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Observation of Scaling of Higher-Order Flow in a Unitary Fermi Gas

This study demonstrates that a unitary Fermi gas exhibits universal early-time evolution across higher-order flow harmonics before transitioning to a viscous acoustic scaling regime, thereby establishing a direct link between collective dynamics in ultracold quantum gases and strongly interacting nuclear matter.

Original authors: Shuxian Yu, Zhijie Zhang, Yunyi Zhao, Shujin Deng, Meng-Zi Huang, Haibin Wu, Yu-Gang Ma

Published 2026-11-04

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CC BY 4.0

Original authors: Shuxian Yu, Zhijie Zhang, Yunyi Zhao, Shujin Deng, Meng-Zi Huang, Haibin Wu, Yu-Gang Ma

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the vast landscape of physics, there is a special class of materials where particles do not act alone but move as a single, coordinated unit. This phenomenon, known as collective flow, occurs when a group of atoms or subatomic particles responds to pressure and shape changes in a way that resembles a fluid rather than a collection of individual billiard balls. Scientists have long studied this behavior in two very different extremes: the super-hot, dense matter created when heavy atomic nuclei smash together at nearly the speed of light, and the ultra-cold clouds of atoms trapped in laboratories on Earth. In both cases, the way the material expands and flows reveals deep secrets about how matter behaves when interactions between particles are at their strongest possible limit. A key question has remained unanswered: how does this coordinated motion develop across different levels of complexity, and how does the internal friction of the material, known as viscosity, eventually slow down or distort these flows?

A team of researchers at East China Normal University and collaborating institutions has now answered these questions by creating a highly controlled version of this extreme matter. They worked with a cloud of lithium-6 atoms, cooled to temperatures just a fraction of a degree above absolute zero. At this extreme cold, the atoms enter a state called the unitary regime, where they interact with each other as strongly as the laws of quantum mechanics allow. The researchers used a clever setup involving a digital micromirror device to shape the light holding these atoms. Instead of the usual smooth, round trap, they programmed the light to create a nearly uniform cloud with specific, engineered bumps and dents around its edge. These deformations ranged from simple ellipses to shapes with up to seven distinct lobes, effectively creating a series of increasingly complex starting points for the experiment.

Once the cloud was prepared in these precise shapes, the researchers suddenly switched off the light holding it in place. This sudden release allowed the gas to expand freely into the vacuum. As the cloud grew, the researchers took pictures of it from different angles to track how the initial bumps and dents evolved into patterns of motion. They measured the flow of the atoms up to the seventh order of complexity, looking for how the different shapes of the initial deformation translated into the final movement of the gas. What they found was a striking pattern of order followed by a breakdown. In the very first moments after the release, the gas behaved with a surprising uniformity. Regardless of whether the cloud started with a simple oval shape or a complex seven-pointed star, and regardless of the size of the cloud, the flow evolved in exactly the same way when measured against a specific timescale. This early behavior matched the predictions of ideal fluid dynamics, where the gas moves without any internal friction.

However, as time passed, this perfect unity began to fade. The different flow patterns started to diverge, and the more complex shapes with higher numbers of lobes began to lose their strength faster than the simpler ones. The researchers discovered that the rate at which these complex flows died out followed a specific rule: the attenuation, or weakening, of the flow increased with the square of the number of lobes. In simpler terms, a flow pattern with four lobes was suppressed much more quickly than one with two, and a pattern with seven lobes was suppressed even more dramatically. This quadratic relationship is a signature of viscous damping, where the internal friction of the fluid acts like a brake on the smaller, faster-moving ripples within the gas. By measuring this effect at different temperatures, the team confirmed that the friction of the gas is the primary cause of this breakdown.

The study provides a clear window into how universal laws of fluid motion give way to the messy reality of friction and heat. The researchers observed that the transition from the initial, perfect expansion to the later, friction-dominated phase happens in a predictable way. They found that the strength of this friction depends on the temperature of the gas, with the damping becoming more pronounced as the gas gets warmer. This work connects the behavior of ultracold atomic gases, which can be manipulated with extreme precision, to the chaotic, high-energy collisions of heavy ions. It shows that the same fundamental principles of how fluids expand and how viscosity smooths out irregularities apply across vastly different scales of nature. By mapping out exactly how these higher-order flows emerge and fade, the researchers have opened a new path for understanding the transport properties of strongly interacting matter, bridging the gap between the quantum world of atoms and the nuclear world of colliding stars.

Technical Summary: Observation of Scaling of Higher-Order Flow in a Unitary Fermi Gas

Problem and Motivation
Collective flow is a fundamental manifestation of strongly interacting quantum matter, observed in systems ranging from ultracold quantum gases to the quark-gluon plasma (QGP) produced in relativistic heavy-ion collisions. In heavy-ion collisions, initial spatial anisotropies convert into momentum correlations, characterized by azimuthal flow harmonics ( $v_n$ ). While elliptic ( $v_2$ ) and triangular ( $v_3$ ) flows are well-studied probes of transport properties, higher-order harmonics offer sensitivity to smaller spatial structures, nonlinear mode coupling, and the breakdown of hydrodynamic behavior. However, in heavy-ion collisions, the fluctuating initial geometry and the reliance on final-state momentum access make it difficult to resolve the dynamical emergence and evolution of specific harmonics during expansion. Ultracold Fermi gases (UFG) offer a complementary platform where initial density geometry can be precisely engineered and the full temporal evolution reconstructed. Despite previous demonstrations of anisotropic expansion and scale-invariant dynamics in UFGs, the dynamical emergence of higher-order flow ( $n > 2$ ) and its dissipative evolution remain unexplored.

Methodology
The authors investigate the nonequilibrium expansion of a unitary Fermi gas (a balanced mixture of $^6$ Li atoms at a Feshbach resonance, $B \approx 832$ G) initially confined in nearly homogeneous potentials with engineered angular deformations.

System Preparation: A digital micromirror device (DMD) generates a programmable repulsive hollow beam to create a near-uniform transverse density bounded by a shape $R(\phi) = R_0 + A \cos[n(\phi - \Phi_n)]$ . The deformation amplitude is fixed at $A/R_0 = 0.25$ , while the harmonic order $n$ is varied from 2 to 7, and the mean radius $R_0$ is varied between 23 and 54 $\mu$ m.
Expansion and Imaging: The optical confinement is suddenly removed, initiating interaction-driven expansion. The gas evolves for a controlled time of flight (TOF) before standard absorption imaging is performed. Simultaneous front and side imaging allows for full reconstruction of the expansion and thermometry via the equation of state.
Data Analysis: The anisotropic flow harmonics are quantified by computing the unweighted, signed angular moment of the column density, $V_n(t)$ . The efficiency of converting initial spatial anisotropy ( $\epsilon_n$ ) into collective flow is measured via the ratio $V_n/\epsilon_n$ .

Key Results

Universal Early-Time Evolution: Upon sudden release, the flow dynamics exhibit a universal behavior across different harmonic orders ( $n=2$ to $7$) and system sizes ( $R_0$ ). When the time axis is rescaled by a geometric timescale $q = nt/R_0$ and further by the sound speed to form an acoustic scale $\tau = c_s q$ , the early-time trajectories for all $n$ , sizes, and temperatures collapse onto a single curve. This behavior is quantitatively described by the hydrodynamic prediction for boundary-driven rarefaction waves: $V_n(t)/|V_n(0)| \simeq -1 + \frac{3}{10}\tau^2$ .
Breakdown of Universality and Harmonic Scaling: At longer times, the universal behavior breaks down, and distinct dynamics emerge for different harmonics. The normalized flow harmonics show an approximately quadratic dependence on the harmonic order scaled by the system size ( $n^2/R_0$ ). Specifically, the logarithmic response follows $\ln(V_n/\epsilon_n) \simeq A_0 - K(n^2/R_0)$ . This scaling is consistent with viscous acoustic attenuation, where shear viscosity preferentially dampens shorter-wavelength excitations.
Temperature Dependence: Measurements at different dimensionless temperatures ( $T/T_F \approx 0.15 - 0.35$ ) reveal that the attenuation coefficient $K$ depends on temperature. The data are consistent with both linear ( $K \propto T/T_F$ ) and square-root ( $K \propto \sqrt{T/T_F}$ ) scalings, reflecting the complex interplay between shear viscosity, expansion speed, and thermal transport in a degenerate, strongly interacting quantum fluid.

Significance and Claims
The paper claims to provide the first experimental observation of the dynamical emergence and evolution of higher-order collective flow (up to the seventh order) in a unitary Fermi gas. The study establishes a direct connection between the universal hydrodynamic expansion of ultracold atomic gases and the anisotropic flow observed in strongly interacting nuclear matter. By resolving the transition from a universal early-time acoustic response to a harmonic-dependent dissipative regime, the work offers new constraints on the interplay between pressure-driven conversion and transport coefficients. The authors posit that this approach opens a route to exploring shear viscosity and nonlinear flow couplings in a controlled quantum system, bridging the gap between atomic physics and the hydrodynamics of the quark-gluon plasma.

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