Three teams of researchers in the US and France have independently developed a new technique to visualize the positions of atoms in real, continuous space, rather than at discrete sites on a lattice. By applying this method, the teams captured “snapshots” of weakly interacting bosons, non-interacting fermions and strongly interacting fermions and made in-situ measurements of the correlation functions that characterize these different quantum gases. Their work constitutes the first experimental measurements of these correlation functions in continuous space – a benchmark in the development of techniques for understanding fermionic and bosonic systems, as well as for studying strongly interacting systems.
Quantum many-body systems exhibit a rich and complex range of phenomena that cannot be described by the single-particle picture. Simulating such systems theoretically is thus rather difficult, as their degrees of freedom (and the corresponding size of their quantum Hilbert spaces) increase exponentially with the number of particles. Highly controllable quantum platforms like ultracold atoms in optical lattices are therefore useful tools for capturing and visualizing the physics of many-body phenomena.
The three research groups followed similar “recipes” in producing their atomic snapshots. First, they prepared a dilute quantum gas in an optical trap created by a lattice of laser beams. This lattice was configured such that the atoms experienced strong confinement in the vertical direction but moved freely in the xy-plane of the trap. Next, the researchers suddenly increased the strength of the lattice in the plane to “freeze” the atoms’ motion and project their positions onto a two-dimensional square lattice. Finally, they took snapshots of the atoms by detecting the fluorescence they produced when cooled with lasers. Importantly, the density of the gases was low enough that the separation between two atoms was larger than the spacing between the sites of the lattice, facilitating the measurement of correlations between atoms.
What does a Fermi gas look like in real space?
One of the three groups, led by Tarik Yefsah in Paris’ Kastler Brossel Laboratory (KBL), studied a non-interacting two-dimensional gas of fermionic lithium-6 (6Li) atoms. After confining a low-density cloud of these atoms in a two-dimensional optical lattice, Yefsah and colleagues registered their positions by applying a technique called Raman sideband laser cooling.
The KBL team’s experiment showed, for the first time, the shape of a parameter called the two-point correlator (g2) in continuous space. These measurements clearly demonstrated the existence of a “fermi hole”: at small interatomic distances, the value of this two-point correlator tends to zero, but as the distance increases, it tends to one. This behaviour was expected, since the Pauli exclusion principle makes it impossible for two fermions with the same quantum numbers to occupy the same position. However, the paper’s first author Tim de Jongh, who is now a postdoctoral researcher at the University of Colorado Boulder in the US, explains that being able to measure “the exact shape of the correlation function at the percent precision level” is new, and a distinguishing feature of their work.
The KBL team’s measurement also provides both two-body and three-body correlation functions for the atoms, making it possible to compare them directly. In principle, the technique could even be extended to correlations of arbitrarily high order.
What about a Bose gas?
Meanwhile, researchers directed by Wolfgang Ketterle of the Massachusetts Institute of Technology (MIT) developed and applied quantum gas microscopy to study how bosons bunch together. Unlike fermions, bosons do not obey the Pauli exclusion principle. In fact, if the temperature is low enough, they can enter a phase known as a Bose-Einstein condensate (BEC) in which their de Broglie wavelengths overlap and they occupy the same quantum state.
By confining a dilute bosonic gas of approximately 100 rubidium atoms in a sheet trap and cooling them to just above the critical temperature (Tc) for the onset of BEC, Ketterle and colleagues were able to make the first in situ measurement of the correlation length in a two-dimensional ultracold bosonic gas. In contrast to Yefsah’s group, Ketterle and colleagues employed polarization cooling to detect the atoms’ positions. They also focused on a different correlation function; specifically, the second-order correlation function of bosonic bunching at T>Tc.
When the system’s temperature is high enough (54 nK above absolute zero, in this experiment), the correlation function is nearly 1, meaning that the atoms’ thermal de-Broglie waves are too short to “notice” each other. But when the sample is cooled to a lower temperature of 6.4 nK, the thermal de-Broglie wavelength becomes commensurate with the interparticle spacing r, and the correlation function exhibits the bunching behavior expected for bosons in this regime, decreasing from its maximum value at r = 0 down to 1 as the interparticle spacing increases.
In an ideal system, the maximum value of the correlation function would be 2. However, in this experiment, the spatial resolution of the grid and the quasi-two-dimensional nature of the trapped gas reduce the maximum to 1.3. Enid Cruz Colón, a PhD student in Ketterle’s group, explains that this experiment is sensitive to parity projection, meaning that the count number of atoms per site is either even or odd. This implies that doubly occupied sites are registered as empty sites, which directly shrinks the measured value of g2
What does an interacting quantum gas look like in real space?
With Yefsah and colleagues focusing on fermionic correlations, and Ketterle’s group focusing on bosons, a third team led by MIT’s Martin Zwierlein found its niche by studying mixtures of bosons and fermions. Specifically, the team measured the pair correlation function for a mixture of a thermal Bose gas composed of sodium-23 (23Na) atoms and a degenerate Fermi gas of 6Li. As expected, they found that the probability of finding two particles together is enhanced for bosons and diminished for fermions.
In a further experiment, Zwierlein and colleagues studied a strongly interacting Fermi gas and measured its density-density correlation function. By increasing the strength of the interactions, they caused the atoms in this gas to pair up, triggering a transition into the BCS (Bardeen-Cooper-Schriefer) regime associated with paired electrons in superconductors. For atoms in a BEC, the density-density correlation function shows a strong bunching tendency at short distances; in the BCS regime, in contrast, the correlation depicts a long-range pairing where atoms form so-called Cooper pairs as the strength of their interactions increases.
By applying the new quantum gas microscopy technique to the study of strongly interacting Fermi gases, Ruixiao Yao, a PhD student in Zwierlein’s group and the paper’s first author, notes that they have opened the door to applications in quantum simulation. Such strongly correlated systems, Yao highlights, are especially difficult to simulate on classical computers.
Women and ethnic-minority groups are still significantly underrepresented in UK astronomy and geophysics, with the fields becoming more white. That is according to the latest demographic survey conducted by the Royal Astronomical Society (RAS), which concludes that decades of initiatives to improve representation have “failed”.
Based on data collected in 2023, the survey reveals more people working in astronomy and solar-system science than ever before, although the geophysics community has shrunk since 2016. According to university admissions data acquired by the RAS, about 80% of students who started undergraduate astronomy and geophysics courses in 2022 were white, slightly less than the 83% overall proportion of white people in the UK.
However, among permanent astronomy and geophysics staff, 97% of British respondents to the RAS survey are white, up form 95% in 2016. The makeup of postgraduate students was similar, with 92% of British students – who accounted for 70% of postgraduate respondents – stating they are white, up from 87% in 2016.
The survey also finds that the proportion of women in professor, senior lecturer or reader roles increased from 2010 to 2023 in astronomy and solar-system science, but has stagnated at lecturer level in astronomy since 2016 and dropped in “solid Earth” geophysics to 19%. The picture is better at more junior levels, with women making up 28% of postdocs in astronomy and solar-system science and 34% in solid Earth geophysics.
A redouble of efforts
“I very much want to see far more women and people from minority ethnic groups working as astronomers and geophysicists, and we have to redouble our efforts to make that happen,” says Robert Massey, deputy executive director of the RAS, who co-authored the survey and presented its results at the National Astronomy Meeting 2025 in Durham last week.
RAS president Mike Lockwood agrees, stating that effective policies and strategies are now needed. “One only has to look at the history of science and mathematics to understand that talent can, has, and does come from absolutely anywhere in society, and our concern is that astronomy and geophysics in the UK is missing out on some of the best natural talent available to us,” Lockwood adds.
The first experimental evidence of the breaking of charge–parity (CP) symmetry in baryons has been obtained by CERN’s LHCb Collaboration. The result is consistent with the Standard Model of particle physics and could lead to constraints on theoretical attempts to extend the Standard Model to explain the excess of matter over antimatter in the universe.
Current models of cosmology say that the Big Bang produced a giant burst of matter and antimatter, the vast majority of which recombined and annihilated shortly afterwards. Today however, the universe appears to be made almost exclusively of matter with very little antimatter in evidence. This excess of matter is not explained by the Standard Model and it existence is an important mystery in physics.
In 1964, James Cronin, Valentine Fitch and colleagues at Princeton University in the US conducted an experiment on the decay of neutral K mesons. This showed that the weak interaction violated CP symmetry, indicating that matter and antimatter could behave differently. Fitch and Cronin bagged the 1980 Nobel Prize for Physics and the Soviet physicist Andrei Sakharov subsequently suggested that, if amplified at very high mass scales in the early universe, CP violation could have induced the matter–antimatter asymmetry shortly after the Big Bang.
Numerous observations of CP violation have subsequently been made in other mesonic systems. The phenomenon is now an accepted part of the Standard Model is parametrized by the Cabibbo–Kobayashi–Maskawa (CKM) matrix. This describes the various probabilities of quarks of different generations changing into each other through the weak interaction – a process called mixing.
Tiny effect
However, the CP violation produced through the CKM mechanism is much smaller effect than would have been required to create the matter left over by the Big Bang, as Xueting Yang of China’s Peking University explains.
“The number of baryons remaining divided by the number of photons produced when the baryons and antibaryons met and produced two photons is required to be about 10-10 in Big Bang theory…whereas this kind of quantity is only 10-18 in the Standard Model prediction.”
What is more, CP violation had never been observed in baryons. “Theoretically the prediction for baryon decay is very imprecise,” says Yang, who is a member of the LHCb collaboration. “It’s much more difficult to calculate it than the meson decays because there’s some interaction with the strong force.” Baryons (mostly protons and neutrons) make up almost all the hadronic matter in the universe, so this left open the slight possibility that the explanation might lie in some inconsistency between baryonic CP violation and the Standard Model prediction.
In the new work, Yang and colleagues at LHCb looked at the decays of beauty (or bottom) baryons and antibaryons. These heavy cousins of neutrons contain an up quark, a down quark and a beauty quark and were produced in proton–proton collisions at the Large Hadron Collider in 2011–2018. These baryons and antibaryons can decay via multiple channels. In one, a baryon decays to a proton, a positive K-meson and a pair of pions – or, conversely, an antibaryon decays to an antiproton, a negative K-meson and a pair of pions. CP violation should create an asymmetry between these processes, and the researchers looked for evidence of this asymmetry in the numbers of particles detected at different energies from all the collisions.
Standard Model prevails
The team found that the CP violation seen was consistent with the Standard Model and inconsistent with zero by 5.2σ. “The experimental result is more precise than what we can get from theory,” says Yang. Other LHCb researchers scrutinized alternative decay channels of the beauty baryon: “Their measurement results are still consistent with CP symmetry…There should be CP violation also in their decay channels, but we don’t have enough statistics to claim that the deviation is more than 5σ.”
The current data do not rule any extensions to the current Standard Model out, says Yang, simply because none of those extensions make precise predictions about the overall degree of CP violation expected in baryons. However, the LHC is now in its third run, and the researchers hope to acquire information on, for example, the intermediate particles involved in the decay: “We may be able to provide some measurements that are more comparable for theories and which can provide some constraints on the Standard Model predictions for CP violation,” says Yang.
“It’s an important paper – an old type of CP violation in a new system,” says Tom Browder of the University of Hawaii. “Theorists will try to interpret this within the context of the Standard Model, and there have already been some attempts, but there are some uncertainties due to the strong interaction that preclude making a precise test.” He says the results could nevertheless potentially help to constrain extensions of the Standard Model, such as CP violating decays involving dark matter proposed by the late Ann Nelson at the University of Washington in Seattle and her colleagues.
This episode of the Physics World Weekly podcast features Travis Humble, who is director of the Quantum Science Center at Oak Ridge National Laboratory.
Located in the US state of Tennessee, Oak Ridge is run by the US Department of Energy (DOE). The Quantum Science Center links Oak Ridge with other US national labs, universities and companies.
Humble explains how these collaborations ensure that Oak Ridge’s powerful facilities and instruments are used to create new quantum technologies. He also explains how the lab’s expertise in quantum and conventional computing is benefiting the academic and industrial communities.
This podcast is supported by American Elements, the world’s leading manufacturer of engineered and advanced materials. The company’s ability to scale laboratory breakthroughs to industrial production has contributed to many of the most significant technological advancements since 1990 – including LED lighting, smartphones, and electric vehicles.
Physics metaphors don’t work, or so I recently claimed. Metaphors always fail; they cut corners in reshaping our perception. But are certain physics metaphors defective simply because they cannot be experimentally confirmed? To illustrate this idea, I mentioned the famous metaphor for how the Higgs field gives particles mass, which is likened to fans mobbing – and slowing – celebrities as they walk across a room.
I know from actual experience that this is false. Having been within metres of filmmaker Spike Lee, composer Stephen Sondheim, and actors Mia Farrow and Denzel Washington, I’ve seen fans have many different reactions to the presence of nearby celebrities in motion. If the image were strictly true, I’d have to check which celebrities were about each morning to know what the hadronic mass would be that day.
I therefore invited Physics World readers to propose other potentially empirically defective physics metaphors, and received dozens of candidates. Technically, many are similes rather than metaphors, but most readers, and myself, use the two terms interchangeably. Some of these metaphors/similes were empirically confirmable and others not.
Shoes and socks
Michael Elliott, a retired physics lecturer from Oxford Polytechnic, mentioned a metaphor from Jakob Schwichtenberg’s book No-Nonsense Quantum Mechanics that used shoes and socks to explain the meaning of “commutation”. It makes no difference, Schwichtenberg wrote, if you put your left sock on first and then your right sock; in technical language the two operations are said to commute. However, it does make a difference which order you put your sock and shoe on.
“The ordering of the operations ‘putting shoes on’ and ‘putting socks on’ therefore matters,” Schwichtenberg had written, meaning that “the two operations do not commute.” Empirically verifiable, Elliott concluded triumphantly.
A metaphor that was used back in 1981 by CERN physicist John Bell in a paper addressed to colleagues requires more footgear and imagination. Bell’s friend and colleague Reinhold Bertlmann from the University of Vienna was a physicist who always wore mismatched socks, and in the essay “Bertlmann’s socks and the nature of reality” Bell explained the Einstein–Podolsky–Rosen (EPR) paradox and Bell’s theorem in terms of those socks.
If Bertlmann stepped into a room and an observer noticed that the sock on his first foot was pink, one could be sure the other was not-pink, illustrating the point of the EPR paper. Bell then suggested that, when put in the wash, pairs of socks and washing temperatures could behave analogously to particle pairs and magnet angles in a way that conveyed the significance of his theorem. Bell bolstered this conclusion with a scenario involving correlations between spikes of heart attacks in Lille and Lyon. I am fairly sure, however, that Bell never empirically tested this metaphor, and I wonder what the result would be.
Out in space, the favourite cosmology metaphor of astronomer and astrophysicist Michael Rowan-Robinson is the “standard candle” that’s used to describe astronomical objects of roughly fixed luminosity. Standard candles can be used to determine astronomical distances and are thus part of the “cosmological distance ladder” – Rowan-Robinson’s own metaphor – towards measuring the Hubble constant.
Retired computer programmer Ian Wadham, meanwhile, likes Einstein’s metaphor of being in a windowless spacecraft towed by an invisible being who gives the ship a constant acceleration. “It is impossible for you to tell whether you are standing in a gravitational field or being accelerated,” Wadham writes. Einstein used the metaphor effectively – even though, as an atheist, he was convinced that he would be unable to test it.
I was also intrigued by a comment from Dilwyn Jones, a consultant in materials science and engineering, who cited a metaphor from the 1939 book The Third Policeman by Irish novelist Flann O’Brien. Jones first came across O’Brien’s metaphor in Walter J Moore’s 1962 textbook Physical Chemistry. Atoms, says a character in O’Brien’s novel, are “never standing still or resting but spinning away and darting hither and thither and back again, all the time on the go”, adding that “they are as lively as twenty leprechauns doing a jig on top of a tombstone”.
But as Jones pointed out, that particular metaphor “can only be tested on the Emerald Isle”.
Often metaphors entertain as much as inform. Clare Byrne, who teaches at a high school in St Albans in the UK, tells her students that delocalized electrons are like stray dogs – “hanging around the atoms, but never belonging to any one in particular”. They could, however, she concedes “be easily persuaded to move fast in the direction of a nice steak”.
Giving metaphors legs
I ended my earlier column on metaphors by referring to poet Matthew Arnold’s fastidious correction of a description in his 1849 poem ”The Forsaken Merman”. After it was published, a friend pointed out to Arnold his mistaken use of the word “shuttle” rather than “spindle” when describing “the king of the sea’s forlorn wife at her spinning-wheel” as she lets the thing slip in her grief.
The next time the poem was published, Arnold went out of his way to correct this. Poets, evidently, find it imperative to be factual in metaphors, and I wondered, why shouldn’t scientists? The poet Kevin Pennington was outraged by my remark.
“Metaphors in poetry are not the same as metaphors used in science,” he insisted. “Science has one possible meaning for a metaphor. Poetry does not.” Poetic metaphors, he added are “modal”, having many possible interpretations at the same time – “kinda like particles can be in a superposition”.
I was dubious. “Superposition” suggests that poetic meanings are probabilistic, even arbitrary. But Arnold, I thought, was aiming at something specific when the king’s wife drops the spindle in “The Forsaken Merman”. After all, wouldn’t I be misreading the poem to imagine his wife thinking, “I’m having fun and in my excitement the thing slipped out of my hand!”
My Stony Brook colleague Elyse Graham, who is a professor of English, adapted a metaphor used by her former Yale professor Paul Fry. “A scientific image has four legs”, she said, “a poetic image three”. A scientific metaphor, in other words, is as stable as a four-legged table, structured to evoke a specific, shared understanding between author and reader.
A poetic metaphor, by contrast, is unstable, seeking to evoke a meaning that connects with the reader’s experiences and imagination, which can be different from the author’s within a certain domain of meaning. Graham pointed out, too, that the true metaphor in Arnold’s poem is not really the spinning wheel, the wife and the dropped spindle but the entirety of the poem itself, which is what Arnold used to evoke meaning in the reader.
That’s also the case with O’Brien’s atom-leprechaun metaphor. It shows up in the novel not to educate the reader about atomic theory but to invite a certain impression of the worldview of the science-happy character who speaks it.
The critical point
In his 2024 book Waves in an Impossible Sea: How Everyday Life Emerges from the Cosmic Ocean, physicist Matt Strassler coined the term “physics fib” or ”phib”. It refers to an attempted “short, memorable tale” that a physicist tells an interested non-physicist that amounts to “a compromise between giving no answer at all and giving a correct but incomprehensible one”.
The criterion for whether a metaphor succeeds or fails does not depend on whether it can pass empirical test, but on the interaction between speaker or author and audience; how much the former has to compromise depends on the audience’s interest and understanding of the subject. Metaphors are interactions. Byrne was addressing high-school students; Schwichtenberg was aiming at interested non-physicists; Bell was speaking to physics experts. Their effectiveness, to use one final metaphor, does not depend on empirical grounding but impedance matching; that is, they step down the “load” so that the “signal” will not be lost.
The second law of thermodynamics demands that if we want to make a clock more precise – thereby reducing the disorder, or entropy, in the system – we must add energy to it. Any increase in energy, however, necessarily increases the amount of waste heat the clock dissipates to its surroundings. Hence, the more precise the clock, the more the entropy of the universe increases – and the tighter the ultimate limits on the clock’s precision become.
This constraint might sound unavoidable – but is it? According to physicists at TU Wien in Austria, Chalmers University of Technology, Sweden, and the University of Malta, it is in fact possible to turn this seemingly inevitable consequence on its head for certain carefully designed quantum systems. The result: an exponential increase in clock accuracy without a corresponding increase in energy.
Solving a timekeeping conundrum
Accurate timekeeping is of great practical importance in areas ranging from navigation to communication and computation. Recent technological advancements have brought clocks to astonishing levels of precision. However, theorist Florian Meier of TU Wien notes that these gains have come at a cost.
“It turns out that the more precisely one wants to keep time, the more energy the clock requires to run to suppress thermal noise and other fluctuations that negatively affect the clock,” says Meier, who co-led the new study with his TU Wien colleague Marcus Huber and a Chalmers experimentalist, Simone Gasparinetti. “In many classical examples, the clock’s precision is linearly related to the energy the clock dissipates, meaning a clock twice as accurate would produce twice the (entropy) dissipation.”
Clock’s precision can grow exponentially faster than the entropy
The key to circumventing this constraint, Meier continues, lies in one of the knottiest aspects of quantum theory: the role of observation. For a clock to tell the time, he explains, its ticks must be continually observed. It is this observation process that causes the increase in entropy. Logically, therefore, making fewer observations ought to reduce the degree of increase – and that’s exactly what the team showed.
“In our new work, we found that with quantum systems, if designed in the right way, this dissipation can be circumvented, ultimately allowing exponentially higher clock precision with the same dissipation,” Meier says. “We developed a model that, instead of using a classical clock hand to show the time, makes use of a quantum particle coherently travelling around a ring structure without being observed. Only once it completes a full revolution around the ring is the particle measured, creating an observable ‘tick’ of the clock.”
The clock’s precision can thus be improved by letting the particle travel through a longer ring, Meier adds. “This would not create more entropy because the particle is still only measured once every cycle,” he tells Physics World. “The mathematics here is of course much more involved, but what emerges is that, in the quantum case, the clock’s precision can grow exponentially faster than the entropy. In the classical analogue, in contrast, this relationship is linear.”
“Within reach of our technology”
Although such a clock has not yet been realized in the laboratory, Gasparinetti says it could be made by arranging many superconducting quantum bits in a line.
“My group is an experimental group that studies superconducting circuits, and we have been working towards implementing autonomous quantum clocks in our platform,” he says. “We have expertise in all the building blocks that are needed to build the type of clock proposed in in this work: generating quasithermal fields in microwave waveguides and coupling them to superconducting qubits; detecting single microwave photons (the clock ‘ticks’); and building arrays of superconducting resonators that could be used to form the ‘ring’ that gives the proposed clock its exponential boost.”
While Gasparinetti acknowledges that demonstrating this advantage experimentally will be a challenge, he isn’t daunted. “We believe it is within reach of our technology,” he says.
Solving a future problem
At present, dissipation is not the main limiting factor for when it comes to the performance of state-of-the-art clocks. As clock technology continues to advance, however, Meier says we are approaching a point where dissipation could become more significant. “A useful analogy here is in classical computing,” he explains. “For many years, heat dissipation was considered negligible, but in today’s data centres that process vast amounts of information, dissipation has become a major practical concern.
“In a similar way, we anticipate that for certain applications of high-precision clocks, dissipation will eventually impose limits,” he adds. “Our clock highlights some fundamental physical principles that can help minimize such dissipation when that time comes.”
NASA’s New Horizons spacecraft has been used to demonstrate simple interstellar navigation by measuring the parallax of just two stars. An international team was able to determine the location and heading of the spacecraft using observations made from space and the Earth.
Developed by an international team of researchers, the technique could one day be used by other spacecraft exploring the outermost regions of the solar system or even provide navigation for the first truly interstellar missions.
New Horizons visited the Pluto system in 2015 and has now passed through the Kuiper Belt in the outermost solar system.
Now, NOIRLab‘s Tod Lauer and colleagues have created a navigation technique for the spacecraft by choosing two of the nearest stars for parallax measurements. These are Proxima Centauri, which is just 4.2 light–years away, and Wolf 359 at 7.9 light–years. On 23 April 2020, New Horizons imaged star-fields containing the two stars, while on Earth astronomers did the same.
At that time, New Horizons was 47.1 AU (seven billion kilometres) from Earth, as measured by NASA’s Deep Space Network. The intention was to replicate that distance determination using parallax.
Difficult measurement
The 47.1 AU separation between Earth and New Horizons meant that each vantage point observed Proxima and Wolf 359 in a slightly different position relative to the background stars. This displacement is the parallax angle, which the observations showed to be 32.4 arcseconds for Proxima and 15.7 arcseconds for Wolf 359 at the time of measurement.
By applying simple trigonometry using the parallax angle and the known distance to the stars, it should be relatively straightforward to triangulate New Horizons’ position. In practice, however, the team struggled to make it work. It was the height of the COVID-19 pandemic, and finding observatories that were still open and could perform the observations on the required night was not easy.
Edward Gomez, of the UK’s Cardiff University and the international Las Cumbres Observatory, recalls the efforts made to get the observations. “Tod Lauer contacted me saying that these two observations were going to be made, and was there any possibility that I could take them with the Las Cumbres telescope network?” he tells Physics World.
In the end, Gomez was able to image Proxima with Las Cumbres’ telescope at Siding Spring in Australia. Meanwhile, Wolf 359 was observed by the University of Louisville’s Manner Telescope at Mount Lemmon Observatory in Arizona. At the same time, New Horizons’ Long Range Reconnaissance Imager (LORRI) took pictures of both stars, and all three observations were analysed using a 3D model of the stellar neighbourhood based on data from the European Space Agency’s star-measuring Gaia mission.
The project was more a proof-of-concept than an accurate determination of New Horizons’ position and heading, with the team describing the measurements as “educational”.
“The reason why we call it an educational measurement is because we don’t have a high degree of, first, precision, and secondly, reproducibility, because we’ve got a small number of measurements, and they weren’t amazingly precise,” says Gomez. “But they still demonstrate the parallax effect really nicely.”
New Horizons position was calculated to within 0.27 AU, which is not especially useful for navigating towards a trans-Neptunian object. The measurements were also able to ascertain New Horizon’s heading to an accuracy of 0.4°, relative to the precise value derived from Deep Space Network signals.
Just two stars
But the fact that only two stars were needed is significant, explains Gomez. “The good thing about this method is just having two close stars as our reference stars. The handed-down wisdom normally is that you need loads and loads [of stars], but actually you just need two and that’s enough to triangulate your position.”
There are more accurate ways to navigate, such as pulsar measurements, but these require more complex and larger instrumentation on a spacecraft – not just an optical telescope and a camera. While pulsar navigation has been demonstrated on the International Space Station in low-Earth orbit, this is the first time that any method of interstellar navigation has been demonstrated for a much more distant spacecraft.
Today, more than five years after the parallax observations, New Horizons is still speeding out of the solar system. It has cleared the Kuiper Belt and today is 61 AU from Earth.
When asked if the parallax measurements will be made again under better circumstances Gomez replied. “I hope so. Now that we’ve written a paper in The Astronomical Journal that’s getting some interest, hopefully we can reproduce it, but nothing has been planned so far.”
In a way, the parallax measurements have brought Gomez full-circle. “When I was doing [high school] mathematics more years ago than I care to remember, I was a massive Star Trek fan and I did a three-dimensional interstellar navigation system as my mathematics project!”
Now here he is, as part of a team using the stars to guide our own would-be interstellar emissary.
The 1920s was an era of transformation. In the US, the “Roaring Twenties” saw industrial growth, the rise of consumerism, and huge social change, marked by jazz music, prohibition and flapper fashion. Europe, meanwhile, was recovering from the devastating First World War, and experiencing political and economic instability alongside flourishing artistic and intellectual movements. And India – which was still under British rule at the time – was embracing Mahatma Gandhi’s policy of non-violence and civil disobedience, accelerating its nationalistic movement towards independence.
Amid worldwide cultural and sociopolitical change, another revolution was unfolding in science, particularly in our understanding of physical phenomena that cannot be explained by the classical laws of physics. Intense efforts were being made by European scientists to reconcile puzzling observations, and ground-breaking ideas were being introduced – such as Max Planck’s hypothesis of “quanta” and Albert Einstein’s quantization of electromagnetism. The first quantum revolution was flourishing.
In the midst of this excitement, a modest man from Bengal in undivided India, Satyendra Nath Bose, was teaching physics at Dacca (now Dhaka) University. He was greatly inspired by the new ideas in physics, and set about trying to solve the big inconsistency with the Plank distribution of black body radiation – the fact that it mixed classical and quantum concepts. Bose introduced the ground-breaking notion of indistinguishability of particles into the evolving quantum theory to rectify the problem, culminating in an equation describing the distribution of energy in the radiation from a black body purely based on quantum physics.
Legacy lives on Satyendra Nath Bose in London, 1925. (Photographer unknown)
Bose’s derivation of Planck’s law impressed Einstein, who had also been trying to solve the problem. He translated the work and submitted it to Zeitschrift für Physik journal on Bose’s behalf. Bose’s novel quantum statistical approach later became known as Bose–Einstein statistics. Einstein followed up with its extension to atoms and the prediction of Bose–Einstein condensates. Bose’s work was a breakthrough for quantum mechanics, and there have since been many discoveries and multiple Nobel prizes awarded for work related to his research. He also laid the foundation for novel technologies that are central to today’s “second quantum revolution”. This exciting era encompasses themes such as quantum computing, communications, sensing and metrology, and materials and devices. Bose’s scientific breakthroughs were not his only contributions to physics at the time.
Competent and capable
Bose lived in an era when women were not welcome in the scientific community in India, as was the case in much of the rest of the world. Infamously, in 1933 biochemist Kamala Sohonie – who went on to be the first Indian woman to get a PhD in a scientific discipline – was denied admission to the Indian Institute of Science by the then-director Chandrasekhara Venkata Raman. Best known for his work on light scattering, Raman believed that women were not competent enough to do scientific research. While Sohonie eventually did get a place, she had to fight hard for it, and Raman enforced certain restrictions. For example, she was on probation for a year and Raman had to approve her work before it could be officially recognized.
Bose on the other hand, did not make any distinction between men and women as far as scientific ability was concerned. In 1951 he welcomed PhD student Purnima Sinha to his group at the University of Calcutta. Despite being the only woman in the team, Sinha succeeded in leaving her indelible imprint on a male-dominated world, helped by the constant guidance and encouragement she received from Bose.
Sinha’s research was on crystallographic and thermal analysis of clay samples taken from all over India. She built sophisticated X-ray instruments using military scrap equipment sold on the streets of Calcutta (now Kolkata) after the Second World War. In 1956 Sinha was awarded her doctorate, becoming the first woman to earn a PhD in physics from Calcutta University (and likely the first woman to get a PhD in physics from an institution in India).
She went on to conduct research in biophysics at Stanford University in the US, and found similarities between clay structure and DNA structure, providing pioneering thoughts on the origin of life. Sinha further broke gender stereotypes by doing masonry work, carpentry and even playing the tabla (a pair of hand drums). Bose was equally supportive of Asima Chatterjee, who started her research on medicinal plant extracts with Bose, and conducted the first small-molecule X-ray diffraction, which was ground-breaking work.
Leading lights
Quantum women Authors of this article, Tanusri Saha-Dasgupta (left) and Rupamanjari Ghosh. (Photos kindly supplied by their subjects)
Tanusri Saha-Dasgupta
Director and senior professor at S N Bose National Centre for Basic Sciences, Tanusri Saha-Dasgupta (co-author of this article) uses computational tools to predict and understand novel quantum systems. A recent objective of her research has been to study extreme sensitivity and colossal response of strongly correlated quantum materials to external perturbations to develop them as quantum sensors. Her research aims to find new quantum information platforms – including detectors and qubits – based on correlated multipolar materials as well as developing novel quantum sensor platforms.
Saha-Dasgupta has been fascinated by scientific research since childhood. Her father was a doctoral researcher in physics when she started school, and she was determined to be a scientist too. She studied physics at Presidency College in Kolkata for her bachelor’s degree. In a class of 22 students, there were only four women, and coming from an all-girls school, it was a challenge to cope in the male-dominated environment. However, her passion for science helped her succeed. Saha-Dasgupta ranked first in her master’s at the University of Calcutta, and carried out her PhD work at the S N Bose Centre affiliated to University of Calcutta.
Following her studies, she did postdocs at the aerospace lab ONERA in Paris, France, and later at the Max Planck Institute in Stuttgart, Germany. Studying abroad was not easy for Saha-Dasgupta, as it was filled with hurdles, including serious illness and being separated from her husband. However, her persistence paid off.
Saha-Dasgupta became the first female director at the S N Bose National Centre for Basic Sciences in 2021. She is a fellow of the American Physical Society and the World Academy of Sciences, as well as all three science academies in India. As a senior professor, she has played a pivotal role in mentoring many students, and has been in a leadership position for several national and international decision-making bodies.
Rupamanjari Ghosh
Rupamanjari Ghosh (co-author of this article) has held multiple prominent positions during her career. She was a professor of physics and dean of the School of Physical Sciences at Jawaharlal Nehru University (JNU) in New Delhi, before moving to Shiv Nadar University (SNU), a new, privately funded research university in the Delhi region. Here she was director of the School of Natural Sciences, and then vice-chancellor of the university. Under her leadership, SNU received the title of “Institution of Eminence” from the government of India within just a few years of its existence.
Born and raised in Kolkata, Ghosh did her undergraduate and master’s degrees at the University of Calcutta. Chosen for “outstanding scholarly ability and the promise of exceptional contributions to scholarship and teaching” she was awarded a Rush Rhees fellowship for her PhD studies at the University of Rochester, New York, in the US, where she was the only female PhD student to graduate under Leonard Mandel.
Ghosh is credited with the discovery of a new source of entangled photons using spontaneous parametric down-conversion, and the first experimental demonstration of two-photon interference exhibiting nonlocality. Her group at JNU has worked extensively on the critical issue of decoherence from a quantum to a classical state in specific models. She also has an international collaboration that explores the process of electromagnetically induced transparency – which is a promising approach for implementing quantum memory.
While science and technology are deeply intertwined, Ghosh emphasizes the importance of inventions in science, often arising from singular, deep ideas, that define the “what” of a problem. She is also a big advocate for equality in physics.
Ghosh continues to mentor the next generation of researchers as a governing or advisory council member at several institutions in India. She has also been extensively involved as an expert with the National Quantum Mission (NQM) of the government of India. Furthermore, she is currently the first and only international member on the advisory board of the Executive Leadership Academy at the University of California, Berkeley, US.
The representation of women in the science and technology sector remains strikingly low, both in terms of job applicants and leadership roles. For example, a survey by the Council of Scientific Industrial Research (CSIR) in 2022 revealed that no woman had held the role of director general of CSIR until August of that year when chemical engineer Nallathamby Kalaiselvi became the first woman to lead the institute – a role that she still holds. Indeed, only five of the 35 CSIR labs were led by women at the time of the survey.
Gender bias and traditional role segregation are some of the key reasons why women remain under-represented in STEM careers in India. Several studies have found that women leave the workforce at key phases in their life – notably when they have children – and are also often rejected when seeking jobs because of gender discrimination.
However, the picture is changing rapidly, aided by educational initiatives and grassroots movements advocating for gender equity. The quickly growing quantum sector is no different, and the need for quantum education is greater than ever, as a shortage of trained researchers is being felt globally.
One person hoping to inspire and educate women and girls about quantum computing is Singapore-based researcher Nithyasri Srivathsan, who founded SheQuantum in 2020. The initiative has built an e-learning platform offering lectures, quantum computing courses and other educational resources, as well as articles and interviews with experts. It was listed by The Quantum Insider as one of the “9 Educational Platforms to get the Quantum Workforce Up & Running“, alongside IBM, Microsoft and MIT xPRO among others.
Another example is Women for Quantum (W4Q), which was set up by a group of female physics professors, mostly based in Europe and Japan, who work in the field of quantum optics, quantum many-body physics and quantum information. In its manifesto, the initiative highlights the “unsatisfactory current situation of women in quantum physics” and calls for a joint effort to make real change in the field.
The tradition continues
Successful succession Swastika Chatterjee (left) and Joyee Ghosh are former students of this article’s authors, continuing the tradition begun by Satyendra Nath Bose of welcoming women into quantum physics. (Photos kindly supplied by their subjects)
The tradition of succession from guru to disciple set up by Satyendra Nath Bose continues. The students of Tanusri Saha-Dasgupta and Rupamanjari Ghosh (see box above) inspired by their passion have now made their mark as established researchers.
Swastika Chatterjee
Swastika Chatterjee is an associate professor at the Indian Institute of Science Education and Research in Kolkata. Her research focuses on understanding quantum effects in Earth phenomena, such as the planet’s magnetism and dynamo motion.
Chatterjee completed her undergraduate degree in physics with chemistry and maths at the University of Delhi, before specializing in condensed-matter physics for her master’s. She went on to do her PhD under Tanusri Saha-Dasgupta at the S N Bose National Centre for Basic Science. Chatterjee got married during her studies, and she submitted her thesis while expecting her child. Her daughter was born just a few days later, and trying to balance motherhood and her career posed a significant challenge, but she succeeded through perseverance and determination. “The workplace environment has evolved significantly over the last decade, thanks to our academic predecessors who fought their way out,” she says.
Joyee Ghosh
An associate professor of physics at the Indian Institute of Technology, Delhi, Joyee Ghosh is working to understand photon–atom interactions at the single-particle level, to be used in quantum networks. Her team’s research involves “trusted-node-free” secure quantum communication, based on free-space and fibre-based entangled photon sources.
Ghosh grew up in Kolkata and then got her master’s and PhD degrees from Jawaharlal Nehru University (JNU), under the supervision of Rupamanjari Ghosh. She went on to do postdoctoral research in Spain as a Marie Curie fellow, and in Germany as an Alexander von Humboldt fellow.
“My journey so far underscores the tenacity and positivity required by women physicists in India to navigate systemic challenges, secure funding and gain recognition in a complex and competitive scientific landscape,” says Ghosh. “I have been fortunate to learn from great teachers and work in some of the best experimental research facilities.”
Celebrating success
The good news is that such efforts seem to be paying off. According to the latest All India Survey on Higher Education (AISHE) (2020–2021) women make up 42.3% of undergraduate, postgraduate, MPhil, and PhD places in STEM education. There has also been a surge in women in all fields of STEM, including quantum science, where they are making significant contributions to the second quantum revolution.
To celebrate the growing presence of women at the forefront of quantum science in India, the S N Bose National Centre for Basic Sciences in Kolkata arranged an international conference in July 2024 on Women in Quantum Science and Technologies. The meeting was part of celebrations marking the 100th anniversary of Bose’s seminal work, highlighting that his legacy encompasses both quantum science and gender equality in physics.
Opportunity for change Women in Quantum Science and Technologies was a three-day conference held in Kolkata in July 2024. (Courtesy: S N Bose National Centre)
The three-day conference consisted of six talks from accomplished female scientists, two panel discussions, three special lectures, 10 invited talks from early-career women working across quantum science and technologies, and a poster session by PhD students. The panel discussions focused on the challenges faced by women in higher education and ways to overcome them, as well as opportunities for women in the quantum arena. Speakers included Rupamanjari Ghosh, Aditi Sen De, Indrani Bose, Anjana Devi, Shohini Ghose and Efrat Shimshoni.
Such events highlight the achievements of women in the field, providing a platform for sharing research and inspiring future generations. This visibility is crucial for normalizing women’s participation in science and encouraging girls to pursue careers in physics and related disciplines.
With the second quantum revolution in progress, and the next likely to be driven by commercial innovations in areas such as cybersecurity, eco-materials and medical advancements, it is important to ensure that these breakthroughs do not reinforce societal inequalities. For that, we need women, and other under-represented groups in physics, to be encouraged into the field to ensure a diverse range of ideas.
To this end, here we highlight some women at the forefront of quantum science in India. The list is far from exhaustive, but it offers a glimpse of the broader picture.
Women at the forefront of quantum science in India
At the quantum frontier Clockwise from top left: Aditi Sen De, Urbasi Sinha, Usha Devi A R and Kasturi Saha. (Photos kindly supplied by their subjects)
Aditi Sen De
Aditi Sen De is a professor of physics at the Harish Chandra Research Institute in Allahabad. Her research exploits quantum mechanical principles to design quantum technologies, such as quantum communication networks, quantum thermal machines, and measurement-based quantum computers. She also characterizes resources responsible for achieving quantum technologies superior to their day-to-day versions.
Sen De was greatly inspired by her mother, a mathematics teacher, and developed a passion for teaching from an early age. “I used to teach using a small blackboard at home, imagining a classroom full of students,” she explains. She completed her bachelor’s degree at India’s oldest women’s college, Bethune College in Kolkata, before pursuing her interest in quantum and statistical physics at the University of Calcutta for her master’s. Alongside her husband – they grew together both personally and professionally – she continued her scientific journey in Europe, completing her PhD at the University of Gdansk in Poland, and then doing postdoctoral research in Germany and Spain.
In 2018 Sen De was awarded the Shanti Swarup Bhatnagar Prize for Science and Technology (now the Vigyan Yuva – Shanti Swarup Bhatnagar Award). Given by the Indian government to recognize talented young scientists in all disciplines, the prize is one of the most prestigious scientific accolades in India. First awarded in 1958, only two women have ever received this honour in the physical sciences category (now physics), out of 103 recipients – a stark reflection of the gender imbalance.
Urbasi Sinha
The only other woman to receive the Bhatnagar award is Urbasi Sinha, a professor at the Raman Research Institute in Bangalore. Her research spans experimental studies on photonic quantum information processing, secure quantum communication, and precision tests of quantum mechanics.
Sinha’s scientific journey was shaped by the constant support of her non-scientist parents, whose encouragement sparked her passion for discovery. After doing her undergraduate degree at Jadavpur University in Kolkata, Sinha went on to do a master’s and PhD at the University of Cambridge, UK. She has gained significant international recognition for her work, with recent honours including the Canada Excellence Research Chair in Photonic Quantum Science and Technologies, the Gates Cambridge Impact Prize, and the Royal Academy of Engineering UK’s Distinguished International Associateship. Sinha has also co-founded a quantum start-up, QuSyn Technologies, and leads a technical group under the NQM.
Meanwhile, as a mother raising a daughter, Sinha maintains a sense of work–life integration by being fully present – giving her complete attention to whatever requires it, whether personal or professional.
“Women in academia are breaking barriers as institutions embrace diversity,” says Sinha. “While explicit obstacles fall through targeted initiatives, the academic community now faces the vital challenge of identifying subtle biases woven into institutional fabric. This evolving awareness promises a future where talent thrives regardless of gender, transforming scholarship through diverse perspectives.”
Usha Devi A R
A professor at Bangalore University, Usha Devi A R is a theorist who has contributed to formulating figures of merit for non-classicality of photonic states – which are crucial for metrology, quantum target detection, quantum digital reading and more. Her team has put forth geometric visualization of spin states, which works like a fingerprint for entanglement and spin-squeezing, needed in metrology.
Devi was born in Thirthahalli town in Karnataka, where she completed her undergraduate degree in sciences. She was top of her class and received a gold medal for her master’s in physics from Mysore University, where she also completed her PhD in 1998. She received the IPA young physicist award in 1997, and was a visiting scientist in Barry Sander’s research group at Macquarie University in Sydney, Australia, in 2003. She also worked in Sandu Popescu’s research group at University of Bristol, UK, under a Commonwealth Academic Fellowship in 2008.
Working as a faculty member at a state-funded university comes with persistent challenges, such as limited resources for research and teaching, and sometimes outdated administrative priorities. “In quantum mechanics, we embrace uncertainty,” Devi says. “In academia, we challenge it – especially as women physicists from state universities.”
Kasturi Saha
Kasturi Saha is an associate professor at the Indian Institute of Technology (IIT) Bombay (Mumbai). She is the project director of Qmet Tech Foundation, the quantum sensing and metrology hub established by IIT Bombay under the National Quantum Mission (NQM) of the Government of India. She is the only female project director among the four NQM hubs established.
Saha was raised in the lively heart of Kolkata’s Wellington Square, in a family filled with engineers and doctors. Drawn to the elegance of physics, she chose it as her major, inspired by the Nobel-winning work on Bose–Einstein condensates. Although she aspired to become a scientist, her decision was initially met with concern and scepticism from her family, who were worried about the challenges of pursuing a career in science – especially as female representation was (and still is) limited.
Despite their concerns, Saha’s parents stood firmly by her side, supporting her throughout every step of her academic journey. After her undergraduate physics degree from St Stephen’s College in Delhi, Saha moved to IIT Delhi for her master’s, and then went to Cornell University in the US for her PhD. As she progressed through her degrees, the gender gap became increasingly apparent, with a sharp decline in the number of women.
Training to be an experimental physicist brought its own set of biases – people often assumed Saha couldn’t handle technical tasks or heavy equipment. These subtle yet persistent doubts made her hyper-aware of her identity – she even stopped wearing pink T-shirts during her PhD. Yet, she persisted, bolstered by mentors including Michal Lipson and Paola Cappellaro.
Beyond academia
Impressive women in quantum science are not limited to academia. Government departments and industry in India can boast of some prominent female leaders. For example, Anindita Banerjee is a product manager for quantum technology projects at the Centre for Development of Advanced Computing (CDACINDIA), a premier research and development organization founded by the Ministry of Electronics and Information Technology. Anupama Ray is an award-winning senior research scientist at IBM Research in Bangalore, where she focuses on developing quantum machine learning algorithms. Meanwhile at Microsoft India and South Asia, Rohini Srivathsa is the chief technology officer, responsible for driving technology innovation and growth across industry and the government.
In addition to the accomplished Indian women working in quantum in their home country, there are several who have built successful careers abroad. Notable cases are Anjana Devi, director of the Institute for Materials Chemistry at the Leibniz Institute for Solid State and Materials Research, Dresden, Germany; Nandini Trivedi, professor of physics at Ohio State University, US; Nilanjana Datta, professor in quantum information theory at the University of Cambridge, UK; Vidya Madhavan, professor of physics at the University of Illinois Urbana-Champaign, US; Shohini Ghose, professor of physics and computer science, and director of research and programmes for the Centre for Women in Science at Wilfrid Laurier University in Waterloo, Canada, and chief technology officer at Quantum Algorithms Institute.
The rise of women in quantum science in India is a tribute to Bose’s legacy, and a sign of a more inclusive and dynamic future. To sustain this momentum, we must create ecosystems that support curiosity, collaboration and equal opportunity – ensuring that every brilliant mind, regardless of gender, has the chance to transform the world.
Researchers in Japan have accelerated muons into the most precise, high-intensity beam to date, reaching energies high as 100 keV. The achievement could enable next-generation experiments such as better measurements of the muon’s anomalous magnetic moment – measurements that could, in turn, that point to new physics beyond the Standard Model.
Muons are sub-atomic particles similar to electrons, but around 200 times heavier. Thanks to this extra mass, muons radiate less energy than electrons as they travel in circles – meaning that a muon accelerator could, in principle, produce more energetic collisions than a conventional electron machine for a given energy input.
However, working with muons comes with challenges. Although scientists can produce high-intensity muon beams from the decay of other sub-atomic particles known as pions, these beams must then be cooled to make the velocities of their constituent particles more uniform before they can be accelerated to collider speeds. And while this cooling process is relatively straightforward for electrons, for muons it is greatly complicated by the particles’ short lifetime of just 2 ms. Indeed, traditional cooling techniques (such as synchrotron radiation cooling, laser cooling, stochastic cooling and electron cooling) simply do not work.
Another muon cooling and acceleration technique
To overcome this problem, researchers at the MUon Science Facility (MUSE) in the Japan Proton Accelerator Research Complex (J-PARC) have been developing an alternative muon cooling and acceleration technique. The MUSE method involves cooling positively-charged muons, or antimuons, down to thermal energies of 25 meV and then accelerating them using radio-frequency (rf) cavities.
In the new work, a team led by particle and nuclear physicist Shusei Kamioka directed antimuons (μ+) into a target made from a silica aerogel. This material has a unique property: a muon that stops inside it gets re-emitted as a muonium atom (an exotic atom consisting of an antimuon and an electron) with very low thermal energy. The researchers then fired a laser beam at these low-energy muonium atoms to remove their electrons, thereby producing antimuons with much lower – and, crucially, far more uniform – velocities than was the case for the starting beam. Finally, they guided the slowed particles into a rf cavity, where an electric field accelerated them to an energy of 100 keV.
Towards a muon accelerator?
The final beam has an intensity of 2 × 10−3 μ+ per pulse, and a measured emittance that is much lower (by a factor of 2.0 × 102 in the horizontal direction and 4.1 × 102 vertically) than the starting beam. This represents a two-orders-of-magnitude reduction in the spread of positions and momenta in the beam and makes accelerating the muons more efficient, says Kamioka.
According to the researchers, who report their work in Physical Review Letters, these improvements are important steps on the road to a muon collider. To make further progress, however, they will need to increase the beam’s energy and intensity even further, which they acknowledge will be challenging.
“We are now preparing for the next acceleration test at the new experimental area dedicated to muon acceleration,” Kamioka tells Physics World. “A 4 MeV acceleration with 1000 muon/s is planned for 2027 and a 212 MeV acceleration with 105 muon/s is planned for 2029.”
In total, the MUSE team expects that various improvements will produce a factor of 105–106 increase in the muon rate, which could be enough to enable applications such as the muon g−2/EDM experiment at J-PARC, he adds.
In 2018, the Muon g-2 Experiment at Fermilab near Chicago, set out to measure the muon’s anomalous magnetic moment to a precision of 140 parts per billion (ppb). This component of the muon’s magnetic moment is the result of several subtle quantum effects and is also known as the muon g-2 – which reflects how the gyromagnetic ratio of the muon deviates from the simple value of two.
After six years of producing, storing, and measuring more than a trillion muons, the collaboration released its long-anticipated final result in June, achieving an unprecedented precision of 127 ppb. This landmark measurement not only solidifies confidence in the experimental value of muon g-2 but also sets a new benchmark as the most precise accelerator-based measurement of a fundamental particle to date.
Studies of the muon g-2 have served as a rigorous test of the Standard Model – physicist’s leading theory describing known particles and forces – for much of the last century. Theoretically, the muon’s anomalous magnetic moment can be predicted from the Standard Model to a similar precision as the experiment. For decades, a persistent discrepancy between prediction and measurement hinted at the possibility of new physics, with experimental results favouring a higher value than the theory. Such a difference, if confirmed, could point to phenomena not accounted for in the Standard Model – potentially explaining unresolved mysteries like the existence of dark matter.
However, extraordinary claims require extraordinary scrutiny. To address the experimental side, Fermilab launched the Muon g-2 Experiment. On the theoretical side, the Muon g-2 Theory Initiative was established as a global collaboration of theorists working to refine the Standard Model prediction using state-of-the-art methods, techniques, and input data.
Problematic contribution
One of the most problematic contributions to the theoretical value is the hadronic vacuum polarization (HVP), historically determined using experimental data as input to complex calculations. While the Theory Initiative has improved these methods, progress has remained limited due to discrepancies in the available experimental data. Crucially, a recent input from the CMD-3 Experiment diverged significantly from previous results, suggesting a larger HVP contribution (see figure below). This, in turn, yields a Standard Model prediction that aligns with the new Fermilab measurement – apparently eliminating the discrepancy and, with it, any evidence of new physics.
Evolving results Summary of the four values of the anomalous magnetic moment of the muon aμ that have been obtained from different experiments and models. The most recent (2025) theory and experiment values are in agreement. (Courtesy: Alex Keshavarzi)
Despite years of investigation, the origin of the CMD-3 tension remains unknown. Its result stands in contrast to a vast catalogue of earlier data from multiple experiments over decades. As a result, the traditional, data-driven approach to estimating the HVP is deemed currently unable to produce a reliable estimate .
Thanks to the efforts of the Theory Initiative, however, the HVP can now also be calculated using lattice QCD (quantum chromodynamics) simulations on supercomputers, reaching a precision comparable to that of the data-driven methods. Multiple independent lattice QCD groups have arrived at consistent values, which also agree with the Fermilab measurement, indicating no discrepancy and thus no sign of new physics. This computational feat, once considered out of reach, marks a major breakthrough. Yet, the tension remains unresolved: Why do lattice QCD and CMD-3 agree, while both conflict with decades of experimental data?
No physics beyond the Standard Model
Given the improved control in lattice QCD, the Theory Initiative has also recently updated its recommended Standard Model prediction with the HVP fully based on lattice results. The resulting value agrees with the Fermilab measurement and currently implies no evidence for physics beyond the Standard Model. However, the Initiative has emphasized that this is far from conclusive. Future predictions are intended to incorporate data-driven estimates again – once the inconsistencies in the experimental input are resolved.
The field now faces two possibilities. One is that the CMD-3 result and lattice QCD are correct. In this case, there is no new physics – but an impressive validation of the Standard Model. The other scenario is that new experimental HVP input data align with the older results, supporting a smaller HVP contribution. This would reintroduce the discrepancy with the Fermilab result, reviving the exciting possibility of new physics. In either case, the inconsistencies between CMD-3, lattice QCD, and the existing data must be explained.
So, is there new physics or not? We know there must be. The Standard Model cannot not explain dark matter, the accelerating expansion of the universe, the absence of antimatter, or the quantum nature of gravity. Precision tests like muon g-2 offer a window into this unknown. That window has not closed – for now it’s propped open.
Where we’ll be in five years is uncertain. The Muon g-2 Theory Initiative will continue to refine predictions and resolve open questions. For now, one thing is clear: the Muon g-2 Experiment at Fermilab has delivered an historic achievement and its legacy will continue to contribute to our understanding of fundamental physics for decades to come.
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