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All-optical technique shines a light on electronic band structure

A new technique for measuring the electronic band structure of solid materials has been unveiled by physicists in Canada. The new method does not require the sample to be placed in a vacuum chamber and can also probe the bulk of a sample – something that some other techniques cannot do. The team believes that its new method could be particularly useful for studying matter under extreme conditions, including samples under extremely high pressure in a diamond anvil.

Angle-resolved photoemission spectroscopy (ARPES) is an important laser-based method for studying the electronic band structure of solid materials. Photons with enough energy to eject electrons from a material are fired at a sample and the energy and momenta of the emitted electrons are then measured. This information reveals the structure of the electronic bands in terms of the energy and momentum of the electrons within them.

Surface science

ARPES has been used extensively by physicists to study a wide range of materials including semiconductors and superconductors – but the technique has some important limitations. Measurements must be done in an ultra-high vacuum (UHV) because the emitted electrons are scattered and absorbed by air. Also, ARPES only probes a thin layer of material near the surface of the sample because the electrons cannot escape from deeper in the bulk.

Now, Paul Corkum and colleagues at the University of Ottawa, the Institut National de la Recherche Scientifique and the National Research Council of Canada have developed a new all-optical technique for studying the band structure of solids that overcomes these problems.

The technique involves exposing a sample to intense pulses of laser light, but with a photon energy much lower than that required to eject an electron from the material. There is a very large electric field associated with such a pulse, which causes an electron to quantum-mechanically tunnel from the top of the valence band to the bottom of the conduction band, thus creating a hole in the conduction band. The electron and hole are then driven by the electric field to high momenta in opposite directions. The electric field itself oscillates, and when the field direction switches, the electron and hole both reverse direction and are reunited. At this point, the electron and hole recombine, giving off a photon that can escape the material and be detected. The energy of the photon is equal to the energy gap between the valence and conduction band at the point of recombination.

To measure the momentum of the electron at recombination, Corkum and colleagues fire a much dimmer pulse from a different-coloured laser light at the sample, at the same time as the intense pulse. By measuring the intensity of the emitted light as a function of the phase between the light in the two laser pulses, the team can work out the momentum of the electron that recombined to produce the emitted photon.

Chemical processes

The electron–hole recombination process occurs very quickly, and this combined with the use of very short laser pulses means that the technique could be used to study changes in band structure over very short timescales.

Corkum says that the technique could prove particularly useful for studying materials under great pressure in a diamond anvil, because diamond is transparent to the laser light used to make the measurements. The method could be used to look at how the band structure of a material changes during catalysis and other chemical processes that cannot be studied in UHV. The study of materials in very high magnetic fields, which would deflect ARPES electrons, should also be possible.

The technique is described in Physical Review Letters.

Radiation blasts render Earth's twin inhospitable to life

Radioactive? Kepler-438b is regularly irradiated by huge flares of radiation from its host star. (Courtesy: Mark A Garlick/University of Warwick)

By Tushna Commissariat

In the past decade or two, exoplanetary research has been booming as NASA’s Kepler telescope and its cohorts have found nearly 2000 exoplanets and 5000 promising candidates. Unsurprisingly, we have been searching long and hard for those planets that could be habitable or are as similar in shape, size and proximity to the host star as the Earth is to the Sun. Indeed, in January this year Kepler scientists announced that they had found the most Earth-like planet to date – Kepler-438b – orbiting within the habitable zone of its host star, the red dwarf Kepler-438, which lies about 470 light-years from Earth.

The planet, which is slightly bigger than our own, was found to be rocky, and, thanks to its location, rather temperate, meaning that it could have flowing water on it – two key factors that astronomers look for when accessing a planet’s habitability. Unfortunately, David Armstrong of the University of Warwick in the UK and colleagues have now found that Earth’s twin is regularly bathed in vast quantities of radiation from its star – a real dampener when it comes to the formation of life as we known it.

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Revealing the hidden connection between pi and Bohr’s hydrogen model

A nearly 400 year-old formula for pi has been spotted in a quantum-mechanics formula for the energy states of the hydrogen atom, according to researchers in the US. Derived by English mathematician John Wallis in 1655, the original formula calculates pi as the product of an infinite series of ratios – it has now emerged from a solution of physicist Niels Bohr’s early 20th-century hydrogen-atom model, which most budding physicists learn.

University of Rochester physicist Carl Hagen was designing homework problems for his graduate quantum-mechanics class when a particular exercise for the hydrogen atom intrigued him. It posed a twist on the Bohr model of hydrogen, which approximates the atom as an electron orbiting a point-like positive nucleus in circles. The Bohr model, while not an accurate description of an atom, is often close enough to the real thing in many situations. It is especially so when teaching physics, because it is one of the few systems that can be solved analytically by Schrödinger’s equation – that is, it can be solved exactly, rather than making approximations or using a computer program.

Varying homework

But instead of solving the Bohr-model problem, Hagen applied the “variational principle” – a technique usually reserved for approximating quantum-mechanical systems that cannot be solved analytically with the Schrödinger equation. The technique involves making an educated guess of the hydrogen’s wavefunction and then optimizing that guess. Hagen found that as the atom’s orbital angular momentum increased, the allowed energies of the predicted atom approached and gradually equalled the analytically found hydrogen energies. Indeed, Hagen noticed that the error of the variational approach was about 15% for the ground state of hydrogen, 10% for the first excited state, and kept decreasing as the excited states grew larger. This was unusual, because the variational approach normally works best for approximations of the lowest energy levels.

Hidden formula

Hagen turned to his colleague, mathematics professor Tamar Friedmann, who found that they could derive Wallis’s infinite product from the ratio of the approximate energies to the exact energies. Friedmann points out how unexpected it is that a centuries-old math formula, derived under completely different motivations, has been lurking in a basic quantum-mechanics problem. Wallis’s original 1655 infinite-series formula, published in his book Arithmetica infinitorum, predates Newton’s invention of calculus, and arose when he was trying to relate the area of a square to the circle inscribed within it.

“Wallis couldn’t have possibly known [the trend] would show up in the hydrogen atom because no-one knew about the hydrogen atom then,” Friedmann says. She adds that, while the formula could have been found ever since Bohr developed his model in 1913, the pair were the first to spot it, probably thanks to their interdisciplinary experience. Their findings suggest that more mathematical formulae could lie in wait in other seemingly well-studied systems.

Universal pi?

“I’m not surprised that pi is in there. Pi is everywhere,” says Drew Milsom, a physicist at the University of Arizona. While the most obvious appearance of pi is the ratio of a circle’s circumference to its diameter, Milsom cites another example in probability studies – known as “Buffon’s needle problem” – that finds that the probability of a falling matchstick landing between two lines is related to pi. What is more surprising, Milsom says, is that Hagen and Friedmann decided to use the variational principle and actually recognized the Wallis formula, which is obscure to most physicists.

It is ultimately unsurprising that the pi formula emerged from the quantum solution because, as Friedmann herself points out, “mathematical formulae come up in physics all the time”. She adds that finding the link “is a manifestation of the ultimate connection between math and physics”, but whether there exists some deeper, fundamental correlation between the two remains unknown.

“Once you see it, it’s clear and beautiful and you can understand it, even if you weren’t able to derive it,” says Friedmann, adding that it could now even be taught to undergraduates. “Physical problems inspire questions in mathematics and vice versa,” Friedmann says. “Mathematics is the language that describes physics. Learning one helps enrich the other.”

The research is described in the Journal of Mathematical Physics.

Is there life on Mars?

In this November episode of the Physics World podcast, astrobiologist Lewis Dartnell addresses these big questions in a conversation with journalist James Dacey. Dartnell’s own research is concerned with examining the micro-organisms that can survive in some of the most extreme conditions here on Earth. By studying the physiology and survival tactics of these so-called extremophiles, astrobiologists hope to gain an understanding of the type of life that could survive in a place like the Martian surface – and where to look for these hardy little creatures on alien worlds.

Dartnell was speaking ahead of a public lecture he gave in London about the possibilities of life beyond the Earth. As well as discussing what we already know about the Martian surface, Dartnell talked about the new possibilities that will come with ExoMars, a mission by the European Space Agency (ESA) set for launch in 2018. Dartnell is working on the design of a Raman-spectroscopy instrument for that mission that will help examine the mineralogy of Mars and identify potential signs of life inside Martian rocks.

The talk was held in an underground tunnel near King’s Cross Station – a venue that resembles the kind of provisional habitat that humans would have to create should we attempt to live on Mars. Watch some highlights from that talk, along with reaction from the audience, in the video above. In addition, the November issue of Physics World is a special issue about extremes in physics, including a feature about how physicists are helping to uncover some of the mysteries of extremophiles on Earth. It includes more about Lewis’ favourite little critter: Deinococcus radiodurrans. Find out how to access that issue here.

Making noise in the quietest room in the Netherlands

Wiggling electrons: an undulator at one of FELIX’s free-electron lasers.

By Tim Wogan in Nijmegen, the Netherlands

Tucked away near the German border is the Dutch city of Nijmegen and Radboud University, which has a treasure trove of fantastical physics facilities. I was in town for a two-day, whistle-stop tour of the university that included the the opening of the FELIX facility. FELIX stands for “free-electron laser for infrared experiments laboratory”. It is a  cavernous chamber housing four free-electron lasers that together can generate high-intensity, tunable radiation with wavelengths anywhere between 3–1500 μm. Something, I was told, that is possible nowhere else in the world.

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Arecibo Observatory faces uncertain future as boss quits

The future of the iconic Arecibo Observatory is at stake following the resignation of Robert Kerr, the facility’s director and principal investigator. Kerr’s departure is reportedly because of the way the National Science Foundation (NSF), which owns the observatory, has sought alternative sources of funding to keep the facility running.

The NSF is facing tight budget constraints following the construction of new facilities such as the Large Synoptic Survey Telescope in Chile. In late October, the foundation sent a letter to the scientific community requesting “viable concepts for the future [of Arecibo]” by the end of the year. Arecibo is a 52-year-old radio telescope with a 305 m collection dish built into a sinkhole depression in Puerto Rico.

Funding cuts

Although work carried out at the facility led to Russell Hulse and Joseph Taylor winning the 1993 Nobel Prize for Physics for discovering the first binary pulsar, a 2006 report from the NSF recommended reducing Arecibo’s annual funding from $10.5m to $4.0m. After lobbying by researchers, the NSF was able to cobble together sufficient funds to keep the observatory open. NASA, for example, adds funding of $2m each year to support the hunt for asteroids that could threaten Earth.

But the financial pressures continue, as funds for Arecibo’s operation compete with research grants for astronomers. The observatory’s situation was not helped by the need for repairs following a magnitude-six earthquake that hit the facility in January 2014.

Search for intelligent life

Earlier this year, Kerr, who had been director since 2011, thought he had a solution: the Breakthrough Listen project – a 10-year, $100m search for intelligent life in the universe that was set up by the Russian entrepreneur Yuri Milner in July. Later that month, Kerr told Scientific American that the project offered to buy observing time on the radio telescope. Yet the NSF – Kerr claims – indicated that accepting the deal would mean the loss of further NSF funding, an action that could, according to Kerr, lead to the “cessation of science operations, and possibly closure”.

The NSF has denied that threat, although it concedes that it could reduce funding if an organization such as Breakthrough Listen takes up some of Arecibo’s observing time. Kerr says that the NSF and SRI International – the contractor that operates the facility together with academic partners – withdrew contact with him following his comments in Scientific American. Kerr resigned as director in October after losing his position as principal investigator.

Astronomer Michael Nolan of the University of Arizona’s Lunar and Planetary Laboratory, who preceded Kerr as Arecibo director, told physicsworld.com that since Kerr stepped down, SRI International has sent in management staff to keep the facility running. Nolan admits that he does not know of any organization that would be willing to take over the operation of Arecibo from the NSF.

Marking time on precision engineering

Adventures in science: the Magna centre in Rotherham, UK
Adventures in science: the Magna centre in Rotherham, UK.

By Susan Curtis

At a time when the UK steel industry is close to meltdown, it felt quite humbling to be standing inside a disused steelworks on the outskirts of Rotherham. In its heyday in the 1970s the colossal plant employed 3000 people and housed six electric arc furnaces that set new records for steel production. Since closing in 1993, the facility has forged a new identity as the Magna Science Adventure Centre, which offers visitors an insight into the steel-making process and its heritage in the area around Sheffield.

Recently, I was at Magna for the annual TRAM conference, which showcases the latest technology advances in the aerospace industry. Organized by the Advanced Manufacturing Research Centre (AMRC), one of the UK’s Catapult centres based at the University of Sheffield and supported by Boeing, TRAM highlights how aircraft makers and their suppliers are improving materials and manufacturing processes to reduce cost and enhance performance. But among the talk of powder metallurgy, high-performance machining and the factories of the future, a presentation by Nick English from the UK-based watchmaker Bremont highlighted manufacturing innovation at a much smaller scale.

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Comic book fusion, Nathan Myhrvold on innovation, and picking winners of the Global Physics Photowalk

Comic book physics. (Courtesy: PPPL)

By Hamish Johnston

The comic book artist Frank Espinosa and Princeton University’s Sajan Saini have joined forces to create a comic book called A Star For Us. The book begins with a brief history of our understanding of nuclear fusion in the Sun and goes on to chronicle the challenges of creating a mini-Sun here on Earth.

Espinosa and Saini – who is a physicist turned professor of writing – spent time with physicists at the Princeton Plasma Physics Laboratory. Espinosa says that he was impressed by the researchers enthusiasm for the future of fusion energy. “I was trying to channel that energy of hope,” he explains.

“The mood of the comic tries to really capture a sense of a vast cosmic scale being made palpable, being made into something that we can realize within our own hands,” says Saini. I agree and you can judge for yourself by downloading a PDF of the comic book free of charge.

The physicist and former chief technology officer at Microsoft, Nathan Myhrvold, has a nice essay in Scientific American about the roles of the private and public sectors in driving technological innovation. He explains that when Microsoft Research was created in 1991, the company was keen on not making the same mistakes as AT&T, IBM and Xerox – which were all in the process of winding down their world-famous research labs. The problem was that these firms funded research in areas that they were not immediately able to exploit commercially. Myhrvold points out that many of the technologies first developed in those labs – including the transistor and giant magnetoresistance data storage – made much more money for fast-moving competitors such as Microsoft than they did for the companies that did the basic research.

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Astronomers gaze upon the oldest stars in the galaxy

The oldest stars in our Milky Way galaxy have been discovered by an international team of researchers. These ancient stars could contain vital clues about how the first stars in the early universe died, and their discovery marks the first time that extremely metal-poor stars have been observed in the central region of the galaxy. The location of the stars suggests that they formed when the Milky Way underwent rapid chemical changes during the first 1–2 billion years of the universe.

After the Big Bang, only elements such as hydrogen, helium and some trace amounts of lithium existed in the universe. Heavier elements such as oxygen, nitrogen, carbon and iron – referred to as “metals” by astronomers – were forged in the extremely high-pressure centres of the first massive stars, which are predicted to have formed within 200 million years after the Big Bang. The metals were scattered across the cosmos when these first stars, known as “population III” stars, quickly burned out and exploded in supernovae. These explosions seeded the universe with the metals to form “population II” stars, which are still “metal-poor” compared with “population I” stars like the Sun.

Not the stars we are looking for?

A true first population-III star has not yet been discovered, although the best evidence for them was found earlier this year in an extremely bright and distant galaxy in the early universe. Astronomers believe that old metal-poor stars would have formed in the central regions or the “bulges” of galaxies, where the effects of gravity were the strongest. The Milky Way bulge underwent a rapid chemical enrichment in the early universe, and this should have created a host of metal-poor stars – indeed, we should find them there even today. However, metal-poor stars have only been found in the outer regions or the “halo” of the Milky Way and not at its centre.

Now, Louise Howes of the Australian National University in Canberra and an international team have used the SkyMapper telescope to identify nearly 500 extremely metal-poor stars in the Milky Way bulge. The team also confirmed that most of these old stars are in tight orbits around the galactic centre, rather than being halo stars passing through the bulge. The researchers also found that the chemical compositions of these stars are, for the most part, similar to typical halo stars of the same metal content (or metallicity). However, some unexpected differences exist when it comes to the amount of carbon in such stars.

Stars with a low metal content look slightly bluer than others, so the team could sift through the millions of stars at the centre and whittle the observations down to 14,000 promising candidates. From those, the researchers identified 500 stars that had less than 100th the amount of iron in the Sun, making it the first extensive catalogue of metal-poor stars in the bulge. Of these, Howse and colleagues focused on 23 candidates that were the most metal-poor, and from these data, they homed in on nine stars with a metal content less than 1000th of the amount seen in the Sun. This includes one star with an iron abundance 10,000 times lower than that of the Sun – now the record-breaker for the most metal-poor star in the centre of the galaxy.

To and fro

To ensure that these stars were truly old – and not those that had formed much later in other parts of the galaxy that were not as dense and are now merely passing through the centre – the researchers used precise measurements and computer simulations to plot the stars’ movement in the sky. This allowed them to predict where the stars came from and where they were moving to. The team found that while some stars were indeed just passing through, seven of them were formed in the bulge and had remained there since.

“These pristine stars are among the oldest surviving stars in the universe, and certainly the oldest stars we have ever seen,” says Howes. “These stars formed before the Milky Way, and the galaxy formed around them.” While it is currently not possible to directly determine the ages of these ancient stars, the researchers say that it could be inferred from data collected by the extended Kepler mission or its successors.

The team’s discovery also challenges current theories about the environment of the early universe from which these stars formed. “The stars have surprisingly low levels of carbon, iron and other heavy elements, which suggests the first stars might not have exploded as normal supernovae,” says Howes. “Perhaps they ended their lives as hypernovae – poorly understood explosions of probably rapidly rotating stars, producing 10 times as much energy as normal supernovae.” If true, such hypernovae would be one of the most energetic things in the universe, and very different from the kinds of stellar explosions that we see today.

The research is published in Nature.

Physicists put the arrow of time under a quantum microscope




Disorder, or entropy, in a microscopic quantum system has been measured by an international group of physicists. The team hopes that the feat will shed light on the “arrow of time”: the observation that time always marches towards the future. The experiment involved continually flipping the spin of carbon atoms with an oscillating magnetic field and links the emergence of the arrow of time to quantum fluctuations between one atomic spin state and another.

“That is why we remember yesterday and not tomorrow,” explains group member Roberto Serra, a physicist specializing in quantum information at the Federal University of ABC in Santo André, Brazil. At the fundamental level, he says, quantum fluctuations are involved in the asymmetry of time.

Egging on

The arrow of time is often taken for granted in the everyday world. We see an egg breaking, for example, yet we never see the yolk, white and shell fragments come back together again to recreate the egg. It seems obvious that the laws of nature should not be reversible, yet there is nothing in the underlying physics to say so. The dynamical equations of an egg breaking run just as well forwards as they do backwards.

Entropy, however, provides a window onto the arrow of time. Most eggs look alike, but a broken egg can take on any number of forms: it could be neatly cracked open, scrambled, splattered all over a pavement, and so on. A broken egg is a disordered state – that is, a state of greater entropy – and because there are many more disordered than ordered states, it is more likely for a system to progress towards disorder than order.

This probabilistic reasoning is encapsulated in the second law of thermodynamics, which states that the entropy of a closed system always increases over time. According to the second law, time cannot suddenly go backwards because this would require entropy to decrease. It is a convincing argument for a complex system made up of a great many interacting particles, like an egg, but what about a system composed of just one particle?

Murky territory

Serra and colleagues have delved into this murky territory with measurements of entropy in an ensemble of carbon-13 atoms contained in a sample of liquid chloroform. Although the sample contained roughly a trillion chloroform molecules, the non-interacting quantum nature of the molecules meant that the experiment was equivalent to performing the same measurement on a single carbon atom, one trillion times.

Serra and colleagues applied an oscillating external magnetic field to the sample, which continually flipped the spin state of a carbon atom between up and down. They ramped up the intensity of the field oscillations to increase the frequency of the spin-flipping, and then brought the intensity back down again.

Had the system been reversible, the overall distribution of carbon spin states would have been the same at the end as at the start of the process. Using nuclear magnetic resonance and quantum-state tomography, however, Serra and colleagues measured an increase in disorder among the final spins. Because of the quantum nature of the system, this was equivalent to an increase in entropy in a single carbon atom.


”It’s easier to dance to a slow rhythm than a fast one”
Roberto Serra, Federal University of ABC 


According to the researchers, entropy rises for a single atom because of the speed with which it is forced to flip its spin. Unable to keep up with the field-oscillation intensity, the atom begins to fluctuate randomly, like an inexperienced dancer failing to keep pace with up-tempo music. “It’s easier to dance to a slow rhythm than a fast one,” says Serra.

Many questions remain

The group has managed to observe the existence of the arrow of time in a quantum system, says experimentalist Mark Raizen of the University of Texas at Austin in the US, who has also studied irreversibility in quantum systems. But Raizen stresses that the group has not observed the “onset” of the arrow of time. “This [study] does not close the book on our understanding of the arrow of time, and many questions remain,” he adds.

One of those questions is whether the arrow of time is linked to quantum entanglement – the phenomenon whereby two particles exhibit instantaneous correlations with each other, even when separated by vast distances. This idea is nearly 30 years old and has enjoyed a recent resurgence in popularity. However, this link is less to do with growing entropy and more to do with an unstoppable dispersion of quantum information.

Indeed, Serra believes that by harnessing quantum entanglement, it may even be possible to reverse the arrow of time in a microscopic system. “We’re working on it,” he says. “In the next generation of our experiments on quantum thermodynamics we will explore such aspects.”

The research is described in Physical Review Letters.

  • What is time? was chosen by Physics World editors as one of the five biggest unanswered questions in physics. In the 25th anniversary issue of the magazine (published in 2013) Adam Frank chronicles what we know and don’t know about the mysterious fourth dimension
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