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arXiv:1502.05022 · Physical Review A

Quasiparticle dispersions and lifetimes in the normal state of the BCS-BEC crossover

Matthew D. Reichl, Erich J. Mueller

Published Apr 22, 2015• 7 citations
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Abstract

We compute the spectral density in the normal phase of an interacting homogenous Fermi gas using a $T$-matrix approximation. We fit the quasiparticle peaks of the spectral density to BCS-like dispersion relations and extract estimates of a ``pseudogap'' energy scale and an effective Fermi wave vector as a function of interaction strength. We find that the effective Fermi wave vector of the quasiparticles vanishes when the inverse scattering length exceeds some positive threshold. We also find that, near unitarity, the quasiparticle lifetimes, estimated from the widths of the peaks in the spectral density, approach values on the order of the inverse Fermi energy. These results are consistent with the ``breakdown of Fermi-liquid theory'' observed in recent experiments.

DOI
10.1103/physreva.91.043627

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We compute the spectral density in the normal phase of an interacting homogenous Fermi gas using a TTT-matrix approximation. We fit the quasiparticle peaks of the spectral density to BCS-like dispersion relations and extract estimates of a pseudogap'' energy scale and an effective Fermi wave vector as a function of interaction strength. We find that the effective Fermi wave vector of the quasiparticles vanishes when the inverse scattering length exceeds some positive threshold. We also find that, near unitarity, the quasiparticle lifetimes, estimated from the widths of the peaks in the spectral density, approach values on the order of the inverse Fermi energy. These results are consistent with the breakdown of Fermi-liquid theory'' observed in recent experiments.
The nature of the normal state of an ultracold Fermi gas in the BCS-BEC crossover regime is an intriguing and controversial topic. While the many-body ground state remains a condensate of paired fermions, the normal state must evolve from a Fermi liquid to a Bose gas of molecules as a function of the interaction strength. How this occurs is still largely unknown. We explore this question with measurements of the distribution of single-particle energies and momenta in a nearly homogeneous gas above T(c). The data fit well to a function that includes a narrow, positively dispersing peak that corresponds to quasiparticles and an "incoherent background" that can accommodate broad, asymmetric line shapes. We find that the quasiparticle's spectral weight vanishes abruptly as the strength of interactions is modified, which signals the breakdown of a Fermi liquid description. Such a sharp feature is surprising in a crossover.
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.
The dispersions, weights, and widths of the peaks of the single-particle spectral function in the presence of pair correlations, for a Fermi gas with either attractive ororor repulsive short-range inter-particle interaction, are determined in the normal phase over a wide range of wave vectors, with a twofold purpose. The first one is to determine how these dispersions identify both an energy scale known as the pseudogap near the Fermi wave vector as well as an additional energy scale related to the contact CCC at large wave vectors. The second one is to differentiate the behaviors of the repulsive gas from the attractive one in terms of crossing versus avoided crossing of the dispersions near the Fermi wave vector. An analogy will also be drawn between the occurrence of the pseudogap physics in a Fermi gas subject to pair fluctuations and the persistence of local spin waves in the normal phase of magnetic materials.
We investigate single-particle excitations and strong-coupling effects in the BCS-BEC crossover regime of a superfluid Fermi gas. Including phase and amplitude fluctuations of the superfluid order parameter within a TTT-matrix theory, we calculate the superfluid density of states (DOS), as well as single-particle spectral weight, over the entire BCS-BEC crossover region below the superfluid transition temperature Tc{T}_{\mathrm{c}}Tc​. We clarify how the pseudogap in the normal state evolves into the superfluid gap, as one passes through Tc{T}_{\mathrm{c}}Tc​. While the pseudogap in DOS continuously evolves into the superfluid gap in the weak-coupling BCS regime, the superfluid gap in the crossover region is shown to appear in DOS after the pseudogap disappears below Tc{T}_{\mathrm{c}}Tc​. In the phase diagram with respect to the temperature and interaction strength, we determine the region where strong pairing fluctuations dominate over single-particle properties of the system. Our results would be useful for the study of strong-coupling phenomena in the BCS-BEC crossover regime of a superfluid Fermi gas.
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.
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.