Observing the Influence of Reduced Dimensionality on Fermionic Superfluids

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Observing the Influence of Reduced Dimensionality on Fermionic Superfluids

Lennart Sobirey, Hauke Biss, Niclas Luick, Markus Bohlen, Henning Moritz, and Thomas Lompe

Phys. Rev. Lett. 129, 083601 – Published 17 August 2022

Abstract

Understanding the origins of unconventional superconductivity has been a major focus of condensed matter physics for many decades. While many questions remain unanswered, experiments have found the highest critical temperatures in layered two-dimensional materials. However, to what extent the remarkable stability of these strongly correlated 2D superfluids is affected by their reduced dimensionality is still an open question. Here, we use dilute gases of ultracold fermionic atoms as a model system to directly observe the influence of dimensionality on the stability of strongly interacting fermionic superfluids. We find that the superfluid gap follows the same universal function of the interaction strength regardless of dimensionality, which suggests that there is no inherent difference in the stability of two- and three-dimensional fermionic superfluids. Finally, we compare our data to results from solid state systems and find a similar relation between the interaction strength and the gap for a wide range of two- and three-dimensional superconductors.

Received 7 December 2021
Accepted 28 June 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.083601

Physics Subject Headings (PhySH)

2-dimensional systems Fermi gases High-temperature superconductors Superfluids Ultracold gases

Atomic, Molecular & Optical

Authors & Affiliations

Lennart Sobirey ^1,*, Hauke Biss ^1,2, Niclas Luick ^1,2, Markus Bohlen ^1,2, Henning Moritz ^1,2, and Thomas Lompe ^1,2

¹Institut für Laserphysik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
²The Hamburg Centre for Ultrafast Imaging, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg

^*lsobirey@physik.uni-hamburg.de

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Vol. 129, Iss. 8 — 19 August 2022

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Images

Figure 1
Excitation spectrum of a 2D Fermi gas in the BEC-BCS crossover. (a) Absorption image showing the density $n (\vec{r})$ of our homogeneous quasi-2D Fermi gas. (b) Sketch of the experimental setup for measuring the excitation spectrum of our system. Two far-detuned laser beams drive a two-photon transition with energy and momentum transfer $ℏ ω = ℏ (ω_{1} - ω_{2})$ and $ℏ q = ℏ | {\vec{k}}_{1} - {\vec{k}}_{2} |$ , and the dynamic structure factor $S (q, ω)$ can be obtained from the resulting heating rate. (c)–(h) Measurements of $S (q, ω)$ taken at different values of the 2D interaction parameter $\ln (k_{F} a_{2 D})$ . For strong attractive interactions (c) the system consists of tightly bound molecules which are excited as unbroken pairs, and consequently $S (q, ω)$ shows the Bogoliubov dispersion of an interacting Bose gas. Moving into the crossover regime [(d), (e), (f)], the pairs become more weakly bound and pair breaking excitations begin to appear at higher momenta. These excitations become more pronounced as we approach the BCS limit where the system shows the expected broad pair breaking continuum [(g), (h)]. In addition to these pair breaking excitations, it is also possible to excite sound waves in the superfluid. These appear in our spectra as a linear mode at low momenta, with a slope that corresponds to the speed of sound in the system and is in excellent agreement with previous measurements [red lines in panels (c)–(h), [8] ]. The data in panel (a) [(c)–(h)] was obtained by averaging over 26 (3–8) individual measurements. The behavior observed in [(c)–(h)] closely resembles results obtained in 3D Fermi gases [7, 9].
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Figure 2
Superfluid gap in the 2D BEC-BCS crossover. (a) Integrated dynamic structure factor $S (ω) = \int S (q, ω) q d q$ at an interaction strength of $\ln (k_{F} a_{2 D}) = 1.6$ , used to determine the gap $Δ$ (dotted red line) from a phenomenological fit (solid red line) to the onset of pair breaking excitations at an energy of $2 Δ$ [9]. (b) Dynamic structure factor $S (q, ω)$ at a fixed momentum transfer of $q = 0.5 k_{F}$ . At these small wave vectors, pair breaking is suppressed and strong driving is required to observe the onset of the pair breaking mode at $2 Δ$ (dotted red line), which causes a strong saturation of the low-energy phononic mode [9]. (c) Measured superfluid gap $Δ$ as a function of the interaction strength. The different symbols distinguish results obtained using the approaches shown in panel (a) [ $S (ω)$ , blue dots] and (b) (low $q$ , light blue diamonds). The contribution of the two-body bound state to the gap is shown as a solid line. (d) Many-body contribution $Δ - E_{B} / 2$ to the superfluid gap $Δ$ . BEC-BCS mean field predictions (dashed line, [68]) are in agreement with our measurement in the BCS regime, but deviate in the strongly correlated crossover regime. Quantum Monte Carlo calculations (gray triangles, [84, 85]) show better agreement in the crossover, but still deviate from the measurements in the BEC regime. Error bars denote $1 σ$ confidence intervals of the fit and are smaller than the symbol size, the data shown in panels (a) [(b)] is the average of 8 (26) individual measurements.
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Figure 3
Comparing the gaps of fermionic superfluids with different dimensionality. Superfluid gap $Δ / E_{F}$ of quasi-2D (blue circles and diamonds) and 3D (red stars) Fermi gases as a function of the chemical potential $μ / E_{F}$ taken from QMC calculations [87, 88]. The measurements of the gap collapse onto a single curve, which is well described by theoretical predictions for the gap in three-dimensional Fermi gases (red line, [89, 90]). Error bars denote $1 σ$ confidence intervals of the fit.
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Figure 4
Fermionic superfluidity in different materials. (a) Dimensionless pair size $ξ k_{F}$ plotted as a function of the dimensionless chemical potential $μ / E_{F}$ . As $ξ k_{F}$ follows the same function of $μ / E_{F}$ regardless of dimensionality, $ξ k_{F}$ can be used as an alternative parametrization of the interaction strength in our strongly interacting Fermi gases. Error bars denote $1 σ$ confidence intervals. (b) Plot of the dimensionless gap $Δ / E_{F}$ against the dimensionless pair size $ξ k_{F}$ for different fermionic superfluids. The Pippard coherence length $ξ_{p} = (ℏ^{2} k_{F} / π m Δ)$ [91] is shown as a dotted line. Remarkably, the superfluid gap is roughly proportional to the inverse of the dimensionless pair size for a wide range of materials that span 5 orders of magnitude in $Δ / E_{F}$ and $ξ k_{F}$ . This observation applies equally to two- and three-dimensional systems, which suggests that strong correlations are more important for the stability of fermionic superfluids than the dimensionality of the system.
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