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A speed limit also applies in the quantum world: Study determines minimum time for complex quantum operations
Even in the world of the smallest particles with their own special rules, things cannot proceed infinitely fast. Physicists at the University of Bonn have now shown what the speed limit is for complex quantum operations. The study also involved scientists from MIT, the universities of Hamburg, Cologne and Padua, and the Jülich Research Center. The results are important for the realization of quantum computers, among other things.
A little trick helps him to do this: While the waiter accelerates his steps, he tilts the tray a bit so that the champagne does not spill out of the glasses. Halfway to the table, he tilts it in the opposite direction and slows down. Only when he has come to a complete stop does he hold it upright again.
Atoms are in some ways similar to champagne. They can be described as waves of matter, which behave not like a billiard ball but more like a liquid. Anyone who wants to transport atoms from one place to another as quickly as possible must therefore be as skillful as the waiter on New Year’s Eve. “And even then, there is a speed limit that this transport cannot exceed,” explains Dr. Andrea Alberti, who led this study at the Institute of Applied Physics of the University of Bonn.
Cesium atom as a champagne substitute
In their study, the researchers experimentally investigated exactly where this limit lies. They used a cesium atom as a champagne substitute and two laser beams perfectly superimposed but directed against each other as a tray. This superposition, called interference by physicists, creates a standing wave of light: a sequence of mountains and valleys that initially do not move. “”We loaded the atom into one of these valleys, and then set the standing wave in motion — this displaced the position of the valley itself,” says Alberti. “”Our goal was to get the atom to the target location in the shortest possible time without it spilling out of the valley, so to speak.””
The fact that there is a speed limit in the microcosm was already theoretically demonstrated by two Soviet physicists, Leonid Mandelstam and Igor Tamm more than 60 years ago. They showed that the maximum speed of a quantum process depends on the energy uncertainty, i.e., how “free” the manipulated particle is with respect to its possible energy states: the more energetic freedom it has, the faster it is. In the case of the transport of an atom, for example, the deeper the valley into which the cesium atom is trapped, the more spread the energies of the quantum states in the valley are, and ultimately the faster the atom can be transported. Something similar can be seen in the example of the waiter: If he only fills the glasses half full (to the chagrin of the guests), he runs less risk that the champagne spills over as he accelerates and decelerates. However, the energetic freedom of a particle cannot be increased arbitrarily. “We can’t make our valley infinitely deep — it would cost us too much energy,” stresses Alberti.
Beam me up, Scotty!
The speed limit of Mandelstam and Tamm is a fundamental limit. However, one can only reach it under certain circumstances, namely in systems with only two quantum states. “In our case, for example, this happens when the point of origin and destination are very close to each other,” the physicist explains. “Then the matter waves of the atom at both locations overlap, and the atom could be transported directly to its destination in one go, that is, without any stops in between — almost like the teleportation in the Starship Enterprise of Star Trek.”
However, the situation is different when the distance grows to several dozens of matter wave widths as in the Bonn experiment. For these distances, direct teleportation is impossible. Instead, the particle must go through several intermediate states to reach its final destination: The two-level system becomes a multi-level system. The study shows that a lower speed limit applies to such processes than that predicted by the two Soviet physicists: It is determined not only by the energy uncertainty, but also by the number of intermediate states. In this way, the work improves the theoretical understanding of complex quantum processes and their constraints.
The physicists’ findings are important not least for quantum computing. The computations that are possible with quantum computers are mostly based on the manipulation of multi-level systems. Quantum states are very fragile, though. They last only a short lapse of time, which physicists call coherence time. It is therefore important to pack as many computational operations as possible into this time. “”Our study reveals the maximum number of operations we can perform in the coherence time,” Alberti explains. “This makes it possible to make optimal use of it.”
The study was funded by the German Research Foundation (DFG) as part of the Collaborative Research Center SFB/TR 185 OSCAR. Funding was also provided by the Reinhard Frank Foundation in collaboration with the German Technion Society, and by the German Academic Exchange Service.
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Early dark energy could resolve cosmology’s two biggest puzzles
A new study by MIT physicists proposes that a mysterious force known as early dark energy could solve two of the biggest puzzles in cosmology and fill in some major gaps in our understanding of how the early universe evolved.
Now, the MIT team has found that both puzzles could be resolved if the early universe had one extra, fleeting ingredient: early dark energy. Dark energy is an unknown form of energy that physicists suspect is driving the expansion of the universe today. Early dark energy is a similar, hypothetical phenomenon that may have made only a brief appearance, influencing the expansion of the universe in its first moments before disappearing entirely.
Some physicists have suspected that early dark energy could be the key to solving the Hubble tension, as the mysterious force could accelerate the early expansion of the universe by an amount that would resolve the measurement mismatch.
The MIT researchers have now found that early dark energy could also explain the baffling number of bright galaxies that astronomers have observed in the early universe. In their new study, reported in the Monthly Notices of the Royal Astronomical Society, the team modeled the formation of galaxies in the universe’s first few hundred million years. When they incorporated a dark energy component only in that earliest sliver of time, they found the number of galaxies that arose from the primordial environment bloomed to fit astronomers’ observations.
“You have these two looming open-ended puzzles,” says study co-author Rohan Naidu, a postdoc in MIT’s Kavli Institute for Astrophysics and Space Research. “We find that in fact, early dark energy is a very elegant and sparse solution to two of the most pressing problems in cosmology.”
The study’s co-authors include lead author and Kavli postdoc Xuejian (Jacob) Shen, and MIT professor of physics Mark Vogelsberger, along with Michael Boylan-Kolchin at the University of Texas at Austin, and Sandro Tacchella at the University of Cambridge.
Big city lights
Based on standard cosmological and galaxy formation models, the universe should have taken its time spinning up the first galaxies. It would have taken billions of years for primordial gas to coalesce into galaxies as large and bright as the Milky Way.
But in 2023, NASA’s James Webb Space Telescope (JWST) made a startling observation. With an ability to peer farther back in time than any observatory to date, the telescope uncovered a surprising number of bright galaxies as large as the modern Milky Way within the first 500 million years, when the universe was just 3 percent of its current age.
“The bright galaxies that JWST saw would be like seeing a clustering of lights around big cities, whereas theory predicts something like the light around more rural settings like Yellowstone National Park,” Shen says. “And we don’t expect that clustering of light so early on.”
For physicists, the observations imply that there is either something fundamentally wrong with the physics underlying the models or a missing ingredient in the early universe that scientists have not accounted for. The MIT team explored the possibility of the latter, and whether the missing ingredient might be early dark energy.
Physicists have proposed that early dark energy is a sort of antigravitational force that is turned on only at very early times. This force would counteract gravity’s inward pull and accelerate the early expansion of the universe, in a way that would resolve the mismatch in measurements. Early dark energy, therefore, is considered the most likely solution to the Hubble tension.
Galaxy skeleton
The MIT team explored whether early dark energy could also be the key to explaining the unexpected population of large, bright galaxies detected by JWST. In their new study, the physicists considered how early dark energy might affect the early structure of the universe that gave rise to the first galaxies. They focused on the formation of dark matter halos — regions of space where gravity happens to be stronger, and where matter begins to accumulate.
“We believe that dark matter halos are the invisible skeleton of the universe,” Shen explains. “Dark matter structures form first, and then galaxies form within these structures. So, we expect the number of bright galaxies should be proportional to the number of big dark matter halos.”
The team developed an empirical framework for early galaxy formation, which predicts the number, luminosity, and size of galaxies that should form in the early universe, given some measures of “cosmological parameters.” Cosmological parameters are the basic ingredients, or mathematical terms, that describe the evolution of the universe.
Physicists have determined that there are at least six main cosmological parameters, one of which is the Hubble constant — a term that describes the universe’s rate of expansion. Other parameters describe density fluctuations in the primordial soup, immediately after the Big Bang, from which dark matter halos eventually form.
The MIT team reasoned that if early dark energy affects the universe’s early expansion rate, in a way that resolves the Hubble tension, then it could affect the balance of the other cosmological parameters, in a way that might increase the number of bright galaxies that appear at early times. To test their theory, they incorporated a model of early dark energy (the same one that happens to resolve the Hubble tension) into an empirical galaxy formation framework to see how the earliest dark matter structures evolve and give rise to the first galaxies.
“What we show is, the skeletal structure of the early universe is altered in a subtle way where the amplitude of fluctuations goes up, and you get bigger halos, and brighter galaxies that are in place at earlier times, more so than in our more vanilla models,” Naidu says. “It means things were more abundant, and more clustered in the early universe.”
“A priori, I would not have expected the abundance of JWST’s early bright galaxies to have anything to do with early dark energy, but their observation that EDE pushes cosmological parameters in a direction that boosts the early-galaxy abundance is interesting,” says Marc Kamionkowski, professor of theoretical physics at Johns Hopkins University, who was not involved with the study. “I think more work will need to be done to establish a link between early galaxies and EDE, but regardless of how things turn out, it’s a clever — and hopefully ultimately fruitful — thing to try.”
“We demonstrated the potential of early dark energy as a unified solution to the two major issues faced by cosmology. This might be an evidence for its existence if the observational findings of JWST get further consolidated,” Vogelsberger concludes. “In the future, we can incorporate this into large cosmological simulations to see what detailed predictions we get.”
This research was supported, in part, by NASA and the National Science Foundation.
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Plant-derived secondary organic aerosols can act as mediators of plant-plant interactions
A new study published in Science reveals that plant-derived secondary organic aerosols (SOAs) can act as mediators of plant-plant interactions. This research was conducted through the cooperation of chemical ecologists, plant ecophysiologists and atmospheric physicists at the University of Eastern Finland.
The study showed that Scots pine seedlings, when damaged by large pine weevils, release VOCs that activate defences in nearby plants of the same species. Interestingly, the biological activity persisted after VOCs were oxidized to form SOAs. The results indicated that the elemental composition and quantity of SOAs likely determines their biological functions.
“A key novelty of the study is the finding that plants adopt subtly different defence strategies when receiving signals as VOCs or as SOAs, yet they exhibit similar degrees of resistance to herbivore feeding,” said Professor James Blande, head of the Environmental Ecology Research Group. This observation opens up the possibility that plants have sophisticated sensing systems that enable them to tailor their defences to information derived from different types of chemical cue.
“Considering the formation rate of SOAs from their precursor VOCs, their longer lifetime compared to VOCs, and the atmospheric air mass transport, we expect that the ecologically effective distance for interactions mediated by SOAs is longer than that for plant interactions mediated by VOCs,” said Professor Annele Virtanen, head of the Aerosol Physics Research Group. This could be interpreted as plants being able to detect cues representing close versus distant threats from herbivores.
The study is expected to open up a whole new complex research area to environmental ecologists and their collaborators, which could lead to new insights on the chemical cues structuring interactions between plants.
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Folded or cut, this lithium-sulfur battery keeps going
Most rechargeable batteries that power portable devices, such as toys, handheld vacuums and e-bikes, use lithium-ion technology. But these batteries can have short lifetimes and may catch fire when damaged. To address stability and safety issues, researchers reporting in ACS Energy Letters have designed a lithium-sulfur (Li-S) battery that features an improved iron sulfide cathode. One prototype remains highly stable over 300 charge-discharge cycles, and another provides power even after being folded or cut.
The team coated iron sulfide cathodes in different polymers and found in initial electrochemical performance tests that polyacrylic acid (PAA) performed best, retaining the electrode’s discharge capacity after 300 charge-discharge cycles. Next, the researchers incorporated a PAA-coated iron sulfide cathode into a prototype battery design, which also included a carbonate-based electrolyte, a lithium metal foil as an ion source, and a graphite-based anode. They produced and then tested both pouch cell and coin cell battery prototypes.
After more than 100 charge-discharge cycles, Wang and colleagues observed no substantial capacity decay in the pouch cell. Additional experiments showed that the pouch cell still worked after being folded and cut in half. The coin cell retained 72% of its capacity after 300 charge-discharge cycles. They next applied the polymer coating to cathodes made from other metals, creating lithium-molybdenum and lithium-vanadium batteries. These cells also had stable capacity over 300 charge-discharge cycles. Overall, the results indicate that coated cathodes could produce not only safer Li-S batteries with long lifespans, but also efficient batteries with other metal sulfides, according to Wang’s team.
The authors acknowledge funding from the National Natural Science Foundation of China; the Natural Science Foundation of Sichuan, China; and the Beijing National Laboratory for Condensed Matter Physics.
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