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arXiv:2102.05911 · Physical Review A

Pairing and the spin susceptibility of the polarized unitary Fermi gas in the normal phase

Lukas Rammelmüller, Y. Hou, Joaquín E. Drut, Jens Braun

Published Apr 21, 2021• 18 citations
arXivHTMLPDF

Abstract

We theoretically study the pairing behavior of the unitary Fermi gas in the normal phase. Our analysis is based on the static spin susceptibility, which characterizes the response to an external magnetic field. We obtain this quantity by means of the complex Langevin approach and compare our calculations to available literature data in the spin-balanced case. Furthermore, we present results for polarized systems, where we complement and expand our analysis at high temperature with high-order virial expansion results. The implications of our findings for the phase diagram of the spin-polarized unitary Fermi gas are discussed in the context of the state of the art.

DOI
10.1103/physreva.103.043330

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We theoretically study the pairing behavior of the unitary Fermi gas in the normal phase. Our analysis is based on the static spin susceptibility, which characterizes the response to an external magnetic field. We obtain this quantity by means of the complex Langevin approach and compare our calculations to available literature data in the spin-balanced case. Furthermore, we present results for polarized systems, where we complement and expand our analysis at high temperature with high-order virial expansion results. The implications of our findings for the phase diagram of the spin-polarized unitary Fermi gas are discussed in the context of the state of the art.
We study in a nonperturbative fashion the thermodynamics of a unitary Fermi gas over a wide range of temperatures and spin polarizations. To this end, we use the complex Langevin method, a first principles approach for strongly coupled systems. Specifically, we show results for the density equation of state, the magnetization, and the magnetic susceptibility. At zero polarization, our results agree well with state-of-the-art results for the density equation of state and with experimental data. At finite polarization and low fugacity, our results are in excellent agreement with the third-order virial expansion. In the fully quantum mechanical regime close to the balanced limit, the critical temperature for superfluidity appears to depend only weakly on the spin polarization.
We present an ab initio determination of the spin response of the unitary Fermi gas. Based on finite temperature quantum Monte Carlo calculations and the Kubo linear-response formalism, we determine the temperature dependence of the spin susceptibility and the spin conductivity. We show that both quantities exhibit suppression above the critical temperature of the superfluid-to-normal phase transition due to Cooper pairing. The spin diffusion transport coefficient does not display a minimum in the vicinity of the critical temperature and drops to very low values D(s)≈0.8ħ/m in the superfluid phase. All these spin observables show a smooth and monotonic behavior with temperature when crossing the critical temperature T(c), until the Fermi liquid regime is attained at the temperature T(*), above which the pseudogap regime disappears.
We calculate the pair susceptibility of an attractive spin-polarized Fermi gas in the normal phase, as a function of the pair momentum. Close to unitarity, we find a strong enhancement of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing fluctuations over an extended region of the temperature-polarization phase diagram, which manifests itself as a pronounced peak in the pair-momentum distribution at a finite pair momentum. This peak should be amenable to experimental observation at achievable temperatures in a boxlike trapping potential, as a fingerprint of FFLO pairing. Our calculations rest on a self-consistent ttt-matrix approach which, for the unitary balanced Fermi gas, has been validated against experimental data for several thermodynamic quantities.
Abstract In a recent paper (2019 Phys. Rev. A 99, 053617), the total number of fermion pairs in a spin-balanced two-component Fermi gas of 6Li atoms was experimentally probed in the normal phase above the superfluid critical temperature, in order to investigate the sectors of pseudogap and preformed-pair in the temperature–coupling phase diagram. Here, we present a theoretical account of these experimental results in terms of an ab initio self-consistent t-matrix calculation, which emphasizes the role of the pair-correlation function between opposite-spin fermions at equilibrium. Good agreement is found between the available experimental data and the theoretical results obtained with no adjustable parameter.
AbstractIn a recent paper (2019 Phys. Rev. A 99, 053617), the total number of fermion pairs in a spin-balanced two-component Fermi gas of 6Li atoms was experimentally probed in the normal phase above the superfluid critical temperature, in order to investigate the sectors of pseudogap and preformed-pair in the temperature–coupling phase diagram. Here, we present a theoretical account of these experimental results in terms of an ab initio self-consistent t-matrix calculation, which emphasizes the role of the pair-correlation function between opposite-spin fermions at equilibrium. Good agreement is found between the available experimental data and the theoretical results obtained with no adjustable parameter.
In the two-component Fermi gas with contact interactions a pseudogap regime, in which pairing correlations are present without superfluidity, can exist at temperatures between the superfluid critical temperature TcT_cTc​ and a temperature T∗>TcT^* > T_cT∗>Tc​. However, the existence of a pseudogap in the unitary limit of infinite scattering length is debated. To help address this issue, we have used finite-temperature auxiliary-field quantum Monte Carlo (AFMC) methods to study the thermodynamics of the spin-balanced homogeneous unitary Fermi gas on a lattice. We present results for the thermal energy, heat capacity, condensate fraction, a model-independent pairing gap, and spin susceptibility, and compare them to experimental data when available. Our model space consists of the complete first Brillouin zone of the lattice, and our calculations are performed in the canonical ensemble of fixed particle number. We find that the energy-staggering pairing gap vanishes above TcT_cTc​ and that T∗T^*T∗ at unitarity, as determined from the spin susceptibility, is lower than previously reported in AFMC simulations.