Chinese Physics B

Shear viscosity of an ultracold Fermi gas in the BCS–BEC crossover

Jing Min, Xiangchuan Yan, Da-Li 大立 Sun 孙, W. Lu, Xin Xie, Xizhi 熙至 Wu 吴, Shi-Guo Peng, Kaijun Jiang

Published Mar 24, 2025• 1 citation

Abstract

Abstract We report on the measurement of shear viscosity in an ultracold Fermi gas with variable temperatures and tunable interactions. A quadrupole mode excitation in an isotropic harmonic trap is used to quantify the shear viscosity of the quantum gas within the hydrodynamic regime. The shear viscosity of the system as a function of temperature has been investigated, and the results closely align with calculations in the high-temperature limit utilizing a new definition of the cutoff radius. Through an adiabatic sweep across the Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein condensate (BEC) crossover, we find that the minimum value of the shear viscosity, as a function of interaction strength, is significantly shifted toward the BEC side. Furthermore, the behavior of the shear viscosity is asymmetric on both sides of the location of the minimum.

DOI: 10.1088/1674-1056/adc403

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Chinese Physics B

Shear viscosity of an ultracold Fermi gas in the BCS–BEC crossover

Jing Min, Xiangchuan Yan, Da-Li 大立 Sun 孙, W. Lu, Xin Xie, Xizhi 熙至 Wu 吴, Shi-Guo Peng, Kaijun Jiang

Published Mar 24, 2025• 1 citation

Publisher

Abstract

DOI: 10.1088/1674-1056/adc403

Related papers

Shear Viscosity and Strong-Coupling Corrections in the BCS–BEC Crossover Regime of an Ultracold Fermi Gas

Daichi Kagamihara, Daisuke Inotani, Yoji Ohashi

We theoretically investigate the shear viscosity $η$ in the BCS-BEC crossover regime of an ultracold Fermi gas with a Feshbach resonance. Within the framework of the strong-coupling self-consistent $T$ -matrix approximation, we examine how a strong pairing interaction associated with a Feshbach resonance affects this transport coefficient, in the normal state above the superfluid phase transition temperature $T_{\rm c}$ . We show that, while $η$ diverges in both the weak-coupling BCS and strong-coupling BEC limits, it becomes small in the unitary regime. The minimum of $η$ is obtained, not at the unitarity, but slightly in the strong-coupling BEC side. This deviation is consistent with the recent experiment on a $^6$ Li Fermi gas. In the weak-coupling BCS regime, we also find that $η$ exhibits anomalous temperature dependence near $T_{\rm c}$ , which is deeply related to the pseudogap phenomenon originating form strong pairing fluctuations.We theoretically investigate the shear viscosity $η$ in the BCS-BEC crossover regime of an ultracold Fermi gas with a Feshbach resonance. Within the framework of the strong-coupling self-consistent $T$-matrix approximation, we examine how a strong pairing interaction associated with a Feshbach resonance affects this transport coefficient, in the normal state above the superfluid phase transition temperature $T_{\rm c}$. We show that, while $η$ diverges in both the weak-coupling BCS and strong-coupling BEC limits, it becomes small in the unitary regime. The minimum of $η$ is obtained, not at the unitarity, but slightly in the strong-coupling BEC side. This deviation is consistent with the recent experiment on a $^6$Li Fermi gas. In the weak-coupling BCS regime, we also find that $η$ exhibits anomalous temperature dependence near $T_{\rm c}$, which is deeply related to the pseudogap phenomenon originating form strong pairing fluctuations.

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We present an ab initio calculation of the shear viscosity as a function of interaction strength in a two-component unpolarized Fermi gas near the unitary limit, within a finite temperature quantum Monte Carlo (QMC) framework and using the Kubo linear-response formalism. The shear viscosity decreases as we tune the interaction strength $\frac{1}{a{k}_{F}}$ from the Bardeen-Cooper-Schrieffer side of the Feshbach resonance towards Bose-Einstein condensation limit and it acquires the smallest value for $\frac{1}{a{k}_{F}}\ensuremath{\approx}0.4$, with a minimum value of ${\frac{\ensuremath{\eta}}{s}|}_{\text{min}}\ensuremath{\approx}0.2\frac{\ensuremath{\hbar}}{{k}_{B}}$, which is about twice as small as the value reported for experiments in quark-gluon plasma ${\frac{\ensuremath{\eta}}{s}|}_{\text{QGP}}\ensuremath{\lesssim}0.4\frac{\ensuremath{\hbar}}{{k}_{B}}$. The Fermi gas near unitarity thus emerges as the most ``perfect fluid'' observed so far in nature. The clouds of dilute Fermi gas near unitarity exhibit the unusual attribute that, for the sizes realized so far in the laboratory, or larger (less than ${10}^{9}$ atoms), can sustain quantum turbulence below the critical temperature, but at the same time the classical turbulence is suppressed in the normal phase.We present an ab initio calculation of the shear viscosity as a function of interaction strength in a two-component unpolarized Fermi gas near the unitary limit, within a finite temperature quantum Monte Carlo (QMC) framework and using the Kubo linear-response formalism. The shear viscosity decreases as we tune the interaction strength $\frac{1}{a{k}_{F}}$ from the Bardeen-Cooper-Schrieffer side of the Feshbach resonance towards Bose-Einstein condensation limit and it acquires the smallest value for $\frac{1}{a{k}_{F}}\ensuremath{\approx}0.4$, with a minimum value of ${\frac{\ensuremath{\eta}}{s}|}_{\text{min}}\ensuremath{\approx}0.2\frac{\ensuremath{\hbar}}{{k}_{B}}$, which is about twice as small as the value reported for experiments in quark-gluon plasma ${\frac{\ensuremath{\eta}}{s}|}_{\text{QGP}}\ensuremath{\lesssim}0.4\frac{\ensuremath{\hbar}}{{k}_{B}}$. The Fermi gas near unitarity thus emerges as the most ``perfect fluid'' observed so far in nature. The clouds of dilute Fermi gas near unitarity exhibit the unusual attribute that, for the sizes realized so far in the laboratory, or larger (less than ${10}^{9}$ atoms), can sustain quantum turbulence below the critical temperature, but at the same time the classical turbulence is suppressed in the normal phase.

arXiv:1504.02560Physical Review ADec 21, 201519 citations

We theoretically investigate the shear viscosity

η

in the BCS-BEC crossover regime of an ultracold Fermi gas with a Feshbach resonance. Within the framework of the strong-coupling self-consistent

T

-matrix approximation, we examine how a strong pairing interaction associated with a Feshbach resonance affects this transport coefficient, in the normal state above the superfluid phase transition temperature

T_{\rm c}

. We show that, while

η

diverges in both the weak-coupling BCS and strong-coupling BEC limits, it becomes small in the unitary regime. The minimum of

η

is obtained, not at the unitarity, but slightly in the strong-coupling BEC side. This deviation is consistent with the recent experiment on a

^6

Li Fermi gas. In the weak-coupling BCS regime, we also find that

η

exhibits anomalous temperature dependence near

T_{\rm c}

, which is deeply related to the pseudogap phenomenon originating form strong pairing fluctuations.

We report on measurements of an elementary surface mode in an ultracold, strongly interacting Fermi gas of

^{6}\mathrm{Li}

atoms. The radial quadrupole mode allows us to probe hydrodynamic behavior in the crossover from Bose-Einstein condensation (BEC) to the Bardeen-Cooper-Schrieffer (BCS) regime without being influenced by changes in the equation of state. We examine the frequency and damping of this mode, along with its expansion dynamics. In the unitarity limit and on the BEC side of the resonance, the observed frequencies agree with standard hydrodynamic theory. However, on the BCS side of the crossover, a striking downshift of the oscillation frequency is observed in the hydrodynamic regime as a precursor to an abrupt transition to collisionless behavior; this indicates coupling of the oscillation to fermionic pairs.

\frac{1}{a{k}_{F}}

from the Bardeen-Cooper-Schrieffer side of the Feshbach resonance towards Bose-Einstein condensation limit and it acquires the smallest value for $\frac{1}{a{k}_{F}}\ensuremath{\approx}0.4$, with a minimum value of ${\frac{\ensuremath{\eta}}{s}|}_{\text{min}}\ensuremath{\approx}0.2\frac{\ensuremath{\hbar}}{{k}_{B}}$, which is about twice as small as the value reported for experiments in quark-gluon plasma ${\frac{\ensuremath{\eta}}{s}|}_{\text{QGP}}\ensuremath{\lesssim}0.4\frac{\ensuremath{\hbar}}{{k}_{B}}$. The Fermi gas near unitarity thus emerges as the most ``perfect fluid'' observed so far in nature. The clouds of dilute Fermi gas near unitarity exhibit the unusual attribute that, for the sizes realized so far in the laboratory, or larger (less than

{10}^{9}

atoms), can sustain quantum turbulence below the critical temperature, but at the same time the classical turbulence is suppressed in the normal phase.