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Could quantum information theory explain universe evolution?

The gravity from entropy (GfE) theory has been used to explain how low-entropy structures such as galaxies emerge and endure in a universe in which entropy increases with time. Using the theory, Ginestra Bianconi of the UK’s Queen Mary University of London has shown how entropy density can decrease locally, while the total entropy of the universe increases.

The laws of thermodynamics are arguably among the most fundamental principles in most areas of physics. Perhaps none more so than the second law of thermodynamics, which states that the entropy of a system must increase over time. Uniquely, it is the only law of physics that captures the direction of time we experience.

Fundamentally, entropy is a measure of disorder: lower entropy means more structure and higher entropy means a less structured system. Increasing entropy is the reason diffusion occurs from a high concentration to a low concentration, gases expand, and coffee goes cold.

Cosmological paradox

It is believed that the evolution of the universe also follows the second law. The early universe was in a state of low entropy, and it has evolved to states of high entropy. It is also true that during this evolution, the universe has given rise to some incredibly complex structures. Galaxies are a prime example of one of these structures, which are low in entropy but have formed in a high-entropy environment. Their creation seemingly violates the second law. This is a longstanding contradiction in the field of cosmology that is motivating the gravitational framework proposed by Bianconi.

In a recent paper called “Thermodynamics of the gravity from entropy theory”, Bianconi, built on her previous work on the GfE theory and applied it to the whole universe to tackle this challenging paradox.

In Einstein’s general theory of relativity, the metric mathematically describes how the space–time of a universe is curved. Mass follows this curvature, and this is how a gravitational force is realized. In quantum mechanics, operators are mathematical objects that can be applied to physical quantum states to transform them (for example the time evolution or reflection of a quantum state).

Quantum relative entropy

The key insight of the GfE theory is that these metrics are treated as quantum operators which encode the geometry of space–time. Quantizing the geometry of space–time in this manner leads to two notions of the metric – one that is the “true” metric, and one that is induced via mass and energy. The distinguishability between the true manifold metric and one that is induced from the mass, and energy is measured by a quantity rooted in quantum information theory, called quantum relative entropy (QRE). It is this interplay between the two geometries measured through QRE that, in this scenario, defines the dynamics of the space–time.

In other words, the QRE leads to equations of motion that describe gravity. Bianconi found that in the low curvature limit, classical general relativity is reproduced exactly from these equations. However, outside of this limit, the equations must be modified by a mathematical object called the ‘G-field’. This G-field generates a dark-energy term that is surprisingly dynamical. Dark energy is thought to drive the universe’s expansion directly. In standard general relativity, dark energy is driven by the static cosmological constant, which is why a surprising dynamical dark energy term from the G-field is an avenue that has the potential to be testable.

Preserving the second law

In a recent paper, Bianconi describes how the GfE theory can be applied to a Friedmann–Robertson–Walker (FRW) metric universe. The FRW model is one from general relativity that provides a first approximation to the universe’s behaviour, displaying simple characteristics such as isotropy (it looks the same in all directions when observed from a single point), homogeneity (globally uniform in distribution of its contents) and expansion (a property observed in the universe).

The expansion is driven by the dominant composition of the universe, such as dark matter, matter, or radiation. As the universe expands, its volume also increases, along with its total entropy. Due to this growth, the local entropy per unit volume decreases over time, as there is the same amount of entropy contained in a now larger unit volume; the entropy density decreases (along with similar decaying behaviour for the local energy density). This decrease in local entropy in a universe of entropy growth provides a mechanism for low-entropy structures such as galaxies and even life forms to be created in an expanding universe.

The question then remains: does this mechanism violate the second law of thermodynamics? Thankfully, Bianconi also answered this question for a non-empty universe described by the FRW metric. To find the total entropy of such a universe, the entropy density must be integrated over a space–time region, which, due to the fact that the volume increases, is a time-dependent quantity. This is a result of the expansion being faster than the decay of the entropy density. For radiation- and matter-dominated universes, then, the entropy is increasing in time, specifically following the second law of thermodynamics even when the entropy density is decreasing locally. To summarize, while entropy density decreases locally, the total entropy of the universe is still increasing in this model.

Bianconi emphasizes that the GfE theory is still in its infancy, and experimental verifications are required. However, this work highlights the intrinsically thermodynamic nature of the GfE theory, which opens new avenues for both classical and quantum gravity. By framing gravity in terms of quantum information and entropy, the theory may offer an alternative route towards quantizing gravity—one of the longstanding challenges in fundamental physics.

Bianconi describes her research in Physical Review D.

Ask me anything: Kiefer Vermeulen – ‘We had to figure everything out on a shoestring budget and on a really challenging timescale’

Kiefer Vermeulen studied applied physics at Delft University of Technology in the Netherlands, where he did his master’s thesis at its QuTech research institute on the topological properties of Majorana quantum bits. He is now head of research at Delft Circuits, where he leads a team of quantum engineers developing the cabling and wiring needed for quantum-based devices.

What skills do you use every day in your job?

When I was at QuTech, I’d work on qubit systems using equipment that was sometimes worth several hundreds of millions of dollars. It’s now very different at Delft Circuits, which is a start-up company, where I have to get by with budgets that may be as little as few hundred dollars. So I need to take problems and condense them down into manageable work packages. After being a junior and then senior researcher at the company, I now lead a team of eight fantastic scientists and one of the most important skills for me is talking. I don’t just mean chatting – but really trying to figure out a problem by talking and listening to different stakeholders.

It’s vital to be able to communicate what might be a very niche understanding of a specific field to a wider audience

If you’re in academia and want to go into industry, it’s vital to be able to communicate what might be a very niche understanding of a specific field to a wider audience. If you can do that, then you can solve problems, which is what being in industry is all about.

What do you like best and least about your job?

I really like innovation. For anyone in industry, the aim is to make money, which means developing and selling products. At Delft Circuits, we make cryogenic cabling for quantum computing, but none of that technology previously existed. We had to do it all ourselves – figuring everything out on a shoestring budget and on a really challenging timescale. That to me is super exciting especially when you’re doing something for the first time ever. As for the least favourite part of the job, raising money – whether it’s to build a lab or a factory – is tough. I’m currently in Denver, I was in Taiwan a few weeks ago, I’ve got three or four meetings coming up elsewhere in the next few weeks because the speed at which you need to do things might even outpace the money you can get for selling the things you have. I also don’t like the sheer amount of e-mails I have to deal with. When I started at Delft Circuits, there were just four members of staff. But now we’re so much bigger, I might get 50 or 100 e-mails a day. I guess I could speed things up by feeding them all into AI but I can’t really do that as a lot of work is confidential.

What do you know today that you wish you knew when you were starting out in your career?

I wish I’d known how important communication is, whether that’s getting your ideas across – or understanding those of other people – and really being able to frame your expertise and explain it to potentially non-technical people. Trust is important too because in start-up companies you all need to rely on each other and work through problems together so that things come to fruition. I also wish I’d known to talk a bit less – and let the other person in a conversation come up with the answers that might be different to your own. When I started out, I always wanted to answer problems quickly – in fact, I had to do that because it was expected of me. But as I’ve started managing and leading teams, I’ve learned to give others the opportunity to go through the same type of brain puzzles and thinking that I went through myself.

A hybrid energy system for heating, cooling and generating electricity

Researchers at the Karlsruhe Institute of Technology (KIT) in Germany and Stanford University in the US have developed an energy-collecting device that can simultaneously cool, produce electricity and generate heat. In their prototype, a radiative cooling layer reached 6.5 °C below ambient temperature while a solar collector generated electricity and reached nearly 111 °C.

“The new system could be installed on the roofs and facades of buildings to provide these three energy services at once,” says Gan Huang, who is head of the Hybrid Solar Technologies lab at KIT. “It could also be attractive for AI data centres that need both intensive power and cooling at the same time.”

As many of us have experienced, summer in the northern hemisphere has been particularly hot this year – a situation that is only likely to worsen in the future as the effects of climate change take hold. With this warming will come the increased need for air conditioning to cool down buildings. The problem is that current compression-based systems consume a lot of electricity and produce large amounts of CO2.

Passive daytime radiative cooling

A potential alternative is passive daytime radiative cooling (PDRC), in which heat is continuously exchanged between objects at different temperatures by absorbing and emitting thermal radiation. When the heat absorbed by the material is less than the energy radiated to outer space, it can cool down during the day – even without electricity.

Our planet naturally experiences this effect by radiating heat out to space. This allows it to cool down at night because its temperature (of around 300 K) is much higher than that of outer space (around 3 K) and there is no incident solar irradiation from the Sun at night.

A good PDRC material needs to satisfy several criteria. For one, it must reflect sunlight strongly at solar spectrum wavelengths (of 0.3 to 2.5 µm) to avoid it heating up. It also needs to emit heat strongly in the long-wave infrared (LWIR) wavelengths (of 8–13 µm) where the atmosphere is more transparent to infrared radiation, so that it can lose energy to the cold sky. Over the past decade, researchers have succeeded in developing a wide range of PDRC materials, including multilayer nanophotonic emitters, single-layer polymers on reflectors and porous ceramics. However, conventional PDRC systems cannot harvest the coldness of outer space and solar energy from the same surface at the same time.

A hybrid PDRC and photovoltaic-thermal collector

In the new work, which is detailed in Cell Reports Physical Science, the KIT researchers made a hybrid PDRC and photovoltaic-thermal collector. The emitting layer in the device, which is transparent, consists of a silica substrate coated with the silicone polymer polydimethylsiloxane. This layer allows sunlight to pass through while simultaneously emitting heat as LWIR radiation through the atmospheric window. Beneath the transparent emitter, a Fresnel lens concentrates the transmitted sunlight onto the (gallium arsenide-based) photovoltaic-thermal collector mounted on a two-axis solar tracker. This is where electricity is generated.

In outdoor experiments performed during the day, the prototype simultaneously achieved cooling of up to 6.5 °C below ambient temperature, an electrical power density of 60.6 W/m² and heating up to 110.8 °C. “This is exciting,” says Huang, “because it shows that the hot Sun and the cold universe can be harvested together, rather than treated as separate resources as has been the case until now.”

The main challenge was ensuring that the solar collector became hot while the radiative cooler stayed cool, he explains. “We achieved this by concentrating the transmitted sunlight onto a much smaller solar collector underneath the transparent cooling layer, so reducing thermal interference between the hot and cold parts in the device.”

The team is now busy improving the efficiency and practical design of its system. “We are already working on a better optical design, improved thermal management and more efficient solar cells,” reveals Huang.

“The Sun is not the only renewable energy resource in the sky, the coldness of outer space is another,” he says. “We believe there are many exciting possibilities for a new generation of energy systems if we learn how to manage both these together.”

Quiz of the week: how far ahead can we predict the weather?

Fancy some more? Check out our puzzles page.

Mercury may not need an ancient dynamo to explain its magnetic crust

A new study using data from a space mission suggests that most of Mercury’s crustal magnetic fields can be explained by iron and other magnetized rocks in the crust responding to the planet’s weak present-day core magnetic field, rather than from an ancient field, as had been inferred previously. Mercury is the only solar-system planet other than Earth to possess both a global magnetic field arising from its core and a crustal magnetic field resulting from rocks that were magnetized in either the present-day or an ancient core field. Present-day (induced) magnetization reveals the location and amount of iron in the crust, whereas ancient (remanent) magnetization records the planet’s dynamo history.

NASA’s MErcury, Surface, Space ENvironment, GEochemistry and Ranging (MESSENGER) mission observed the planet in 2011–2015. Data from the mission are allowing scientists to explore the strength and distribution of Mercury’s magnetic field. During the mission, a last-minute decision was made “to reduce the orbit altitude thereby allowing crustal fields to be detected” explains Lon Hood at the Lunar and Planetary Laboratory at the University of Arizona. He has worked extensively on Mercury’s crustal magnetism using the MESSENGER data but was not involved in the new study.

Crustal magnetism was expected to be “partly due to remanent magnetization dating from the time when the crustal sources formed in the planetary magnetic field,” Hood says. This interpretation is drawn from earlier analyses of the mission data. But a key challenge in understanding the crustal magnetic field remained – how to delineate the contributions of induced and remanent magnetization. Separating the relative contributions of ancient and present-day induced magnetization on the crustal magnetic field can reveal new ways of understanding the spatial abundance of magnetic rocks, variations of magnetic properties of crustal minerals, and the dynamo history of Mercury.

New insights from old data

The new study, led by Catherine Johnson at the University of British Columbia in Vancouver, uses field observations of Mercury’s crustal magnetic fields from MESSENGER to develop a magnetization model of the planet and identify sources of its magnetization. The researchers calculated the expected induced magnetization strength using the low-altitude observations with assumptions on the crustal thickness, magnetic mineralogy, iron content, and the present-day core field.

In line with previous studies, the researchers found that the largest magnetization strengths occur in the Caloris region, along with localized signals elsewhere. The spatial pattern of magnetization strength, however, does not consistently match the variation in near-surface iron content seen in MESSENGER spectroscopic data. Instead, magnetization strength correlates with crustal thickness, up to about 30 km, suggesting the magnetized rocks are concentrated within the upper part of the crust.

The researchers found that induced magnetization is relatively small, given the low iron content of the planet’s crust and its weak core field – about a hundred times weaker than Earth’s. Even so, they estimate that induced magnetization can fully account for the calculated magnetization strength across more than 85% of the area north of 38 °N. This assumes it extends through the crustal column to a depth of about 30 km, which means that no remanent magnetization is required to explain the observed crustal field over that majority of the mapped region. Areas where induced magnetization does not explain the observed crustal fields may be the result of iron delivered by ancient asteroid impacts, which would locally increase the induced magnetization. Elsewhere, a contribution from remanent magnetization may be required to explain the observed fields.

Towards better characterization

On Earth, the robust separation of induced and remanent magnetizations requires laboratory measurements of rock samples. For Mercury no such samples exist, so the magnetic properties of its crust must be inferred from satellite observations constrained by assumptions about the composition and magnetic behaviour of its rocks. The delineation in the new study depends on “assumptions about magnetic mineralogy that cannot be verified due to the lack of returned samples”, says Hood.

Better characterization of the crust’s low-field magnetic susceptibility – currently inferred from a limited number of laboratory measurements on meteorites and minerals believed to resemble Mercury’s crust – can advance our understanding of Mercury’s crustal fields. Better core-field models and higher-resolution iron maps from the European–Japanese BepiColombo mission could help. This mission comprises two spacecraft that launched in 2018 and is expected to run until 2029.

However, Hood says “there are no current plans for either spacecraft to approach near enough to the planet to detect or map more of the crustal magnetic field”. Although the spacecraft will eventually descend below 100 kilometres, giving us a first look at the southern hemisphere. Indeed, we may have a long wait before we have the complete picture because Hoods says, ” there are no plans to obtain samples of Mercury’s crustal rocks, which are needed to definitively determine the origin of the crustal magnetization”.

The researchers report their findings in PNAS.

Non-reciprocal interactions keep particles in collective motion

Illustration of non-reciprocal interactions
Breaking action–reaction symmetry Non-reciprocal interactions occur when one particle influences another more strongly than it is influenced in return. This figure shows how unequal electrohydrodynamic attraction between differently sized particles generates non-reciprocal interactions and self-propelled particle pairs. (Courtesy: Yutaka Sumino, Tokyo University of Science, Japan)

Attractive interactions between particles do not necessarily lead to these particles aggregating. This is the new finding from researchers at the Tokyo University of Science in Japan who say this behaviour comes from non-reciprocal interactions amongst particles of different sizes that exert unequal forces on each other. These interactions could serve as a general design principle for creating active matter with a structure that continuously reorganizes rather than simply relaxing towards a static state.

Nature abounds with examples of active matter, with some well-known examples being flocks of birds, fish and insects, sheets of biological cells and swarms of bacteria. Researchers have been trying to copy this collective behaviour and make synthetic active materials – such as self-propelled colloids and dense phases of mechanically driven biopolymers – in the laboratory. Before such applications see the light of day, however, they need to first understand the fundamental physics of these systems.

In their new study, a team led by Yutaka Sumino and Kiwamu Yoshii of Tokyo University of Science’s department of applied physics, came across a system in which colloidal particles interact through electrohydrodynamic flow. “We found that mixing particles of two different sizes in such a system completely changed the collective behaviour of these particles,” explains Sumino. “Instead of forming increasingly large crystal-like aggregates, as is the case for particles with the same size, the system remained highly dynamic.”

The physicists’ experiment involved suspending polystyrene colloidal particles with radii of 1 and 1.5 µm in water and confining them between transparent indium tin oxide-coated electrodes. This set up allowed them track more than 10,000 particles and quantitatively analyse their dynamics for more than an hour, as opposed to just a few minutes in previous such studies.

Newton’s third law holds

When the researchers applied an alternating electric field to the system, they observed electrohydrodynamic flows around the particles, the strength of which increased strongly as the size of the particles became bigger. The electrohydrodynamic-mediated attractive interactions therefore became asymmetric, they explain, something that causes larger particles to attract smaller ones more strongly. This imbalance leads to non-reciprocal interactions, meaning that a larger particle pushes a smaller one, but a smaller one doesn’t push back.

While the effective interaction between the particles appears to break Newton’s third law, it doesn’t because there is no violation of momentum conservation, explains Sumino: momentum is transferred to the surrounding fluid through the induced flows and is ultimately dissipated through friction with the substrate.

The researchers also observed that particles of different sizes spontaneously pair together to form asymmetric structures with a distinct front and tail. These pairs behave as self-propelled units and move through the suspension – even though individual particles cannot propel themselves. As more self-propelled pairs form, they assemble into larger clusters, but these clusters do not continue growing into large aggregates and instead repeatedly fragment, rearrange themselves and reform. Importantly, they note: “the larger particle tends to be at the front of these moving pairs. This head-heavy size asymmetry, together with excluded-volume interactions, promotes the fragmentation of larger clusters and thereby prevents continuous coarsening”.

Sumino and Yoshii combined their experiments with numerical simulations, thereby identifying non-reciprocal pair motion as the microscopic origin of this behaviour.

The results, they say, suggest that non-reciprocal interactions can serve as a general design principle for creating active materials with structures that continuously reorganize rather than simply relaxing toward a static state. “An interesting aspect,” explains Sumino, “is that self-propulsion does not need to be built into each individual particle: it can emerge collectively from non-reciprocal interactions between particles that do not self-propel on their own.”

If such interactions can be controlled externally, they could provide a way to design microscopic systems that collectively gather, transport, fragment or mix materials, he tells Physics World. “Possible directions include programmable active materials and microrobotic systems, although these applications are still some way off.”

Reporting their findings in Physical Review Letters, the researchers say they would now like to understand how general this non-reciprocal mechanism is and whether the same principle – collective activity emerging from non-reciprocal interactions – can be transferred to other experimental systems. In the system studied in this work, the strength of the non-reciprocity depends on parameters such as particle size, composition and the applied electric field. By systematically tuning these parameters, they aim to explore what other types of collective states can be generated and whether transitions between them can be controlled.

“A more detailed hydrodynamic analysis of the system is also needed to develop a quantitative understanding of the interactions and ultimately predict the collective motion of the colloids,” says Sumino.

Doubts cast on ‘superradiant neutrino laser’ proposal

Could radioactive atoms in a Bose–Einstein condensate (BEC) form a “superradiant neutrino laser”? According to a paper published last year by Benjamin Jones of the University of Manchester and  Joseph Formaggio of the Massachusetts Institute of Technology the answer is “yes”. We were intrigued by this proposal and commissioned the freelance physics writer Tim Wogan to write an article for us.

As part of his reporting, Wogan sought the opinion of a BEC expert – James Thompson of NIST, JILA and the University of Colorado in Boulder. Thompson told us that he was sceptical of the viability of such a device – in particular, he pointed out that the de Broglie wavelength of the emitted neutrinos is much too short for superradiance to occur.

Now, another physicist (Wolfgang Ketterle, who shared a Nobel prize for his pioneering work on BECs) has published two papers that cast doubt on Jones and Formaggio’s proposal. All three papers are published in a very prestigious journal, so this is a scientific debate of note.

So what is superradiance, and how could it be used to create a source of coherent neutrinos?

Coherent burst

Superradiance was originally envisioned in an ensemble of excited atoms, each of which can decay by emitting a photon. Normally, the rate at which photons are emitted from such an ensemble is simply proportional to the number of atoms present. Double the number of atoms, and the rate of emission will double. However, if the ensemble is dense enough that the wavelength of the emitted photons is much longer than the separation between neighbouring atoms, the emission of a single photon will involve all of the atoms. What is more, the superradiant emission rate is proportional to square of the number of atoms. The result is short, intense burst of coherent radiation. It is this coherence that has caused some to refer to superradiant lasers – although the physics of lasers is different.

Jones and Formaggio’s proposal involves radioactive atoms that decay with the emission of a neutrino, rather than a photon. Their idea is to cool an ensemble of these atoms to near absolute zero so that it forms a BEC. This is a unique form of matter that can be described as a macroscopic quantum state. Under this condition, the duo argued that neutrinos would be emitted rapidly from a superradiant state.

Now, Ketterle, Yu-Kun Lu and Hanzhen Lin at the Massachusetts Institute of Technology argue in two papers that such a superradiant neutrino laser is an impossibility. As well as backing up Thompson’s concerns about the short wavelength of the neutrinos, they point out that the atoms produced by the neutrino decays are fermions, and this precludes superradiance. They also showed that the recoil of atoms after neutrino emission would not allow the coherent emission of neutrinos to occur.

I think this is a fascinating subject and I hope that Jones and Formaggio can revive their proposal, because a BEC-based neutrino laser would be very cool!

You can read more about the debate in an article in Physics by Thompson and colleagues.

 

 

Porous material offers the benefits of graphene in 3D

My guest in this episode of the Physics World Weekly podcast is Marco Caffio, who is co-founder of iGii. The UK-based company has developed a porous 3D carbon nanomaterial called Gii, which it manufactures for a range of customers and applications.

Caffio describes Gii as a 3D version of graphene that delivers many of the useful electronic, structural and chemical properties of that 2D wonder material. Unlike graphene, which can be difficult to manufacture and integrate into devices, Caffio explains that Gii can be customized for use in practical technologies such as chemical sensors, batteries and heaters.

We also chat about the genesis of the company and Caffio offers career advice to physicists who are keen on working in the materials-technology sector.

How far ahead can we predict the weather?

What will the weather be like tomorrow, or next week or, indeed, in a month’s time? Today’s numerical weather predictions can easily answer the first two parts of this question, but they fall short beyond about 14 days. New work on predictability limits by scientists at the University of Miami and the NOAA Cooperative Institute for Marine and Atmospheric Studies (CIMAS) say that this maximum could be extended to around 129 days – but probably no further. Whether this limit can be reached in practice, however, will depend on future improvements in forecasting technologies, they say.

Numerical weather prediction was developed in the late 1940s. Indeed, it was one of the first major applications of electronic computers. As these have advanced, so have the predictions. Indeed, thanks to ever more sophisticated mathematical models capable of analysing increasing amounts of observational data, we can now predict, for example, when hurricanes will occur as far as eight days in advance – something that was deemed impossible even a few decades ago. But how far ahead can such predictions be made?

Previous attempts to determine this predictability limit have largely relied on analysing the behaviour of very small perturbations in the atmosphere. These tiny errors, however, are inaccessible either observationally or via numerical modelling, explains Zoltan Toth of the NOAA who led this new study together with his colleague Wei Zhang. “These past studies therefore had to make some assumptions about the behaviour of the small errors, and these assumptions are necessarily somewhat arbitrary.”

Analysing the energetic balance of the atmosphere

The method developed by Toth, Zhang and their colleagues makes no reference to this error behaviour and instead goes back to analysing the energetic balance of the atmosphere, which continually absorbs solar radiation on the molecular level. In their approach, the researchers began by considering how our planet’s atmosphere would behave as a closed system, the deterministic dynamics of which preserves information about its initial state, assumed to be perfectly known. In theory, such a hypothesis would allow forecasts of the atmosphere’s behaviour right out to infinity. This is not possible in reality, they explain, because the atmosphere is obviously not a closed system: it receives and emits radiation. In the real atmosphere, the phases of photons in sunlight are completely random and cannot be determined, injecting quantum-scale uncertainty into the atmosphere.

These unknown quantum characteristics act as noise and destroy any retained information, beginning first of all on the smallest scales, explain the researchers. As these scales become bigger, noise eventually affects all parts of the system. When the total energy in the atmosphere is entirely replaced, the ability to make any prediction is completely lost.

“Using the relatively well-measured quantities of total energy in the atmosphere and the incoming and outgoing solar radiation fluxes at its upper boundary, we estimate that the range of skilful forecasts could potentially be extended from 14 days as at present to 129 (±7) days at the most,” explains Toth.

Very different from the mainstream discourse

“This result is very different from the mainstream discourse about atmospheric predictability, which to this day is strongly influenced by early publications in the field,” adds Toth. “More recently even, the authors of a 2018 article in the Bulletin of the American Meteorological Society speculated on whether current forecast systems are reaching their limits for when it comes to predicting tropical cyclones. In 2020, we argued that this limit is at least decades, if not much farther away.”

The theoretical foundation for the new methodology to determine the time limit of predictability is rather simple, he says. “At its core is a conceptual realization, which came to us intuitively. This is that the energy turnover time (that is, the time it takes for all energy in the atmosphere to be replaced by incoming solar radiation) is equivalent to the upper limit of predictability.”

While there is no complex mathematics involved, Toth notes that he and his colleagues had to find a way to describe the technique in a readily understandable way – something that was not easy, he admits, given the complexity of the subject.

Looking ahead, the researchers, who detail their present work in Advances in Atmospheric Sciences, are now looking into several other independent ways to estimate the limit of predictability. “There is no doubt, this limit has a theoretical feel to it,” Toth tells Physics World. “Yet there are a number of very practical implications for both traditional equation- and AI-based modelling of the atmosphere following on from the theory of predictability that we are also exploring in a series of ongoing studies.”

Skyrmion topology makes long-distance optical communications more robust

Researchers at the University of the Witwatersrand (Wits) in Johannesburg, South Africa, have succeeded in harnessing a relatively unexplored property of light – its topology – to robustly transfer information through the atmosphere. The work could advance the development of more reliable long-distance optical communications, including space-based ones, and connect remote and underserved communities worldwide.

Their work is detailed in two separate studies, one based on classical and the other on quantum optics. These studies show that the topological information can remain remarkably robust – even when the states of light carrying this information are subject to the severe distortions caused by atmospheric turbulence. Instead of relying entirely on increasingly sophisticated hardware or computational algorithms to correct atmospheric distortions before or after light transmission, the new concept provides a fundamentally different way of thinking about robust optical communication in complex environments, such as air or water, they say.

Both studies are based on the same fundamental idea: creating an optical topological structure known as a skyrmion in a light field and testing whether it remains robust when it passes through a distorting environment, explains Andrew Forbes, who is head of the Structured Light Lab at the Wits School of Physics. Skyrmions are quasiparticles with a two-dimensional, knot-like structure and were first observed in magnetic materials. They have, however, recently been seen in electromagnetic fields and the electric field of light waves. Here, the swirling structures are created by twisting the polarization or spin vectors of light in space so that every polarization is found exactly once, twice, three times and so on – the count being the skyrmion number. Skyrmions are topologically stable, which means that external perturbations do not affect them in any way.

Real-world test

In the first study, Forbes and colleagues used laser light with a wavelength of 532 nm shaped into various vectorial beams using a spatial light modulator and a modified Mach–Zehnder interferometer to generate optical skyrmions with skyrmion numbers of 1, 2 and 3. These numbers, which are always whole integers, describe how twisted the vortex-like structure of the skyrmion is. They then sent the laser light through a 270-m-long real-world free-space optical link located on Wits’ Braamfontein campus in the centre of Johannesburg.

The researchers measured the topology of the skyrmions with a Stokes polarimetry setup and found that the skyrmion number remains robust in a wide variety of atmospheric conditions, ranging from “calm, cool morning air to the highly erratic and intense distortions at midday” when it is hotter. “This result holds true even when the vectorial polarization of the underlying laser beam has been highly scrambled by atmospheric turbulence effects – and was therefore unrecognizable,” says Forbes.

In-built correlations

In the second work, the team created the topology through the in-built correlations between two photons entangled in their optical angular momentum (OAM). The OAM quantum states are not themselves stable in distorting environments and the information they encode is easily lost. The researchers investigated the robustness of a skyrmion with a skyrmion number of 1 in a controlled laboratory environment by studying photons in media with varying levels of turbulence.

The result? Despite local distortions, the skyrmions maintained topological numbers close to 1. This, they say, suggests the topological number is fundamentally decoupled from modal crosstalk induced by the turbulence and the spreading of an individual photon’s OAM.

Despite the very different physical systems, both experiments reveal a similar result, says Forbes: the conventional properties of optical fields can be strongly degraded by distortions, while the topological information encoded in those states remains remarkably robust. Together, the two works demonstrate that topology can be harnessed in both classical and quantum optical systems as a robust carrier of information in very different communication and information-processing scenarios.

Robust protection

Topology is a concept that appears throughout physics, from fundamental particle physics to magnetism and condensed matter systems. In many of these systems, explains Forbes, topology comes with a physical protection mechanism – such as an energy barrier – that explains why a topological structure is resistant to external disturbances. In optics, however, the situation is rather different. Optical topologies can be created and manipulated with relative ease, but their robustness is not necessarily guaranteed by any particular underlying physical protection mechanism. “We therefore wanted to address a fundamental question: how robust is optical topology when light encounters a real-world, highly distorting environment?

“The atmosphere provides a particularly interesting testbed because it is highly relevant to optical sensing and communications and represents an extreme case where the distortions vary rapidly both in space and time,” he tells Physics World. “Demonstrating robustness in this setting was therefore both a fundamental test of the dynamics and resilience of optical topologies and an indication of its potential practical value.”

Hurdles and challenges

One of the major challenges was simply doing precision optical experiments outdoors, he adds. “We had to contend with the unpredictability of nature: changes in sunlight and temperature, wind, rain and even the thermal expansion of buildings, which can affect optical alignment, making it difficult to maintain stable measurements over long periods.”

Another hurdle to overcome was to find a way of measuring the optical topology itself. Existing methods to do this can be quite sensitive to experimental noise and imperfections, so the researchers say they had to carefully distinguish genuine changes in the optical channel from apparent changes introduced by the measurement process. Ultimately, this meant developing new ways to both obtain and process the experimental data so that they could reliably track the topological properties of the light despite the noise that was present.

Applications include free-space optical, satellite and space communications, and linking remote or underserved communities, where atmospheric turbulence and the lack of physical infrastructure can present significant challenges, says Forbes. “More broadly, topology could be useful beyond communication,” he adds. “Indeed, its underlying robustness could potentially be exploited for optical sensing, information processing and other applications where light has to propagate through complex or noisy environments.”

The quantum experiment adds another possibility, he notes. “We know that entanglement decays in real-world conditions that are not pristine.  Our work shows that despite this, the quantum information stored in the topology remains intact.  This may allow us to distribute information across a quantum network in a more reliable and robust manner.”

Looking ahead, the Wits researchers say they will now assess whether the robustness they have observed extends to other kinds of challenging environments, such as underwater and biological tissue, where scattering, birefringence and other phenomena can be much more prevalent than in the atmosphere.

“We also want to develop detectors and techniques for measuring optical topology,” says Forbes. “Improving how we characterize these structures will be important for moving from proof-of-principle experiments towards practical applications.

“Finally, we would like to actually exploit the robustness of the topology we have identified in high-speed communication experiments. This means implementing realistic communication protocols and investigating how much information can be reliably transmitted using a ‘topological alphabet’.”

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