two theories.
The Bose-Einstein condensate to Bardeen-Cooper-Schrieffer crossover in ultracold Fermi gases creates an ideal environment to enrich our knowledge of many-body systems. It is relevant to a wide range of fields from condensed matter to astrophysics. The nature of pairing in strongly interacting Fermi gases can be readily studied. This aids our understanding of related problems in high-Tc superconductors, whose mechanism is still under debate due to the large interaction parameter. Here, we calculate the dynamical properties of a normal, trapped strongly correlated Fermi gas, by developing a quantum cluster expansion. Our calculations for the single-particle spectral function agree with recent rf spectroscopy measurements, and clearly demonstrate pseudogap pairing in the strongly interacting regime.
We theoretically investigate the recent photoemission-type experiment on40K Fermi gases done by JILA group. Including pairing fluctuations within a strong-coupling T-matrix theory, as well as effects of a harmonic trap within the local density approximation, we calculate photoemission spectra in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region. We show that the energy resolution of the current photoemission experiment is enough to detect the pseudogap phenomenon. We also show how the pseudogap in single-particle excitations continuously changes into the superfluid gap, as one decreases the temperature below the superfluid phase transition temperature. Our results would be useful for the study of single-particle properties of ultracold Fermi gases in the BCS-BEC crossover.
BCS-Bose-Einstein condensation (BEC) crossover is effected by increasing pairing strength between fermions from weak to strong in the particle-particle channel, and has attracted a lot of attention since the experimental realization of quantum degenerate atomic Fermi gases. Here we study the effect of the (often dropped) particle-hole channel on the zero T gap Δ(0), superfluid transition temperature Tc, the pseudogap at Tc, and the mean-field ratio 2Δ(0)/, from BCS through BEC regimes, using a pairing fluctuation theory which includes self-consistently the contributions of finite-momentum pairs and features a pseudogap in single particle excitation spectrum. Summing over the infinite particle-hole ladder diagrams, we find a complex dynamical structure for the particle-hole susceptibility χph, and conclude that neglecting the self-energy feedback causes a serious over-estimate of χph. While our result in the BCS limit agrees with Gor'kov et al., the particle-hole channel effect becomes more complex and pronounced in the crossover regime, where χph is reduced by both a smaller Fermi surface and a big (pseudo)gap. Deep in the BEC regime, the particle-hole channel contributions drop to zero. We predict a density dependence of the magnetic field at the Feshbach resonance, which can be used to quantify χph and test different theories.