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arXiv:1003.1538 · Physical Review Letters

Pseudogap Pairing in Ultracold Fermi Atoms

Hui Hu, Xia-Ji Liu, P. D. Drummond, Hui Dong

Published Jun 18, 2010• 80 citations
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Abstract

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.

DOI
10.1103/physrevlett.104.240407

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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.
The crossover from weak-coupling Bardeen-Cooper-Schrieffer (BCS) pairing to a Bose-Einstein condensate (BEC) of tightly bound pairs, as a function of the attractive interaction in Fermi systems, has long been of interest to theoretical physicists. The past decade has seen a series of remarkable experimental developments in ultracold Fermi gases that have realized the BCS-BEC crossover in the laboratory, bringing with it fresh new insights into the very strongly interacting unitary regime in the middle of this crossover. In this review, we start with a pedagogical introduction to the crossover and then focus on recent progress in the strongly interacting regime. Although our focus is on new theoretical developments, we also describe three key experiments that probe the thermodynamics, transport, and spectroscopy of the unitary Fermi gas. We discuss connections between the unitary regime and other areas of physics—quark-gluon plasmas, gauge-gravity duality, and high-temperature superconductivity—and conclude with open questions about strongly interacting Fermi gases.
Ultracold atomic gases are a powerful tool to experimentally study strongly correlated quantum many-body systems. In particular, ultracold Fermi gases with tunable interactions have allowed to realize the famous BEC-BCS crossover from a Bose-Einstein condensate (BEC) of molecules to a Bardeen-Cooper-Schrieffer (BCS) superfluid of weakly bound Cooper pairs. However, large parts of the excitation spectrum of fermionic superfluids in the BEC-BCS crossover are still unexplored. In this work, we use Bragg spectroscopy to measure the full momentum-resolved low-energy excitation spectrum of strongly interacting ultracold Fermi gases. This enables us to directly observe the smooth transformation from a bosonic to a fermionic superfluid that takes place in the BEC-BCS crossover. We also use our spectra to determine the evolution of the superfluid gap and find excellent agreement with previous experiments and self-consistent T-matrix calculations both in the BEC and crossover regime. However, toward the BCS regime a calculation that includes the effects of particle-hole correlations shows better agreement with our data.
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 theoretically investigate excitation properties in the pseudogap regime of a trapped Fermi gas. Using a combined TTT-matrix theory with the local density approximation, we calculate strong-coupling corrections to single-particle local density of states (LDOS), as well as the single-particle local spectral weight (LSW). Starting from the superfluid phase transition temperature Tc{T}_{\mathrm{c}}Tc​, we clarify how the pseudogap structures in these quantities disappear with increasing the temperature. As in the case of a uniform Fermi gas, LDOS and LSW give different pseudogap temperatures T∗{T}^{*}T∗ and T∗∗{T}^{**}T∗∗ at which the pseudogap structures in these quantities completely disappear. Determining T∗{T}^{*}T∗ and T∗∗{T}^{**}T∗∗ over the entire BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region, we identify the pseudogap regime in the phase diagram with respect to the temperature and the interaction strength. We also show that the so-called back-bending peak recently observed in the photoemission spectra by the JILA group may be explained as an effect of pseudogap phenomenon in the trap center. Since strong pairing fluctuations, spatial inhomogeneity, and finite temperatures are important keys in considering real cold Fermi gases, our results would be useful for clarifying normal-state properties of this strongly interacting Fermi system.
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 crossover from weak coupling Bardeen-Cooper-Schrieffer (BCS) pairing to a Bose-Einstein condensate (BEC) of tightly bound pairs, as a function of the attractive interaction in Fermi systems, has long been of interest to theoretical physicists. The past decade has seen a series of remarkable experimental developments in ultracold Fermi gases that has realized the BCS-BEC crossover in the laboratory, bringing with it fresh new insights into the very strongly interacting unitary regime in the middle of this crossover. In this review, we start with a pedagogical introduction to the crossover and then focus on recent progress in the strongly interacting regime. While our focus is on new theoretical developments, we also describe three key experiments that probe the thermodynamics, transport and spectroscopy of the unitary Fermi gas. We discuss connections between the unitary regime and other areas of physics -- quark-gluon plasmas, gauge-gravity duality and high temperature superconductivity -- and conclude with open questions about strongly interacting Fermi gases.