🔬 mesoscale physics

Neutron Scattering studies of the density dependence of One-dimensional Quantum Fluids

This paper presents neutron scattering results demonstrating that as the filling fraction of one-dimensional $^4$ He in a templated porous material increases, the central liquid core maintains a fixed density while its spatial extent grows, resulting in excitations distinct from higher-dimensional superfluids.

Original author: Sutirtha Paul, Rahul Soni, Garfield Warren, Adrian Del Maestro, Paul E. Sokol

Published 2026-11-11

📖 5 min read🧠 Deep dive

CC BY 4.0

Original author: Sutirtha Paul, Rahul Soni, Garfield Warren, Adrian Del Maestro, Paul E. Sokol

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 author. For technical accuracy, refer to the original paper. Read full disclaimer

In the vast landscape of physics, matter behaves differently depending on how much space it has to move. In our everyday three-dimensional world, particles can drift in any direction, forming familiar states like liquids and solids. But when scientists squeeze matter into a space so narrow that it can only move in a single line, the rules change completely. This is the realm of one-dimensional quantum fluids. In these tight corridors, particles cannot pass one another, and their behavior is governed by a unique set of laws where they act less like individual marbles and more like a single, collective wave. Understanding how these fluids behave is crucial because it helps scientists test the fundamental theories that describe how the universe works at the smallest scales, from the behavior of electrons in computer chips to the nature of superfluids that flow without friction.

A team of researchers recently set out to create and study such a one-dimensional fluid using helium, the lightest noble gas. Helium is a favorite subject for physicists because it remains liquid even at the coldest temperatures imaginable, and its atoms interact in ways that are both simple and profound. To force helium into a one-dimensional line, the scientists used a special type of glass called MCM-41, which is filled with millions of tiny, parallel tunnels. However, these tunnels were originally too wide to force the helium to behave as a single line. To solve this, the researchers first coated the inside of every tunnel with a thin layer of argon gas. This coating acted like a shrink-wrap, effectively narrowing the tunnels until they were just wide enough to hold a single file of helium atoms. Once prepared, they filled these narrowed tunnels with helium and used a powerful beam of neutrons to watch how the atoms moved and reacted to energy.

The experiment focused on what happens as more helium is added to the system. Previous computer simulations had suggested a specific scenario: as helium is added, the first few layers would stick tightly to the glass walls, forming solid rings. Any extra helium would then pile up in the very center of the tunnel, forming a liquid core. The prevailing idea was that as you added more helium, this central liquid core would simply get denser, with the atoms packing closer together. The researchers expected to see the properties of this liquid change as the density increased. Instead, they found something surprising. As they increased the amount of helium from a small amount up to a much larger quantity, the fundamental nature of the liquid in the center did not change at all. The speed of the waves moving through the liquid and the spacing between the atoms remained exactly the same, regardless of how much helium was added.

This discovery led the team to a different conclusion about how the liquid forms. Rather than a single, uniform stream of liquid that gets denser and denser, the helium appears to form in separate, isolated clusters or segments within the tunnels. As more helium is added, these liquid segments grow longer or new ones appear in empty tunnels, but the density of the liquid within each segment stays constant. It is as if the liquid is filling up a series of small, disconnected rooms rather than a single long hallway that is being squeezed tighter. The researchers confirmed this by measuring how the liquid responded to heat. They found that the unique quantum behavior of this liquid persisted even as the temperature rose, only fading away when the heat became strong enough to disrupt the delicate quantum order.

The study also revealed the precise energy required to disturb this one-dimensional state. By heating the sample and watching the signal from the liquid fade, the team calculated that it takes an energy equivalent to 19 degrees above absolute zero to break the quantum order. This is a significant finding because it shows that this one-dimensional state is robust and can exist at temperatures far higher than those required for helium to become a superfluid in its normal, three-dimensional form. The fact that the liquid's internal structure remains unchanged while the total amount of helium increases suggests that the system is not a simple, continuous fluid. Instead, it behaves like a collection of distinct, one-dimensional quantum liquids, each maintaining its own perfect density while the overall system expands to fill the available space.

These results provide a clear picture of how quantum matter organizes itself when strictly confined. The researchers demonstrated that by using a pre-plated argon layer to shrink the pores, they could reliably create a one-dimensional environment for helium. The fact that the liquid's density remained fixed while the total filling increased rules out the idea of a continuously compressing core. Instead, the evidence points to a model where the liquid grows in extent, filling more of the available tunnel space without changing its internal character. This work offers a rare, direct look at a state of matter that is theoretically predicted but difficult to observe, confirming that one-dimensional quantum fluids can be created and studied in a controlled laboratory setting. The findings suggest that the behavior of these fluids is governed by a stable, local density that resists change, offering a new perspective on how quantum systems adapt to extreme confinement.

Technical Summary: Neutron Scattering Studies of the Density Dependence of One-Dimensional Quantum Fluids

Problem and Motivation
One-dimensional (1D) quantum systems exhibit fundamental behaviors distinct from their two- and three-dimensional counterparts, specifically defying the quasi-particle paradigm in favor of collective excitations described by Tomonaga-Luttinger liquid (TLL) theory. While TLL predictions have been tested in low-density fermionic systems, nanowires, and ultracold gases, there remains a need to study 1D quantum liquids with realistic, strong interatomic interactions. Liquid helium ( $^4$ He) offers an ideal model system for this purpose, yet the primary challenge lies in confining helium to length scales comparable to its correlation length (sub-nanometer) to achieve true 1D behavior. Previous attempts using nanofabricated pores or mesoporous silica have shown signatures of reduced dimensionality but lacked direct spectroscopic confirmation of 1D dynamics across varying densities.

Methodology
This study employs inelastic neutron scattering to investigate the excitation spectrum of $^4$ He confined within MCM-41, a templated porous glass with nanometer-scale 1D pores. To achieve the necessary confinement, the pores were preplated with a monolayer of argon (Ar) at high temperatures, effectively reducing the pore diameter from $\sim30$ Å to $\sim20$ Å. This geometry is predicted by simulations to form three solid helium layers adjacent to the pore walls, leaving a central 1D liquid core.

Experiments were conducted at the Spallation Neutron Source using the Cold Neutron Chopper Spectrometer (CNCS). Measurements were performed on samples with varying filling fractions (ranging from 10.51 to 15.00 mmol/g) at temperatures between 1.5 K and 6 K. Incident neutron energies of 6, 12, and 28 meV were utilized to access different momentum ( $Q$ ) and energy ( $E$ ) transfers. The data was analyzed to extract the dynamic structure factor $S(Q, E)$ , focusing on the excitation threshold and dispersion relations of the confined fluid.

Key Contributions and Results
The primary contribution of this work is the systematic investigation of the density dependence of the 1D liquid core within the argon-preplated MCM-41 pores. The key findings include:

Emergence of 1D Behavior: No significant inelastic scattering characteristic of a TLL was observed at the lowest filling (10.51 mmol/g), consistent with the formation of strongly bound, localized solid layers. The 1D liquid phase emerges only above a threshold filling of approximately 11 mmol/g.
Density Independence of Excitation Parameters: Contrary to theoretical models suggesting that the density of the core liquid would evolve continuously as more helium is added, the extracted Luttinger parameter ( $K_L$ ) and Fermi momentum ( $k_F$ ) showed no systematic variation with pore filling. The values remained constant at $K_L \approx 1.06$ and $k_F \approx 0.82$ Å $^{-1}$ across the entire range of fillings where the liquid phase was present.
Linear Intensity Scaling: While the excitation parameters were density-independent, the relative scattering intensity increased linearly with the filling fraction above the threshold. This suggests that the 1D liquid forms in clustered regions or separated segments that grow in extent (or number) as more helium is added, rather than a single uniform phase where the local density increases.
Temperature Dependence: Measurements at a fixed filling (13.51 mmol/g) revealed that $K_L$ and $k_F$ remain statistically unchanged as temperature increases from 1.5 K to 6 K. However, the overall scattering intensity decreases with temperature, following a thermally activated behavior with an activation energy of $\Delta \approx 19$ K. TLL behavior is observed at the highest temperature studied (6 K), which is within the regime where TLL behavior is expected ( $T \ll 13$ K), supporting the identification of this phase as a TLL.

Significance and Claims
The authors posit that the observed density independence of the excitation spectrum indicates that the 1D liquid core forms in clustered regions with a fixed local density, rather than a uniformly expanding phase. The growth of the 1D liquid upon increasing filling is interpreted as the expansion of these liquid segments or the filling of additional pores, rather than a change in the intrinsic density of the fluid.

The study confirms that argon-preplated MCM-41 is a viable platform for studying 1D quantum fluids with strong interactions. The observation of TLL signatures at temperatures up to 6 K, which is well below the characteristic temperature of $\sim13$ K required for TLL behavior, supports the identification of this phase as a robust Tomonaga-Luttinger liquid. The work provides experimental validation for the existence of a 1D liquid core in confined helium and offers a new perspective on how such liquids organize within nanopores, challenging the assumption of continuous density evolution in favor of a segmented growth model.

Technical Summary: Neutron Scattering Studies of the Density Dependence of One-Dimensional Quantum Fluids

More like this