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arXiv:2311.16788 · Physical Review A

Spectral properties and observables in ultracold Fermi gases

Eugen Dizer, Jan Horák, Jan Martin Pawlowski

Published Jun 5, 2024• 5 citations
arXivHTMLPDF

Abstract

We calculate nonperturbative self-consistent fermionic and bosonic spectral functions of ultracold Fermi gases with the spectral functional approach. This approach allows for a direct real-time computation of nonperturbative correlation functions, and in the present work we use spectral Dyson-Schwinger equations. We focus on the normal phase of the spin-balanced Fermi gas and provide numerical results for the full fermionic and bosonic spectral functions. The spectral functions are then used for the determination of the equation of state, the Tan contact, and ejection rf spectra at unitarity. These results are compared to experimental data, the self-consistent $T$-matrix approach, and lattice results. Our approach offers a wide range of applications, including the ab initio calculation of transport and spectral properties of the superfluid phase in the BCS-BEC crossover.

DOI
10.1103/physreva.109.063311

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We calculate nonperturbative self-consistent fermionic and bosonic spectral functions of ultracold Fermi gases with the spectral functional approach. This approach allows for a direct real-time computation of nonperturbative correlation functions, and in the present work we use spectral Dyson-Schwinger equations. We focus on the normal phase of the spin-balanced Fermi gas and provide numerical results for the full fermionic and bosonic spectral functions. The spectral functions are then used for the determination of the equation of state, the Tan contact, and ejection rf spectra at unitarity. These results are compared to experimental data, the self-consistent TTT-matrix approach, and lattice results. Our approach offers a wide range of applications, including the ab initio calculation of transport and spectral properties of the superfluid phase in the BCS-BEC crossover.
The strongly attractive Fermi gas in the BCS-BEC crossover is efficiently described in terms of coupled fermions and fermion pairs, or molecules. We compute the spectral functions of both fermions and pairs in the normal state near the superfluid transition using a Keldysh formulation in real frequency. The mutual influence between fermions and pairs is captured by solving the self-consistent Luttinger-Ward equations: These include both the damping of fermions by scattering off dressed pairs and the decay of pair states by dissociation into two dressed fermions. The pair spectra encode contact correlations between fermions and form the basis for computing dynamical response functions and transport properties.
Taking into account the effect of the generalized Gor'kov and Melik—Barkhudarov (GMB) approximation, we calculate the radio-frequency spectra of balanced and homogeneous ultracold Fermi gases within the framework of the non-self-consistent T-matrix approximation at unitarity in the normal phase. The corresponding equations are numerically calculated on the real frequency axis directly. It is found that our results agree well with the experimental result of the radio-frequency spectroscopy [Phys. Rev. Lett. 101 (2008) 140403].
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 will present recent experimental work on the thermodynamics of strongly interacting Fermi gases. We have developed a general method to probe with high precision the Equation of State (EoS) of locally homogeneous ultracold gases. This allows stringent tests of recent many-body theories. First, we focus on the finite-temperature EoS of the unpolarized unitary gas. Precise thermometry is provided by adding to the Fermi gas of 6Li a trace of bosonic 7Li. We show that the low-temperature properties of the strongly interacting normal phase are well described by Fermi liquid theory and we localize the superfluid transition. Second, we address the zero-temperature EoS of the spin-polarized system in the BEC-BCS crossover. Surprisingly, despite strong interactions, the polarized phase behaves as a mixture of two ideal gases: a Fermi gas of majority atoms and a non-interacting gas of dressed quasi-particles, the Fermi polarons. We also obtain the equation of state of the superfluid state as a function of interaction strength, that we compare to Monte Carlo simulations and to the Lee-Huang-Yang corrections for low-density bosonic and fermionic superfluids.
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.