Tunneling Transport of Unitary Fermions across the Superfluid Transition

G. Del Pace, W. J. Kwon, M. Zaccanti, G. Roati, and F. Scazza

Phys. Rev. Lett. 126, 055301 – Published 4 February 2021

Abstract

We investigate the transport of a Fermi gas with unitarity-limited interactions across the superfluid phase transition, probing its response to a direct current (dc) drive through a tunnel junction. As the superfluid critical temperature is crossed from below, we observe the evolution from a highly nonlinear to an Ohmic conduction characteristic, associated with the critical breakdown of the Josephson dc current induced by pair condensate depletion. Moreover, we reveal a large and dominant anomalous contribution to resistive currents, which reaches its maximum at the lowest attained temperature, fostered by the tunnel coupling between the condensate and phononic Bogoliubov-Anderson excitations. Increasing the temperature, while the zeroing of supercurrents marks the transition to the normal phase, the conductance drops considerably but remains much larger than that of a normal, uncorrelated Fermi gas tunneling through the same junction. We attribute such enhanced transport to incoherent tunneling of sound modes, which remain weakly damped in the collisional hydrodynamic fluid of unpaired fermions at unitarity.

Received 30 July 2020
Accepted 12 January 2021

DOI:https://doi.org/10.1103/PhysRevLett.126.055301

Physics Subject Headings (PhySH)

Fermi gases Fermionic condensates Josephson effect Quantum transport Quasiparticles & collective excitations Superfluidity Transport phenomena

Josephson junctions Tunnel junctions

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Authors & Affiliations

G. Del Pace^1,2,3,*, W. J. Kwon ^2,3, M. Zaccanti ^2,3, G. Roati^2,3, and F. Scazza ^2,3,†

¹Department of Physics and Astronomy, University of Florence, 50019 Sesto Fiorentino, Italy
²European Laboratory for Nonlinear Spectroscopy (LENS), 50019 Sesto Fiorentino, Italy
³Istituto Nazionale di Ottica del Consiglio Nazionale delle Ricerche (CNR-INO), 50019 Sesto Fiorentino, Italy

^*delpace@lens.unifi.it
^†scazza@lens.unifi.it

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 126, Iss. 5 — 5 February 2021

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
A current-driven tunnel junction between resonant Fermi gases across the superfluid transition. (a) Experimental realization of a tunneling dc drive by dynamical optical potentials. The surface of a DMD displaying the junction geometry, composed of a central barrier and two end caps, is projected onto the atoms through a $NA ≃ 0.5$ objective, creating a repulsive potential $V (r)$ . The barrier is set in uniform motion at velocity $v$ by playing a sequence of images on the DMD at the desired frame rate, and is swept over a distance $δ x$ along the $x$ axis. (b) In situ absorption images of the atomic density at unitarity, acquired immediately after completing a $δ x ≃ 10 μ m$ barrier translation. The column-integrated density profiles $n_{2 D} (x, y)$ are shown for an injected current $I_{ext} ≃ 3.9 \times 10^{5} s^{- 1}$ at (i) $T = 0.08 (1) T_{F}$ and (ii) $T = 0.18 (1) T_{F}$ . While no density difference is visible between the two reservoirs for the colder sample, the hotter one displays a density increase in the left reservoir, producing a chemical potential bias $Δ μ \neq 0$ across the junction.
Reuse & Permissions
Figure 2
Breakdown of dc tunneling supercurrents in strongly interacting Fermi gases. (a) Current-potential $I − Δ μ$ characteristics of the junction at unitarity for different gas temperatures $T / T_{F}$ (see legend). Solid lines represent fits of experimental data with a RCSJ circuit model [31]. The fitted values for the maximum supercurrent $I_{s, \max}$ are denoted by arrows on the bottom axis. Error bars denote the standard deviation of the mean (s.e.m.) from averaging over $\sim 10$ experimental realizations. (b) $I_{s, \max}$ at unitarity as a function of the reduced temperature $T / T_{F}$ . Vertical (horizontal) error bars combine the standard error on $I_{s, \max}$ (temperature) with statistical errors from averaging typically two independent extractions. The shaded region indicates the calculated $I_{s, \max}$ (see text), considering a 10% uncertainty around the nominal barrier width and a 3.5% uncertainty on the calculated $E_{F}$ . The barrier height is fixed at $V_{0} / μ_{0} ≃ 0.7$ , where $μ_{0} \approx 0.6 E_{F}$ [50]. The dashed vertical line marks the predicted critical temperature $T_{c}$ for the superfluid transition at unitarity [30]. (c) Critical temperature $T_{0} / T_{F}$ for the disappearance of Josephson currents as a function of interaction strength $(k_{F} a)^{- 1}$ . Experimental results are compared with the theoretically obtained $T_{c}$ from Ref. [29] (green dashed line).
Reuse & Permissions
Figure 3
Bias-independent tunneling conductance $G$ as a function of $T / T_{F}$ , measured at unitarity under the same experimental conditions of Fig. 2. (a) $G$ is normalized to the conductance per spin component $G_{0} = 102 (15) h^{- 1}$ of a noninteracting Fermi gas, measured at $T = 0.21 (1) T_{F}$ with an equivalent barrier height $V_{0} / μ_{0} ≃ 0.73$ . Vertical (horizontal) error bars combine the standard error on the extracted conductance (temperature) with statistical errors from averaging typically two independent extractions. The dashed vertical line locates the theoretical critical temperature $T_{c}$ at unitarity [30]. (b) Experimentally obtained $I_{s, \max} / G$ as a function of $T / T_{F}$ .
Reuse & Permissions
Figure 4
Charging rate $G E_{c}$ as a function of the adimensional barrier strength $η_{b} = (k_{F} d) \times \sqrt{V_{0} / E_{F}}$ [31] for (a) a superfluid unitary gas at $T = 0.06 (1) T_{F} ≃ 0.3 T_{c}$ , (b) a unitary gas at $T = 0.20 (1) T_{F} ≃ T_{c}$ , and (c) a normal attractive Fermi gas with $(k_{F} a)^{- 1} ≃ - 0.82$ at $T = 0.20 (1) T_{F} ≃ 2.8 T_{c}$ [61]. In panel (a), $E_{F} / h ≃ 6 kHz$ (data taken from Ref. [25]), while $E_{F} / h ≃ 11 kHz$ in panel (b) and (c). Vertical and horizontal error bars result from the standard error on $G$ and the experimental uncertainty on $V_{0}$ , respectively. Solid lines represent linear fits of $\log G E_{c}$ . In the inset of panel (a), the measured $G^{1 / 2}$ and $I_{s, \max}$ are compared within the same $η_{b}$ range.
Reuse & Permissions

Physical Review Letters