Breakdown of the Fermi Liquid Description for Strongly Interacting Fermions

Yoav Sagi, Tara E. Drake, Rabin Paudel, Roman Chapurin, and Deborah S. Jin

Phys. Rev. Lett. 114, 075301 – Published 19 February 2015

Abstract

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.

Received 7 October 2014

DOI:https://doi.org/10.1103/PhysRevLett.114.075301

Authors & Affiliations

Yoav Sagi, Tara E. Drake, Rabin Paudel, Roman Chapurin, and Deborah S. Jin^*

JILA, National Institute of Standards and Technology and the University of Colorado, and the Department of Physics, University of Colorado, Boulder, Colorado 80309-0440, USA

^*Corresponding author. jin@jilau1.colorado.edu.

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Vol. 114, Iss. 7 — 20 February 2015

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Figure 1
Atom PES data. (a) We take data above $T_{c}$ in the strongly interacting region of the BCS-BEC crossover [19]. After initially preparing the gas at small, positive $a$ , the magnetic field is swept adiabatically to a final value within the BCS-BEC crossover, where $| (k_{F} a)^{- 1} | < 1$ . (b) Schematically, a rf photon, which has a negligible momentum, transfers an atom from the strongly interacting state (blue line) to a weakly interacting state (green line). The energy and momentum of the atom in the strongly interacting state are extracted from the measured momentum of the spin-flipped atom and the rf detuning $ν$ [13]. The detuning, $ν$ , of the rf frequency is varied to obtain data for a wide range of $E$ and $k$ . (c) Immediately following the rf pulse and before time-of-flight expansion, two orthogonally propagating hollow-core beams optically pump atoms at the edges of the outcoupled atom cloud into a dark state [20, 21]. The durations of both the rf pulse and optical pumping are short compared to the motion of atoms in the trap. (d) (lower panel) In these example plots of PES data, the color represents the probability distribution of atoms at a given $E$ and $k$ in the strongly interacting gas. We estimate that the error bar of $(k_{F} a)^{- 1}$ is 0.03. $E = 0$ is the energy of a free atom at rest and the white line shows the free-particle dispersion $E = k^{2}$ . (d) (upper panel) Our two-mode fit function includes a fermionic quasiparticle part, shown on the left with $m^{*} = 1.05$ , $E_{0} = - 0.1$ , $μ = 0.5$ , and $T = 0.25$ , and an incoherent part, shown on the right with $E_{p} = 1.5$ and $T_{p} = 0.7$ .
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Figure 2
EDCs for atom PES data near unitarity. Data (circles) and fits (lines) are shown for several example traces at fixed $k$ through the PES data at $(k_{F} a)^{- 1} = - 0.08$ . These traces are often called energy distribution curves, or EDCs. Here, the fitting parameters are $Z = 0.37 \pm 0.03$ , $m^{*} = 1.22 \pm 0.03$ , $T = 0.24 \pm 0.02$ , $E_{0} = - 0.33 \pm 0.02$ , $μ = 0.19 \pm 0.04$ , $E_{p} = 0.23 \pm 0.04$ , $T_{p} = 1.09 \pm 0.08$ , where the error margins are for one standard deviation and also include a 5% uncertainty in $E_{F}$ . For this fit, the reduced $χ^{2}$ is 1.2.
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Figure 3
$Z$ and effective mass. (a) The quasiparticle spectral weight $Z$ decreases as $(k_{F} a)^{- 1}$ increases. Using a linear fit to the range $- 0.5 \leq (k_{F} a)^{- 1} \leq 0.3$ , we find that $Z$ vanishes at $(k_{F} a)^{- 1} = 0.28 \pm 0.02$ (dashed line); this marks the breakdown of a Fermi liquid description. The blue circles come from fits of a large range of data, from 0 to 1.5 $k_{F}$ . The red squares show the result of restricting the fit to 0.7 to 1.3 $k_{F}$ , and they show a similar trend and slightly larger error bars. (b) The quasiparticle effective mass $m^{*}$ is shown for the region where $Z > 0$ . Interactions increase $m^{*}$ , and the data (circles) agree surprisingly well with the theoretical prediction for the limiting case of the Fermi polaron (solid line) [10, 37]. Restricting the fit to EDCs close to the Fermi surface produces similar results with increased error bars (red squares).
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Figure 4
The contact parameter. From the PES data, we extract the contact per particle (in units of $k_{F}$ ) for a homogeneous Fermi gas above $T_{c}$ as a function of the interaction strength $(k_{F} a)^{- 1}$ . The contact measured from the tail of the rf line shape [23], using data for $h ν \geq 5 E_{F}$ , is shown in blue circles, while the contact extrapolated from the fits of the PES data is shown in red squares. Remarkably, even though we limited the fits of the PES data to $k \leq 1.5$ and $E \geq - 3$ , a region with a relatively small contribution of short-range correlations [21, 32, 33, 42], we find that the contact from the PES fits is consistent with the contact measured from the tail of the momentum-integrated rf line shape. For comparison with the data, we also plot the BCS (dashed black line) and BEC (dashed magenta line) limits, given by $4 (k_{F} a)^{2} / 3$ and $4 π (k_{F} a)^{- 1}$ , respectively [33], the non-self-consistent t-matrix at $T = 0$ (dotted blue line) and its Popov version at $T_{c}$ (dashed-dotted red line) [44], and the self-consistent t-matrix model at $T = 0$ (double-dotted green line) [18]. Interestingly, we find that the contact measured above $T_{c}$ agrees well with the $T = 0$ theories.
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