Pair correlations in the normal phase of an attractive Fermi gas

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.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.

arXiv:1912.04802New Journal of PhysicsJun 22, 202012 citations

Pair fraction in a finite-temperature Fermi gas on the BEC side of the BCS-BEC crossover

Thomas Paintner, Daniel Kai Hoffmann, Manuel Jäger +8 more

We investigate pairing in a strongly interacting two-component Fermi gas with positive scattering length. In this regime, pairing occurs at temperatures above the superfluid critical temperature; unbound fermions and pairs coexist in thermal equilibrium. Measuring the total number of these fermion pairs in the gas we systematically investigate the phases in the sectors of pseudogap and preformed pair. Our measurements quantitatively test predictions from two theoretical models. Interestingly, we find that already a model based on classical atom-molecule equilibrium describes our data quite well.We investigate pairing in a strongly interacting two-component Fermi gas with positive scattering length. In this regime, pairing occurs at temperatures above the superfluid critical temperature; unbound fermions and pairs coexist in thermal equilibrium. Measuring the total number of these fermion pairs in the gas we systematically investigate the phases in the sectors of pseudogap and preformed pair. Our measurements quantitatively test predictions from two theoretical models. Interestingly, we find that already a model based on classical atom-molecule equilibrium describes our data quite well.

arXiv:1803.10598Physical Review AMay 28, 201916 citations

Strong correlations in the normal phase of an attractive Fermi gas

Michele Pini

The purpose of this thesis is the study of an attractive Fermi gas in the normal phase throughout the BCS-BEC crossover by means of diagrammatic approaches based on the t-matrix approximation. More specifically, the calculation is implemented by including different degrees of self-consistency in the t-matrix equations, from the non-self-consistent to the fully self-consistent (or Luttinger-Ward) approach. In the first part of the thesis, we perform a systematic and unbiased comparative study of all the five variants of the t-matrix approach with different degrees of selfconsistency considered thus far in the literature. The analysis is performed by calculating several thermodynamic and dynamical quantities of the spin-balanced Fermi gas in the normal phase within all the approaches. We also compare these results with the available quantum Monte Carlo (QMC), diagrammatic Monte Carlo (DMC) and experimental data. In the comparison, the fully self-consistent t-matrix approach turns up to be the best to describe thermodynamic quantities, however for dynamical quantities partially or non-self-consistent approaches appear to work better. In the second part of the thesis, we investigate pairing correlations in the normal phase of the spin-balanced system within the fully self-consistent t-matrix approach. We first calculate the pair correlation function g↑↓(ρ) and the pair coherence length ξpair for various couplings and temperatures. We then develop a new approach, based on the two-body Green’s function formalism, to calculate the number of preformed pairs in the normal phase. The approach is used to describe the experimental data on this quantity by the group of Prof. Denschlag in Ulm. In order to compare our calculation with the experiment, the fully self-consistent t-matrix approach is extended to consider a Fermi gas in a harmonic trapping potential. In general, very good agreement is found with experimental data. In the final part of the thesis, we present some preliminary results for the spinimbalanced Fermi gas, focusing on the temperature-coupling-polarization phase diagram and on T = 0 and finite T thermodynamic quantities. In this analysis, we show that the Luttinger theorem for an imbalanced Fermi gas at T = 0 is satisfied within the fully self-consistent t-matrix approach, and we present the extension of the calculation of the pair correlation function g↑↓(ρ) to the spin-imbalanced case.The purpose of this thesis is the study of an attractive Fermi gas in the normal phase throughout the BCS-BEC crossover by means of diagrammatic approaches based on the t-matrix approximation. More specifically, the calculation is implemented by including different degrees of self-consistency in the t-matrix equations, from the non-self-consistent to the fully self-consistent (or Luttinger-Ward) approach. In the first part of the thesis, we perform a systematic and unbiased comparative study of all the five variants of the t-matrix approach with different degrees of selfconsistency considered thus far in the literature. The analysis is performed by calculating several thermodynamic and dynamical quantities of the spin-balanced Fermi gas in the normal phase within all the approaches. We also compare these results with the available quantum Monte Carlo (QMC), diagrammatic Monte Carlo (DMC) and experimental data. In the comparison, the fully self-consistent t-matrix approach turns up to be the best to describe thermodynamic quantities, however for dynamical quantities partially or non-self-consistent approaches appear to work better. In the second part of the thesis, we investigate pairing correlations in the normal phase of the spin-balanced system within the fully self-consistent t-matrix approach. We first calculate the pair correlation function g↑↓(ρ) and the pair coherence length ξpair for various couplings and temperatures. We then develop a new approach, based on the two-body Green’s function formalism, to calculate the number of preformed pairs in the normal phase. The approach is used to describe the experimental data on this quantity by the group of Prof. Denschlag in Ulm. In order to compare our calculation with the experiment, the fully self-consistent t-matrix approach is extended to consider a Fermi gas in a harmonic trapping potential. In general, very good agreement is found with experimental data. In the final part of the thesis, we present some preliminary results for the spinimbalanced Fermi gas, focusing on the temperature-coupling-polarization phase diagram and on T = 0 and finite T thermodynamic quantities. In this analysis, we show that the Luttinger theorem for an imbalanced Fermi gas at T = 0 is satisfied within the fully self-consistent t-matrix approach, and we present the extension of the calculation of the pair correlation function g↑↓(ρ) to the spin-imbalanced case.

Feb 19, 20200 citations

Nature of pairing correlations in the homogeneous Fermi gas at unitarity

Scott Jensen, C. N. Gilbreth, Y. Alhassid

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 $T_c$ and a temperature $T^* > T_c$ . 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 $T_c$ and that $T^*$ at unitarity, as determined from the spin susceptibility, is lower than previously reported in AFMC simulations.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 $T_c$ and a temperature $T^* > T_c$. 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 $T_c$ and that $T^*$ at unitarity, as determined from the spin susceptibility, is lower than previously reported in AFMC simulations.

Jan 18, 20181 citation

Pairing and Phase Separation in a Polarized Fermi Gas

Guthrie B. Partridge, Wenhui Li, Ramsey I. Kamar +2 more

We report the observation of pairing in a gas of atomic fermions with unequal numbers of two components. Beyond a critical polarization, the gas separates into a phase that is consistent with a superfluid paired core surrounded by a shell of normal unpaired fermions. The critical polarization diminishes with decreasing attractive interaction. For near-zero polarization, we measured the parameter beta = -0.54 +/- 0.05, describing the universal energy of a strongly interacting paired Fermi gas, and found good agreement with recent theory. These results are relevant to predictions of exotic new phases of quark matter and of strongly magnetized superconductors.We report the observation of pairing in a gas of atomic fermions with unequal numbers of two components. Beyond a critical polarization, the gas separates into a phase that is consistent with a superfluid paired core surrounded by a shell of normal unpaired fermions. The critical polarization diminishes with decreasing attractive interaction. For near-zero polarization, we measured the parameter beta = -0.54 +/- 0.05, describing the universal energy of a strongly interacting paired Fermi gas, and found good agreement with recent theory. These results are relevant to predictions of exotic new phases of quark matter and of strongly magnetized superconductors.

arXiv:cond-mat/0511752ScienceDec 23, 2005957 citations

Pairing effects in the normal phase of a two-dimensional Fermi gas

F. Marsiglio, P. Pieri, Andrea Perali +2 more

In a recent experiment [M. Feld et al., Nature (London) 480, 75 (2011); B. Fr\"ohlich et al., Phys. Rev. Lett. 109, 130403 (2012)], a pairing gap was detected in a two-dimensional (2D) Fermi gas with attractive interaction at temperatures where superfluidity does not occur. The question remains open as to whether this gap is a pseudogap phenomenon or is due to a molecular state. In this paper, by using a $t\ensuremath{-}\text{matrix}$ approach, we reproduce quite well the experimental data for a 2D Fermi gas, and set the boundary between the pseudogap and molecular regimes. We also show that pseudogap phenomena occurring in 2D and 3D can be related through a variable spanning the BCS-BEC crossover in a universal way.In a recent experiment [M. Feld et al., Nature (London) 480, 75 (2011); B. Fr\"ohlich et al., Phys. Rev. Lett. 109, 130403 (2012)], a pairing gap was detected in a two-dimensional (2D) Fermi gas with attractive interaction at temperatures where superfluidity does not occur. The question remains open as to whether this gap is a pseudogap phenomenon or is due to a molecular state. In this paper, by using a $t\ensuremath{-}\text{matrix}$ approach, we reproduce quite well the experimental data for a 2D Fermi gas, and set the boundary between the pseudogap and molecular regimes. We also show that pseudogap phenomena occurring in 2D and 3D can be related through a variable spanning the BCS-BEC crossover in a universal way.

arXiv:1406.7761Physical Review BFeb 9, 201549 citations

T_c

and a temperature

T^* > T_c

. 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

T_c

and that

T^*

at unitarity, as determined from the spin susceptibility, is lower than previously reported in AFMC simulations.