Since medieval times, the phenomenon of water flowing uphill has been considered miraculous, as exemplified by one of the Seven Wonders of Fore Abbey performed by St Fechin. However, in the quantum realm, superfluid helium ⁴He can achieve this gravity-defying feat. It can climb out of any container as a thin film that moves so quickly the container is drained in minutes.

Of the many strange effects witnessed in superfluids at low temperatures, those in thin films are among the most elusive for experimental investigation. Previously, helium films were only observed directly using X-rays. While this technique can determine the nanoscale profile of helium film, it is limited to temperatures above 1 K due to the high levels of energy deposition and cannot be used to distinguish between helium isotopes.

I am proud to be part of a team of scientists from the ISIS Neutron and Muon Source, Lancaster University and Oak Ridge National Laboratory who rose to the challenge of studying superfluid helium films. We saw an opportunity to use neutron reflectometry, which has a number of advantages in studying these systems. Unlike particle or X-ray beams, the weak interaction of neutrons with matter substantially reduces the problem of overheating, enabling experiments down into the milliKelvin temperature range. Additionally, ⁴He and ³He have very different neutron scattering cross-sections, as well as very different absorption cross-sections, enabling the isotopes to be distinguished.

Nevertheless, there were still challenges to overcome in our experiments. Firstly, ⁴He is a weak neutron scatterer, while ³He is one of the strongest neutron absorbers. As such, a slab of liquid ³He even just a fraction of millimetre thick will absorb almost all the neutrons that hit its surface. Secondly, the ultra-low temperature sample environment, required to keep the sample below 1K, adds a level of complexity. And last but not least, the mechanical vibrations from equipment can easily disturb the delicate helium film. To deal with these challenges, we chose the ISIS reflectometer, POLREF, which is known for its extremely high sensitivity and good resolution, for this experiment. We also implemented crucial anti-vibration measures on the cryogen-free dilution refrigerator that was used to cool the sample down to sub-Kelvin temperatures.

Ultimately, we ran two neutron beam experiments – one on a pure ⁴He film, and the other on a 0.1% ³He in ⁴He mixture film. Having collected the experimental data successfully, we realised that our work had really just begun! We needed to convert reflectivity data into the scattering and absorption density profiles that would allow us to present the data in a way that makes the physical meaning more evident. For this, we employed Bayesian modelling techniques, which required both a lot of mental effort and computing time.

In discussing the experimental results, it’s worth mentioning that the two helium isotopes are governed by different quantum statistics. While ⁴He obeys Bose-Einstein statistics, ³He obeys Fermi-Dirac statistics. As expected, the first experiment with a pure ⁴He film demonstrated very little change throughout the whole temperature range, which is typical for a Bose liquid. However, the addition of 0.1 % of ³He Fermi particles into the ⁴He film changed the situation drastically. We observed a phase-separated ³He/⁴He mixture film at 0.17 K and noted the gradual dissolution of the ³He top layer into ⁴He with increasing temperature. What’s more, some surprising behaviour in the helium mixture at 0.3 K hints at an as-yet unstudied geometrically restricted phase transition. Perhaps even more surprising was the restoration of the layered structure at 1.5 K.

From my point of view, the most intriguing observation of the experiment is the dramatic transition in the ³He-⁴He mixture film at 0.3 K. The scattering density and neutron absorption profiles showed that, instead of a homogeneous superfluid helium film, we observed a disordered quasi-layer that must contain some ³He. Right now, we don’t have enough data to speculate about the nature of the transition, but something dramatic is definitely going on in this area.

I also believe that this study offers a unique window into the quantum world. Not only does it demonstrate the well-known behaviour of a bosonic ⁴He superfluid, but it also highlights how adding even a tiny droplet of fermionic ³He can disrupt the delicate states present in superfluids at ultra-low temperatures, stopping the uphill flow of liquid. This experiment also serves as a testament to the power of neutron techniques in studying quantum systems, hinting at unexplored phenomena in thin helium mixture films.

I am optimistic about the possible applications of this knowledge. For example, superfluid helium films are a limiting factor in the performance of powerful dilution refrigerators used to cool quantum computers. Understanding the behaviour of these films could significantly enhance the cooling power of these remarkable machines. Another promising application is in the realm of quantum computer qubits. Recent advances have shown that qubits based on surface electrons on cryogenic substrates, including superfluid helium film, achieve a record high decoherence time. Understanding the properties of helium films is crucial for the development of these types of qubits.

I immensely enjoyed working with my co-authors on these experiments. We made a fantastic team of scientists driven by a shared passion for discovery and innovation. Each member brought unique expertise and perspectives, creating a collaborative and intellectually stimulating environment. Our combined efforts and shared excitement over each breakthrough made the research process not just productive but genuinely enjoyable. I am deeply grateful to them for their dedication and creativity, which significantly contributed to the success of this study.