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Pseudogap state of ultracold fermion-boson mixtures in the Bogoliubov regime

Kai Ji, Andreas Komnik

Published Feb 17, 2016• 0 citations
OpenAlex

Abstract

We study the dynamical response of ultracold fermion-boson mixture in the Bogoliubov regime, where the interactions between fermions and bosonic excitations (phonons) are described by an effective Frohlich model under the Bogoliubov approximation. We show that the pseudogap feature which was previously found in quantum Monte Carlo simulations and which cannot be recovered by simple approximations, can be accurately reproduced with the help of vertex corrections. Using diagrammatic technique we compute Bragg spectra as well as the momentum dependent force-force correlation function. We show that both of them are heavily affected by the pseudogap effect at low impurity densities in both 1D and 2D systems.

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•Jan 1, 2014•0 citations
We study the dynamical response of ultracold fermion-boson mixture in the Bogoliubov regime, where the interactions between fermions and bosonic excitations (phonons) are described by an effective Frohlich model under the Bogoliubov approximation. We show that the pseudogap feature which was previously found in quantum Monte Carlo simulations and which cannot be recovered by simple approximations, can be accurately reproduced with the help of vertex corrections. Using diagrammatic technique we compute Bragg spectra as well as the momentum dependent force-force correlation function. We show that both of them are heavily affected by the pseudogap effect at low impurity densities in both 1D and 2D systems.
We study the dynamical response of ultracold fermion-boson mixtures in the Bogoliubov regime, where the interactions between fermionic impurities and bosonic excitations (phonons) are described by an effective Fr\"ohlich model under the Bogoliubov approximation. A characteristic suppression of the single-particle spectral weight is found in the small-momentum region where the impurity band and phonon mode intersect. Using a diagrammatic technique we compute the Bragg spectra as well as the momentum-dependent force-force correlation function. We find that both of them are heavily affected by the spectral weight suppression effect at low impurity densities in both one- and two-dimensional systems. We show that the spectral weight suppression feature in Bragg spectra, which was previously found in quantum Monte Carlo simulations and which cannot be recovered by the random phase approximation, can be accurately reproduced with the help of vertex corrections.
The pseudogap is a ubiquitous phenomenon in strongly correlated systems, such as high-T c superconductors, ultracold atoms, and nuclear physics.Whereas pairing fluctuations inducing the pseudogap are known to be enhanced in low-dimensional systems, such effects have not been explored well in one of the most fundamental one-dimensional models, that is, Gaudin-Yang model.In this paper, we show how the pseudogap effect emerges in the single-particle excitation in this system using a diagrammatic approach.Fermionic single-particle spectra exhibit a unique crossover from the double-particle dispersion to the pseudogap state with increasing the attractive interaction and the number density at finite temperature.Surprisingly, our results of thermodynamic quantities in unpolarized and polarized gases show an excellent agreement with the recent quantum Monte Carlo and complex Langevin results, indicating the validity of our approach even in the region where the pseudogap appears.
We investigate fluctuation effects in a single-component ultracold Fermi gas with a p-wave interaction. Within the framework of a strong-coupling T-matrix theory, we calculate the single-particle density of states (DOS) at the superfluid phase transition temperature Tc. Starting from the weak-coupling regime, we show that the so-called pseudogap structure develops in DOS, with increasing the strength of a pairing interaction. However, in contrast to the case of s-wave interaction (where the pseudogap size in DOS monotonically increases with increasing the interaction strength), the pseudogap structure is found to gradually disappear in the strong-coupling regime. We point out that this non-monotonic behavior of pseudogap originates from the momentum dependence of p-wave interaction. Our results clarify how the symmetry of pairing interaction affects pseudogap phenomena in strongly correlated fermion systems.
Exploratory simulations of Bose-Fermi mixtures on the three-dimensional optical lattice at finite temperature are performed by adopting the lattice quantum chromodynamics technique. We analyze the bosonic superfluid transition and its dependence on the strength of the boson-fermion coupling. The particle densities and the pair occupancies are also studied to understand the effect of the boson-fermion coupling to the microscopic properties of the system. The effect of the induced fermion-fermion interaction by the boson density fluctuation is clearly seen.
A recent boson-fermion (BF) binary gas mixture model is extended to include: (i) anisotropy of the BF interaction and (ii) momentum-independent Coulomb repulsions. It is applied to account for the peculiarities of the pseudogap observed as function of absolute temperature T and concentration x of holes doped onto the CuO 2 planes and to study the further transformation of the pseudogap into the real superconducting gap, as T is lowered. Using two-time Green functions it is shown that pair breakings depend on the separation between the boson and fermion spectra of the BF mixture. As this separation shrinks, the pair-breaking ability of the Coulomb interaction weakens and disappears at the BEC T c , i.e., at the T below which a complete softening of bosons occurs. Simultaneous inclusion of both effects (i) and (ii) produces, as T is lowered, "islands" in momentum space of incoherent Cooper pairs above the Fermi sea. These islands grow upon further cooling and merge together just before T c is reached. The new extended BF model predicts a pseudogap phase in 2D high-T c superconductors with lines of points, or loci, on the Fermi surface along which the pseudogap vanishes. This explains the origin of T-dependent "Fermi arcs" observed in ARPES experiments.
We consider a Bose-Fermi mixture with a broad and tunable Feshbach resonance allowing to change continuously the attraction between bosons and fermions from weak to strong coupling. We set up a diagrammatic formalism which includes both the Bose-Fermi tunable attraction and the Bose-Bose repulsion at zero temperature. Remarkably, we find that for boson density smaller than or equal to the fermion density, the boson condensate fraction does not depend on the density imbalance across most of the resonance. In the limit of vanishing boson concentration, we find very good agreement with previous results for the polaron quasi-particle residue obtained in the context of strongly polarized Fermi-Fermi mixtures [1]. We calculate also the boson and fermion chemical potentials and momentum distribution functions and, when the condensate fraction vanishes, we recover the results of our previous works for the normal phase [2,3]. In addition, we calculate the effective masses and Fermi steps for the unpaired and composite fermions. We find that the Fermi step of the unpaired fermions remains pinned to the value given by the Fermi radius of a free Fermi gas across most of the resonance, in agreement with the Luttinger’s theorem [4], until molecules start to form (g≈1). The formation of molecules is signalled by the appearance of a second pole in the boson-fermion propagator, which marks the access to a regime where bosons, fermions and molecules cohexist, and by the presence of a Fermi step for the composite fermions, which is related to the density of molecules. Finally, we find quite a good agreement between our results for the condensate fraction and Quantum Monte Carlo calculations [5].