A new phase of solid superionic ice has been created for the first time in the laboratory. By heating a tiny sample of ultrapure water while compressing it to extreme pressures, physicists at the French Alternative Energies and Atomic Energy Commission (CEA) succeeded in forming an ice phase that features a hexagonal close-packed (hcp) structure and liquid-like hydrogen diffusing through a solid lattice of oxygen atoms. This demonstration could help us better understand the structure of ice giant planets such as Uranus and Neptune, which may harbour this form of ice deep within their interiors.

Unlike water’s familiar liquid, vapour and ice phases, superionic ice can only exist when water is subjected to tens or even hundreds of GPa of pressure at temperatures above 1000-2000 K. Under these conditions, theory predicts that hydrogen ions (protons) diffuse so readily through empty sites in water’s oxygen lattice that the material’s ionic conductivity may exceed 100 Siemens per centimetre, making it almost as conductive as metals. The melting temperature of this form of ice is also extremely high, reaching several thousand kelvin as new ice structures develop that feature a close-packed oxygen lattice.

Diamond anvil cells and X-ray diffraction spectra

To create super-high pressures in the laboratory, researchers typically use diamond anvil cells, which are tiny cavities in which samples are tightly compressed between the tips of two opposing diamond surfaces. In the new work, a CEA team led by physicists Alexis Forestier and Gunnar Weck added two high-thermal-conductivity cup-shaped discs made of boron-doped diamond to the diamond anvil surfaces. This set-up enabled them to apply pressure while heating their 12 micron-sized sample uniformly with lasers, thereby avoiding the large temperature gradients that complicate measurements in conventional diamond anvil cells.

Forestier, Weck and colleagues heated their sample of ultrapure water from 300 to 2630 K while applying pressures between 80 and 229 GPa. Thanks to the Extremely Brilliant Source’s sub-micron beam – part of the ID27 beamline at the European Synchrotron Research Facility in Grenoble – they were able to obtain high-quality X-ray diffraction spectra despite the small size of their sample. According to the CEA researchers, these spectra clearly showed a new hexagonal close-packed (hcp) phase of superionic ice emerging alongside a previously observed face-centred cubic (fcc) phase across a pressure range of 130-200 GPa and temperatures above 1800 K.

A link to Uranus and Neptune

The discovery brings the total number of superionic phases of water to three, with the other being the body-centred cubic phase first observed in 2016. But that’s not all. Forestier, Weck and colleagues say that their results, which they report in Physical Review Letters, could also help explain the magnetic fields of Uranus and Neptune.

Unlike the Earth’s magnetic field, these fields are skewed and off-centre with respect to the planets’ axis of rotation. These properties have led scientists to hypothesize that instead of being generated by the motion of molten iron in the planet’s core (as on Earth), the magnetic fields of Uranus and Neptune could arise from conductive superionic warm dense ice (composed of water, ammonia and methane) in the planets’ outer third.

“The experimental observation of this new hcp superionic phase now provides a rationale for incorporating its mechanical properties and ionic conductivity into these models of planetary interiors,” Forestier says. “Indeed, this phase can coexist with the fcc superionic phase and become more stable at higher pressures (above 150–200 GPa), and so probably exist deeper within the inner shell of these ice giants.”

The researchers’ next step will be to precisely define regions of the phase diagram where pressure and temperature are stable; map out the transition lines between the different phases (molecular and superionic); and understand how the new hcp phase behaves as it melts. This will help confirm whether these phases are stable and present within Uranus and Neptune, Forestier tells Physics World.

“We also want to obtain more direct experimental signatures of superionic behaviour, beyond the thermal expansion we observed,” Weck adds. “Brillouin spectroscopy measurements, for example, could reveal anomalies in the speed of sound, strengthening the evidence for proton diffusion.”

The post New type of superionic water ice observed for the first time appeared first on Physics World.

In the 1980s, scientists measured quantized jumps in the energy of ions for the first time. In the 2000s, it was photons’ turn. Now, thanks to a tour de force of device engineering and nanofabrication, researchers at Stanford University in the US are reporting that phonons – mechanical vibrations like those that carry sound – also display this quantum behaviour.

“We could see it by eye [in the data], which was very satisfying,” team leader Amir Safavi-Naeini tells Physics World. “I’ve been fascinated with the interface between the quantum world and the classical world and trying to move that interface closer to daily experience…and now we have mechanical objects.”

Laying the groundwork

The Stanford team’s recipe for observing quantum jumps in phonons begins with thin films of lithium niobate (LiNbO₃). Although bulk samples of this material had been available since the 1950s, the commercialization of thin-film LiNbO₃ a decade ago was a game changer for Safavi-Naeini and his colleagues once they worked out how to process the material.

Because LiNbO₃ is piezoelectric, placing it under stress – from a vibration, say – produces a voltage. This voltage allows vibrational quanta to couple to superconducting qubits, after which the qubit states can be “read out” to determine whether a phonon was present or not.

The problem was that initially, the phonons had lifetimes of only 800 nanoseconds – well short of the millisecond the team needed to observe them falling from an excited state to the ground state. Extending these phonon coherence times “took a lot of work by a number of graduate students in my group,” Safavi-Naeini says.

After probing various sources of dissipation, including material properties that cause quantum excitations to lose coherence, the researchers realized that surface defects were key offenders. They therefore switched from polymer processing, which left a residue, to shadow masks that superimpose one chip over the other and evaporate metal through it. “There were probably three generations of students that worked on getting that four to five orders of magnitude increase in the performance of the devices,” Safavi-Naeini says.

Once they’d extended their phonon lifetimes, the researchers had to find a way of combining their “very clean, long-lived” mechanical and superconducting systems without destroying either. For this, Safavi-Naeini credits past and present students Takuma Makihara and Erik Szakiel, who spent most of their PhDs tackling issues with the mechanical oscillators before finding a way to couple them to the superconducting systems. “That was the last piece,” Safavi-Naeini recalls. “Once we had that, we could do these experiments.”

Spot the missing phonon

Because the superconducting qubits detect whether an even or odd number of phonons is present in the LiNbO₃ (which at very low energies amounts to determining whether a phonon is there at all), they are effectively performing a parity measurement. That could make the Stanford team’s system useful for quantum error correction, where the goal is to find out whether an error has crept in without actually measuring the quantum states, since doing so would destroy their useful quantum characteristics.

One of the most common sources of error in superconducting qubits is the loss of an excitation, such as when a phonon decays. However, if data is encoded into phonons in pairs and the system detects an odd number of them, this loss becomes apparent without measuring all the states. This so-called “binomial” code has already been implemented for microwave photons, and Safavi-Naeini explains that it works best for long-lived particles – a further benefit of the team’s long-lived phonons.

Protein and gravity measurements

The Stanford researchers are now collaborating with Michael Roukes and colleagues at the California Institute of Technology (Caltech) to explore possible applications in high-precision measurements of single protein masses. They are also interested in fundamental science questions such as whether it’s possible to generate entanglement between mechanical systems through gravitational fields.

However, Safavi-Naeini cautions that their phonon lifetimes would need to be much longer – a factor of 10 for error correction and mass spectrometry, and for gravity perhaps as much as six orders of magnitude, with further modifications to the experimental set-up also required – before they can achieve these goals. “The hope is that by figuring out the fundamental sources of loss in these materials we can build our way up to those experiments in the coming decade,” he says. “Every time you improve, you hit some new source of noise, you understand it, then you can deal with it, and then you go to the next one. It’s a fun physics problem.”

The research is published in Science.

The post Sound waves come in quantum jumps appeared first on Physics World.

Researchers in the Netherlands have shown that they can turn off the dipole moment of molecules that are normally polar, drastically altering the molecules’ behaviour in low-energy collisions. The discovery – which was only possible after the team cleared a major experimental hurdle – has implications for ultracold chemistry and could also lead to a better understanding of polarity, with benefits for quantum simulation and computation.

Chemical reactions are full of complexity and chaos, making them hard to study at the atomic and molecular level. Before attempting to do so, scientists typically cool the reactants to just above absolute zero, which restricts their movement and vibrations. Despite these restrictions, however, interactions between ultracold molecules remain poorly understood, especially when the molecules have an electric dipole moment.

In 2023 experimental physicist Bas van de Meerakker and theorist colleagues at the Radboud University Nijmegen in the Netherlands shone a ray of light on this murky area by studying the collision cross-section (that is, the likelihood that collisions will take place) between molecules of ammonia (NH₃) at low energies. Their simulations showed that this cross-section falls off sharply as the energy decreases. This contradicts the classical picture of polarity, which suggests that the cross-section should continuously increase.

A big turn off

The Radboud team explained this discrepancy by noting that in the classical picture, polar molecules such as ammonia have a permanently asymmetric charge distribution – a dipole moment – due to the arrangement of the bonds between their constituent atoms. The quantum mechanical picture, in contrast, depicts an isolated molecule in a specific quantum state as having a definite parity, or symmetry. Because of this symmetry, the molecule’s net dipole moment in the lab frame is exactly zero.

According to this quantum picture, collisions between polar molecules at high speeds (high energies) cause these opposite parity states to mix via interactions between the molecules’ electrostatic fields. In the process, they essentially “turn on” each other’s dipole moments, causing them to attract each other and increasing the collision cross-section. At low speeds, however, the molecules cannot get close enough to trigger this mutual mixing. As a result, their dipole moments effectively switch off, and their collision rates drop drastically.

On a collision course

The Radboud team’s next step was to prove experimentally that this is indeed what happens. However, colliding cold molecules generally requires using electric fields to merge two molecular beams. When molecules in the two beams have very similar dipole moments, this is very difficult, because using an electric field to steer one beam automatically affects the path of the other. The risk is that the beams never overlap at all.

To overcome this obstacle, van de Meerakker and colleagues combined a 2.6 m Stark decelerator, a curved hexapole guide and a merged quadrupole/hexapole trap into a device that can overlap the beams at just the right position, with minimal angle between them. In this way, they achieved sufficient overlap to observe low-energy collisions. They then experimentally verified the predicted energy-dependent changes in cross-section for NH₃-NH₃ collisions, while also showing that this dependence is different when they replace hydrogen atoms with deuterium (NH₃-ND₃ or ND₃-ND₃ collisions).

Under control

According to van de Meerakker, the fact that cross sections drop at low energies could make it hard to perform experiments that require scattering to take place in crossed or merged beams. On the other hand, experiments in which dipolar molecules are stored in traps could benefit, as lower inelastic cross-sections mean fewer molecules are lost from the trap.

As for future work, van de Meerakker says the team plans to add a controlled electric field to the beam overlap region. The mechanism they discovered is expected to respond extremely sensitively to this field, with even small electric fields changing cross sections by orders of magnitude and thereby providing a “knob” with which to control collision outcomes. “It was exactly this type of control that sparked our interest in cold and ultracold molecules two decades ago, and it is very exciting that this is now within reach in our scattering experiments,” van de Meerakker tells Physics World.

Tim Langen, a physicist at Austria’s Vienna University of Technology who was not involved in this research, describes it as important because it provides experimental evidence for a phenomenon that had mainly been discussed theoretically. In his view, the results support the idea that effective dipolar interactions become strongly suppressed at low collision energies. He also finds the experimental approach “impressive” as it enables measurements in a regime that was previously difficult to access. “Overall, I find the work convincing and expect it to be of broad interest to researchers working on cold and ultracold molecules,” Langen concludes.

The research is published in Nature Chemistry.

The post Collisions between dipolar molecules ‘switch off’ at low energies appeared first on Physics World.

In the mid-1970s a graduate student wrestling with a deceptively simple quantum problem uncovered one of the most haunting images in modern physics. The pattern seemed almost impossibly intricate: delicate wings assembled from infinitely nested bands and gaps, a self-similar pattern born from the motion of electrons in a crystal under a magnetic field. First published in 1976 (Phys. Rev. B 14 2239), it came to be known as Hofstadter’s butterfly, after its discoverer Douglas Hofstadter.

Half a century later, the butterfly has not faded into scientific nostalgia. If anything, it has become even more important – reappearing in new materials, new experiments and in places no-one imagined when it was first plotted. Recent research by Kazuki Ikeda from the University of Massachusetts and Yaron Oz at Stony Brook University suggests that related patterns may even surface in the physics of black holes (J. High Energy Phys. 2026 38).

Each new realization adds another chapter to a story that is not really about a single graph, or even a single discovery, but about the unity of patterns across the physical world. A structure first seen in a simple model has become a symbol of how richness can emerge from basic rules, how beauty can arise from constraint, and how the quantum world still harbours forms strange enough to surprise us.

How the butterfly got its wings

What makes Hofstadter’s butterfly so compelling is the remarkable story of its birth and, more importantly, how far it has travelled from its original birthplace. Like many scientific breakthroughs, its discovery was fairly obscure initially and owed a great deal to luck. In 1974 Hofstadter – son of the 1961 Nobel-prize-winning nuclear physicist Robert Hofstadter – had just dropped out of graduate school at Stanford University in the US and was “in despair” according to friend and physicist Francisco Claro.

Having just completed a PhD with the renowned solid-state physicist Gregory Wannier at the University of Oregon, Claro suggested that Hofstadter should approach Wannier as well. As it happened, Wannier had been struggling with a problem that had puzzled him for years: he could not obtain an analytical solution to Harper’s equation, which describes the motion of electrons on a 2D crystal lattice subjected to a perpendicular magnetic field.

Named after P G Harper, who was a graduate student of Rudolf Peierls at the University of Birmingham, UK, this classic “magnetic problem” displayed a mysterious sensitivity to whether the magnetic flux was a rational or irrational number. It was a feature that immediately captured Hofstadter’s imagination and, with the rational–irrational dichotomy echoing in his mind, Hofstadter began his PhD studies at Oregon by immersing himself in solving the problem.

But he soon found himself equally stuck. Frustrated by the analytical approaches often discussed at the time, he pursued a different path: numerical computation. Using a programmable Hewlett Packard desktop calculator that by today’s standards looks laughably primitive, he displayed the numerical solutions graphically as the energy of electrons versus magnetic flux Φ per unit cell of the lattice. At that moment, he became convinced that he had uncovered the true structure of the problem. “All at once my eyes were opened,” Hofstadter recalls.

What he found was a complex recursive shape (or fractal in today’s terminology) hidden within the energy spectrum of electrons in a magnetic field. Resembling a butterfly, Hofstadter brought his hand-plotted diagram, which he codenamed “Gplot”, to Wannier, who was not impressed. According to Hofstadter, Wannier dismissed the result as “numerology” and even threatened to withdraw the PhD student’s funding.

But after nearly a year, Wannier came to recognize the validity and significance of Hofstadter’s work, ultimately awarding Hofstadter his PhD and accepting the butterfly as a legitimate description of the energy spectrum of electrons moving on a 2D lattice in a magnetic field. Wannier even added to the butterfly’s story with a paper titled “A result not dependent on rationality for Bloch electrons in a magnetic field (Phys. Status Solidi b 88 757). This work, along with further studies with Claro, introduced a set of integers uniquely labelling every gap in the graph, providing a simplified description of the spectrum (Phys. Rev. B 19 6068).

Statements about states

Hofstadter’s butterfly is more than a beautiful graph. It is a map of what happens when quantum particles are caught between two competing kinds of order: the regular periodicity of a crystal lattice and the circular orbits of a magnetic field. When these two scales contend with one another, the energy spectrum does something extraordinary. Instead of varying smoothly, it fragments into a hierarchy of allowed and forbidden energies, referred to as bands and gaps, respectively.

Zoom in on one region and new structures emerge. Zoom in again and the pattern repeats, endlessly varied yet ruled by strict mathematical order. It is one of the rare instances in which fractal geometry appears not only in abstract mathematics or artistic imagination, but in the measurable behaviour of matter itself.

The deep connection between this theoretical pattern and real-world matter became clear through an exotic quantum phenomenon known as the integer quantum Hall effect. It was discovered experimentally by Klaus von Klitzing at the Max Planck Institute for Solid-State Physics in 1980 – a breakthrough that earned him the Nobel Prize in Physics five years later.

The classical Hall effect is what happens when a voltage is produced in a bulk conductor at right angles to an applied magnetic field. Similarly, the quantum Hall effect is the appearance of a voltage across opposite faces of a thin 2D semiconductor when a current is passed along the plane of the material and a magnetic field applied perpendicularly it. But there is one big difference in the quantum version.

If you slowly increase the power of the magnet, the transverse electrical conductance does not grow steadily. Instead, it jumps up sharply, with plateaus in between like steps on a staircase. In other words, it assumes quantized values given by integer multiples of the fundamental constant e²/h, where h is Planck’s constant and e is the charge on an electron.

In 1982 the British physicist David Thouless and his collaborators at the University of Washington, Seattle, made another remarkable discovery: the effect, they found, is topological. Topology is the study of the global properties of objects and topological invariants are those properties that do not change regardless of how much you try to deform a given object.

Thouless and colleagues found that the integers underlying the quantum Hall effect are topological invariants arising from the global topology of the electronic wave functions. This seminal work, which was published in 1982 (Phys. Rev. Lett. 49 405), significantly contributed to Thouless earning the 2016 Nobel Prize in Physics, which he shared with Duncan Haldane and Michael Kosterlitz for their work on “topological phase transitions and topological phases of matter”.

How all of this relates to Hofstadter’s butterfly is simple: the butterfly model describes all integer quantum Hall states, where the integers of Hall conductivity label the gaps in Hofstadter’s butterfly – the exact same integers that Wannier and Claro introduced in the butterfly spectrum (figure 1). In other words, the butterfly is not merely a chart of recursively split energy levels; it is also a coded map of topology in quantum matter under a magnetic field.

A pattern repeating across physics

That connection places it squarely within one of the central themes of modern condensed-matter physics, namely the realization that certain physical properties are protected not by local details, but by global features of the quantum state. But what is fascinating is that in the 50 years since Hofstadter’s butterfly was discovered, physicists have found that the same spectral architecture in it can also arise in a remarkable range of settings. It has appeared, for example, in other lattice geometries, in engineered semiconductor devices and in so-called moiré materials.

The butterfly’s migration into moiré systems has been especially fruitful. Such materials are created by stacking two atomically thin materials onto each other with a slight twist, creating a moiré pattern with different properties from the individual layers. Utilizing moiré materials, in research that began in 2013 led by Philip Kim of Columbia University (Nature 497 598) and continues apace with a team led by Ali Yazdani of Princeton University (Nature 639 60), the butterfly structure can now be tuned, probed and in some cases directly imaged on modern quantum platforms.

Over the last 50 years, the butterfly itself has also evolved into other forms. For instance, in some systems, the butterfly emerges without an external magnetic field. As a team of researchers led by Xu-Tao Wan from East China Normal University showed in 2025 (Phys. Rev. Lett. 136 033401), the fractal pattern can be controlled by twist angle – that is, by geometry alone.

Each time physicists add a new layer of realism – spin, interactions, periodic driving or lattice complexity – the butterfly adapts, and re-emerges in new forms, so long as it is not overwhelmed by strong interactions, disorder or thermal effects

In other realistic systems, electron spin – the particle’s intrinsic magnetic orientation, absent from the original simplified model – becomes an essential part of the physics. Even when a magnetic field splits the system into spin-up and spin-down states via Zeeman splitting, the butterfly spectrum survives. More striking still, the butterfly can emerge independently for each spin state, as Xiaomeng Liu and Zhida Liu of Cornell University discovered in 2025 (Nature Phys. 21 1873).

This persistence of the fractal structure, despite the added complexity introduced by spin, highlights the extraordinary robustness and universality of the underlying quantum phenomenon. More generally, what these new iterations of Hofstadter’s butterfly reveal is that what once looked like a specialized theoretical curiosity now seems more like a recurring motif in quantum matter.

Indeed, this is part of its enduring fascination: each time physicists add a new layer of realism – spin, interactions, periodic driving or lattice complexity – the butterfly adapts, and re-emerges in new forms, so long as it is not overwhelmed by strong interactions, disorder or thermal effects. This durability prompted a friend to once joke that whenever he undergoes an MRI scan, he cannot help wondering what kind of butterfly his body might be producing.

Beauty from simplicity

As my friend’s joke reveals, there is something unmistakably human about the butterfly’s appeal. Physicists are drawn to it not only for its usefulness, but for its beauty. It belongs to that rare class of scientific objects whose visual grace seems to gesture toward deeper truths. And yet its deepest charm may lie in the fact that its immense complexity grows from remarkable simplicity.

Beneath the intricate pattern are integers, recursion relations and number-theoretic structures that connect it to fairly simple geometric patterns, including the Farey tree, the tree of Pythagorean triplets and fractal packings such as the Apollonian gasket. In fact, this complicated quantum fractal admits a surprisingly simple geometric description: the butterfly landscape can be organized as a hierarchical lattice of trapezoids, bringing it into close parallel with geometric fractals such as the Sierpiński gasket (figure 2). It is extraordinary to think that this geometric harmony underlies such a complex and beautiful graph.

Fifty years on, Hofstadter’s butterfly remains exactly what great scientific ideas are supposed to be: elegant, prolific and unfinished. That interplay of beauty, mathematics and physical reality is what keeps the butterfly alive. Its evolution under interactions, spin effects and new forms of engineered geometry continues to reveal unexpected physics. And with each turn, the butterfly reminds us of something rare and precious in science: that the universe can hide immense complexity within simple forms, and that sometimes, if we are lucky, those forms are beautiful enough to be unforgettable.

The post Hofstadter’s butterfly turns 50: a fractal hiding in quantum matter appeared first on Physics World.