You may never have heard of an “inverse problem”, but as Roy Pike of King’s College London explains in this video, it is a way of looking at many different questions within science. It refers to a method of estimating data that are not there. Or to be more precise, it refers to the process of estimating data that are not obtainable using direct measurements – perhaps because they are lost during an experiment, or perhaps because they were never measured accurately in the first place.
Pike gives the example of a pinhole camera used to produce an image of an object. A “direct problem” would be to work out how the image will appear, which can be done by using tools such as Maxwell’s equations and propagation diffraction theory to calculate how the light will disperse. An “inverse problem”, however, would be to calculate the nature of the object based on the data contained in the image you have produced, as some data are inevitably not present, particularly at the blurred edges of the image. “The direct problem is relatively easy, the inverse one is impossible,” says Pike.
In order to make educated guesses at the missing data in these situations, researchers such as Pike have a range of mathematical tools at their disposal.
You can also watch this video about how an inverse approach is being applied within speech science.
A quantum analogue of data compression has been demonstrated for the first time in the lab. Physicists working in Canada and Japan have squeezed quantum information contained in three quantum bits (qubits) into two qubits. The technique could pave the way for a more effective use of quantum memories and offers a new method of testing quantum logic devices.
Compression of classical data is a simple procedure that allows a string of information to take up less space in a computer’s memory. Given an unadulterated string of, for example, 1000 binary values, a computer could simply record the frequency of the 1s and 0s, which might require just a dozen or so binary values. Recording the information about the order of those 1s and 0s would require a slightly longer string, but it would probably still be shorter than the original sequence.
Quantum data are rather different, and it is not possible to simply determine the frequencies of 1s and 0s in a string of quantum information. The problem comes down to the peculiar nature of qubits, which, unlike classical bits, can be a 1, a 0 or some “superposition” of both values. A user can indeed perform a measurement to record the “one-ness” of a qubit, but such a measurement would destroy any information about that qubit’s “zero-ness”. What is more, if a user then measures a second qubit prepared in an identical way, he or she might find a different value for its “one-ness” – because qubits do not specify unique values but only the probability of measurement outcomes. This latter trait would seem to preclude the possibility of compressing even identical qubits, because there is no way of predicting what classical values they will ultimately manifest as.
A way forward
In 2010 physicists Martin Plesch and Vladimír Bužek of the Slovak Academy of Sciences in Bratislava realized that, while it is not possible to compress quantum data to the same extent as classical data, some compression can be achieved. As long as the quantum nature of a string of identically prepared qubits is preserved, they said, it should be possible to feed them through a circuit that records only their probabilistic natures. Such a recording would require exponentially fewer qubits, and would allow a user to easily store the quantum information in a quantum memory, which is currently a limited resource. Then at some later time, the user could decide what type of measurement to perform on the data.
“This way you can store the qubits until you know what question you’re interested in,” says Aephraim Steinberg of the University of Toronto. “Then you can measure x if you want to know x; and if you want to know z, you can measure z – whereas if you don’t store the qubits, you have to choose which measurements you want to do right now.”
Now, Steinberg and his colleagues have demonstrated working quantum compression for the first time with photon qubits. Because photon qubits are currently very difficult to process in quantum logic gates, Steinberg’s group resorted to a technique known as measurement-based quantum computing, in which the outcomes of a logic gate are “built in” to qubits that are prepared and entangled at the same source. The details are complex, but the researchers managed to transfer the probabilistic nature of three qubits into two qubits.
A nice trick
Plesch says that this is the first time that compression of quantum data has been realized, and believes Steinberg and colleagues have come up with a “nice trick” to make it work. “This approach is, however, hard to scale to a larger number of qubits,” Plesch adds. “Having said that, I consider the presented work as a very nice proof-of-concept for the future.”
Steinberg thinks that larger-scale quantum compression might be possible with different types of qubits, such as trapped ions, which have so far proved easier to manage in large ensembles. A practical use for the process would be in testing quantum devices using a process known as quantum tomography, in which many identically prepared qubits are sent through a quantum device to check that it is functioning properly. With quantum compression, says Steinberg, one could perform the tomography experiment and then decide later what aspect of the device you wanted to test.
But in the meantime, says Steinberg, the demonstration provides another perspective on the strangeness of the quantum world. “If you had a book filled just with ones, you could simply tell your friend that it’s a book filled with ones,” he says. “But quantum mechanically, that’s already not true. Even if I gave you a billion identically prepared photons, you could get different information from each one. To describe their states completely would require infinite classical information.”
CERN has been celebrating its 60th anniversary all this month, but it was in fact six decades ago today – on Wednesday 29 September 1954 – that the lab’s convention was ratified by its first 12 member states: Belgium, Denmark, France, Germany, Greece, Italy, the Netherlands, Norway, Sweden, Switzerland, the UK and Yugoslavia.
It’s been five days since the metaphorical dust settled on the apparent “discovery” of the B-mode polarization of the cosmic microwave background that was reported in March. The claim came from the team behind the Background Imaging of Cosmic Extragalactic Polarization (BICEP2) telescope at the South Pole, and much has been said since about what was then hailed as one of the biggest scientific discoveries of the decade.
One of my favourite radio programmes is The Life Scientific, in which the physicist Jim Al-Khalili talks to leading scientists about their lives and work. Al-Khalili introduces this week’s guest as “the pin-up of particle physics”, whose remarkable career has taken him from playing keyboards in pop bands, to winning a Royal Society University Research Fellowship to do particle physics, to hosting one of the BBC’s most popular science programmes.
Physics in Japan is set for a major boost after the education ministry asked for a massive 18% increase for its 2015 science and technology budget to take it to $11.1bn. Support for major facilities – including the SPring-8 synchrotron and the SACLA X-ray free-electron laser, both in Hyōgo Prefecture, and the Japan Proton Accelerator Research Complex (J-PARC) in Tokaimura – would rise 15.6% to $960m. The finance ministry, however, is likely to squeeze the requested amounts before the budget, which takes effect from next April, goes before the legislature in December.
The money for SACLA and SPring-8 would mean the facilities could run for an additional 750 and 1000 hours, respectively, and also fund an upgrade at SACLA. At J-PARC, the cash would go on overall operations plus maintenance and safety upgrades. The ministry’s request also includes $11m to finish the Large-Scale Cryogenic Gravitational Wave Telescope (also known as KAGRA).
Built in the Ikenoyama Mountain in Kamioka, KAGRA features two 3 km-long arms forming an “L” for the detector plus two access tunnels. Some 7.7 km of tunnels were completed earlier this year that will be used for the experiment. “[The budget allocation] would allow us to complete equipment development and installation,” says KAGRA project director Takaaki Kajita, who is based at the University of Tokyo’s Institute for Cosmic Ray Research in Kashiwa. The facility is expected to be complete by the end of next year and start operations in 2017.
For ongoing international projects, the ministry is seeking $54m for Japan’s contribution to the Thirty Meter Telescope being built on Mauna Kea in Hawaii, as well as $260m for ITER, the experimental fusion reactor currently under construction in Cadarache, France.
The ministry also aims to spend $1m to continue studies for the proposed International Linear Collider (ILC), which Japan has expressed an interest in hosting. This year the government set up a committee to investigate the scientific case for the facility, with sub-committees looking at technical issues and cost. Satoru Yamashita, a physicist at the University of Tokyo who chairs Japan’s ILC Strategy Council, says the country took a step towards international support for the $10bn project with initial political-level discussions with the US in July. “There is still a lot to do,” adds Yamashita.
The list is long of unsolved problems in physics. Still, if you surveyed a number of people in the discipline they would probably agree on a few choices. There would be the question of why neutrinos have a small but significant mass, contradicting the zero mass specified by the current Standard Model of particle physics. Their lists would also include the nature of dark matter, that elusive substance that is thought to make up more than four-fifths of all matter in the universe. And there would probably also be a mention of why the universe is here at all – that is, why all the matter we see today was not annihilated by an equal amount of antimatter shortly after the Big Bang.
What if just one type of particle could solve all these problems? The idea may sound too simple to be true, but it is exactly the possibility raised by the sterile neutrino. A hypothetical particle that does not interact via any of nature’s four known forces except gravity, the sterile neutrino would be the universe’s most ghostly entity. Yet its effects would be very real: it could solve three of the biggest mysteries in physics, and maybe others besides.
Sterile neutrinos are not a new proposition – their theoretical history dates back to the 1970s – but until recently they have been only of niche interest. That is because for a long time the main driving force of particle physics has been pushing the “energy frontier” – the obvious example being the Large Hadron Collider (LHC) at the European lab CERN, which has been trying to crack open nature’s secrets with ever-stronger collisions. Once the LHC started to collect data in 2010, many physicists were expecting to be flooded with a torrent of new particles, particularly those given by supersymmetry – a popular theory that aims to solve many problems in physics by partnering the currently known elementary particles with a host of meatier “sparticles”. But when the LHC’s floodgates were opened, the river was dry: no new physics has been found.
With hopes for evidence of supersymmetry waning, lesser-studied topics such as sterile neutrinos are beginning to garner more attention. But disappointments at the high-energy frontier have not been the only prompt for a change in fashion. In the past few years, strong new evidence for sterile neutrinos has been found in nuclear reactors, bolstering the existing evidence from particle accelerators and radioactive sources. And, earlier this year, astrophysicists examining data from X-ray telescopes uncovered the first tentative evidence of sterile-neutrino dark matter in the distant cosmos. Emboldened by such results, many researchers are beginning to think the long-awaited breakthrough in particle physics may come not in a slew of different types of particle, but just one.
The long-awaited breakthrough in particle physics may come not in a slew of different particles but just one
“If we found a sterile neutrino, it would be the first time we were totally outside the Standard Model,” says experimental physicist Roxanne Guenette at the University of Oxford in the UK. “It would be a small extension, but with implications as important as discovering supersymmetry.”
Back to normality
The theoretical motivation for sterile neutrinos owes a lot to studies of normal neutrinos, which are sometimes called “active neutrinos” by comparison. These particles are themselves rather ghostly, interacting via only gravity and the weak force, and not via nature’s other two known forces, the strong and the electromagnetic. They were first proposed in the 1930s by the Austrian theorist Wolfgang Pauli to account for missing energy in nuclear decay, and were discovered about two decades later by experimental physicists including the Americans Clyde Cowan and Frederick Reines, the latter of whom won the 1995 Nobel Prize for Physics for the work. We now know that active neutrinos come in three types or “flavours”, one for each charged lepton: the electron neutrino, the muon neutrino and the tau neutrino (each with an associated antiparticle).
To and fro Nobel physicist Ray Davis demonstrated that neutrinos oscillate between different flavours, and therefore have mass. (Courtesy: Brookhaven National Laboratory)
According to the original Standard Model, these three neutrinos were supposed to be massless, but that criterion soon began to crumble. In 1968 a team led by Ray Davis at the Brookhaven National Laboratory in the US found that it could detect only about a third of the electron neutrinos predicted to be arriving at its detector from fusion processes in the Sun, a result that was confirmed 20 years later by the Kamiokande experiment in Japan. Then, in 1998, a larger version of Kamiokande called SuperKamiokande, or SuperK, confirmed another strange result, this time about neutrinos generated in the atmosphere by cosmic rays. Theoretical models had predicted that there ought to be twice as many muon neutrinos generated by cosmic rays as electron neutrinos – but the researchers found roughly equal numbers of each.
Together, these solar and atmospheric anomalies – which led to Nobel prizes in 2002 for Davis and for Masatoshi Koshiba of SuperK – demonstrated that neutrinos must change flavour or “oscillate” as they travel. In Davis’s experiment the detector was sensitive only to electron neutrinos, and had therefore been oblivious to those that had oscillated into muon or tau neutrinos en route from the Sun. Meanwhile, oscillations taking place between the atmosphere and ground level had skewed the precise ratio of muon-to-electron neutrinos that the SuperK researchers had expected.
The fact that neutrinos oscillate suggested that they had mass, for if they didn’t, they would travel at the speed of light, and would not experience any time in which to oscillate. More specifically, though, the oscillations suggested that the three flavour states of neutrinos – electron, muon and tau – were actually mixtures of three distinct mass states. A neutrino in a pure flavour state contains a certain ratio of these three mass states, but during propagation these get out of step with one another. After a distance, the ratio of the mass states can become so distorted that, upon detection, the neutrino manifests as a different flavour altogether; what was once a muon neutrino might instead appear as an electron neutrino; and so on.
Equal share The SuperKamiokande experiment in Japan confirmed that there are equal numbers of muon and electron neutrinos. (Courtesy: Kamioka Observatory, University of Tokyo)
Although oscillations imply mass, particle physicists struggle to directly measure the individual masses of active neutrinos because the masses are so small; instead, they have access only to the difference between squared masses – specifically, the difference between the first and second squared-mass states, Δm122, and the difference between the second and third squared-mass states, Δm232. These parameters can be calculated by studying neutrinos that have been generated in particle accelerators or nuclear reactors and then have travelled great distances, typically hundreds or thousands of kilometres. The energy of neutrinos, E, and the distance over which they oscillate, L, are the two most important parameters for calculating the squared-mass differences, because the probability of oscillation is a function of both Δm2 and L/E.
CurrentlyΔm122 looks to be about 7 × 10–5 eV2, whileΔm232 looks to be about 2.3 × 10–3 eV2, making active neutrinos more than a million times lighter than the next lightest particle, the electron. In 1996, however, physicists working on the Liquid Scintillator Neutrino Detector (LSND) experiment at the Los Alamos National Laboratory in the US found a considerable proportion of electron antineutrinos in a beam of muon antineutrinos generated in an accelerator just 30 m away. The neutrino energy and oscillation distance suggested the existence of a mass-squared difference of around 1 eV2 – far greater than eitherΔm122 orΔm232, which alone are sufficient to define the three known neutrinos.
If the mass-squared difference given by the LSND was real, it suggested the existence of a fourth type of neutrino. But if there were a fourth neutrino, it could not be ordinary: experiments at CERN had already shown that there could be only three neutrinos coupling to the weak force in this mass range. In other words, the fourth neutrino, if it exists, must be largely immune, or “sterile”, to the weak force: it could interact only via gravity.
Breaking the model
If neutrino oscillations were troublesome enough for the Standard Model, the existence of a sterile neutrino would be its downfall. Since the Standard Model’s formulation in the late 1960s, no new particles have been found outside it; the Higgs boson, discovered in 2012 at the LHC, was considered to be the final piece of the Standard Model jigsaw.
If neutrino oscillations were troublesome enough for the Standard Model, the existence of a sterile neutrino would be its downfall
Still, the LSND’s result was not accepted outright, and other physicists set out to check it. At the beginning of this century, researchers at the Mini Booster Neutrino Experiment (MiniBooNE) – a detector at Fermilab in the US consisting of 720 tonnes of mineral oil lined with more than a thousand photomultiplier tubes – examined a beam of muon neutrinos arriving from a source 500 m away. The result, announced in 2007, was null: unlike the LSND result, no oscillations were found for the 1 eV2 mass-squared difference. But many physicists believed that could be because MiniBooNE was using neutrinos, not antineutrinos, and was therefore not a proper comparison. Three years later, the MiniBooNE team had repeated the experiment using antineutrinos and had a new result: a spike in electron antineutrinos – and support for the LSND’s finding.
“When one experiment gives an extremely unexpected result, people are very sceptical,” says Guenette, who is working on the successor to the MiniBooNE experiment. “People thought [the LSND result] was more likely a problem with the detector. So when the MiniBooNE result came out, everybody said ‘Hmm’. It was unlikely to be a detector problem, because both detectors were different.”
The search continues Physicist Georgia Karagiorgi at the MiniBooNE neutrino experiment. Karagiorgi wrote her thesis on the search for antineutrino oscillations and is moving on to search for sterile neutrinos at the successor to MiniBooNE – MicroBooNE. (Courtesy: Fermilab/Reidar Hahn)
In the year after the MiniBooNE confirmation, support for the sterile neutrino was bolstered from a very different set of sources: nuclear reactors. Inside reactors, nuclear fission generates various neutron-rich nuclei that subsequently beta-decay into lighter nuclei. Beta decay always involves the emission of an electron or antielectron (positron), and almost always involves the emission of an electron neutrino or antineutrino.
In 2011 David Lhuillier at the Alternative Energies and Atomic Energy Commission in Saclay, France, and colleagues re-evaluated the number of electron antineutrinos that nuclear reactors ought to have been emitting over the past 30 years, and found that, between 10 and 100 metres from the reactors, they were coming up about 6% short. At this proximity, and with the energies involved, the electron antineutrinos were unlikely to be oscillating into any of the known active neutrinos, so the most obvious explanation was that some of them were oscillating into a fourth, more massive neutrino.
Perhaps the reactor evidence for sterile neutrinos should not have been surprising. Beginning in 1995, the solar neutrino experiments GALLEX at the Gran Sasso National Laboratory in Italy and SAGE at the Baksan Neutrino Observatory in Russia used known radioactive sources – chromium-51 and argon-37, both of which undergo “inverse” beta decay – for detector calibration. Again, the experimentalists had found a deficit in the expected count rate of electron neutrinos, this time of 5–20%. Nonetheless, it has been Lhuillier and colleagues’ more recent analysis of nuclear reactors that has really made people take notice of sterile neutrinos.
“Our work on the prediction of neutrino flux was initially completely disconnected from this topic,” says Lhuillier. “Today we still don’t know if sterile neutrinos exist or not, but our work triggered new interest.”
In February this year, evidence for sterile neutrinos went extraterrestrial. Searching through data from the European Space Agency’s XMM-Newton space telescope and NASA’s Chandra X-ray telescope, two independent groups – Esra Bulbul at the Harvard-Smithsonian Center for Astrophysics in the US and colleagues, and Alexey Boyarsky at Leiden University in the Netherlands and colleagues – found an excess of X-rays at about 3.5 keV. The researchers are cautious in drawing firm conclusions, but again there is an obvious explanation: the decay of dark matter in the distant cosmos. Being invisible, yet still interacting with gravity, sterile neutrinos would be an ideal candidate for dark matter, and 3.5 keV is about the energy of the X-rays into which they are expected to decay.
Front-page news
Solving the mystery of dark matter would be a major breakthrough in physics – one that would certainly make the front page of newspapers worldwide. But sterile neutrinos could solve several other mysteries, too. One of these is why the universe today is composed largely of matter and not antimatter: the Big Bang ought to have generated equal amounts of each, so the fact that they did not annihilate each other entirely – and that the universe as we know it exists at all – suggests that matter somehow managed to win over.
Many particle physicists believe the dominance of matter is a result of a phenomenon known as charge–parity (CP) violation. Preservation of CP is a technical way of saying that antiparticles interact in exactly the same way as their particle counterparts, albeit in mirror-reverse. In the Standard Model, CP is enforced by a symmetry in the theory that underpins particle interactions. But no such symmetry exists in the blueprint for sterile neutrinos, which means that when they decay they could more readily produce matter than antimatter. Perhaps, in the early universe, a decay of sterile neutrinos en masse laid the foundations for the matter-based planets, stars and galaxies we see today.
Then there are the neutrino masses themselves. These cannot be explained easily by the Higgs, which gives the masses of many other particles in the Standard Model, because the neutrinos would have to couple to it in an oddly weak manner. However, their masses could be explained with the so-called seesaw mechanism. The details of this are complex, but the idea is that heavy sterile neutrinos would “mix” with the known active neutrinos, lifting their masses slightly above zero. In fact, the seesaw mechanism, which was developed by the Swiss theoretical physicist Peter Minkowski and others in the 1970s, provided the first theoretical basis for sterile neutrinos.
Dark matter, CP violation, neutrino masses – at a glance you might wonder why the sterile neutrino has not always been a target for experimental particle physics. The reason probably lies in the nature of the sterile neutrino itself. While the results from terrestrial accelerator, reactor and radioactive-source experiments are mostly compatible with a mass-squared difference of about 1 eV2, dark matter would need a mass-squared difference of the order of 1 keV2, and CP violation would need a mass-squared difference of 100 GeV2 or more. Somewhat frustratingly, the original solar and atmospheric active-neutrino oscillations give no hint of what the masses of the sterile-neutrino should be. “Their mass can be anything – from 0.05 eV to 1015 GeV,” says Oleg Ruchayskiy, a particle physicist at the Swiss Federal Institute of Technology in Lausanne. “Really anything.”
One might think the simplest solution to three mysteries would be the existence of three sterile neutrinos – one to account for the oscillations seen in the LSND and other terrestrial experiments (with a mass of ~1 eV), one to account for dark matter (~1 keV) and one to account for the dominance of matter via CP violation (~100 GeV). To be sure, the existence of three sterile neutrinos would neatly mirror the known existence of three active neutrinos. But it turns out that even this scenario is problematic, because CP violation alone actually requires the existence of two sterile neutrinos with masses of around 100 GeV – meaning that if sterile neutrinos are to solve all the mysteries, there must be more than three of them. Partly for that reason, cosmologists often ignore the oscillations seen in the LSND and elsewhere and see sterile neutrinos only as a solution to dark matter and CP violation; for this scenario, they turn to a model known as the neutrino minimal standard model, which contains the three sterile neutrinos necessary for that purpose. If theorists do want to clear up the terrestrial oscillation results as well, they will have to turn to a heftier Grand Unified Theory, which can contain four – or indeed many more – sterile neutrinos.
Sterile neutrinos may not be as simple a solution to the biggest mysteries as they might at first seem
So, sterile neutrinos may not be as simple a solution to the biggest mysteries as they might at first seem. Still, there appears to be a growing desire among particle physicists to find out, once and for all, whether they exist.
Cosmic clue A mysterious X-ray signal observed in the Perseus Cluster could be produced by the decay of sterile neutrinos. (Courtesy: NASA/CXC/SAO/E Bulbul et al.)
For sterile neutrinos at dark-matter masses (those at kilo-electronvolt scales), X-ray telescopes such as XMM-Newton, Chandra and the Japan Aerospace Exploration Agency’s Suzaku could provide more data that will settle the question. Although these cannot provide direct evidence for sterile neutrinos, a signal that varies correctly in proportion to the source – that is, more X-rays emanating from galaxy clusters than from emptier regions of space – would be strong evidence in favour of sterile-neutrino dark matter.
Meanwhile, studies of the cosmic microwave background (CMB) – the oldest light in the universe – can provide constraints on how light a sterile neutrino could be. Any particle with a very small mass can travel at relativistic speeds – that is, close to that of light – enabling it to transport energy quickly from one region of space to another. In the early universe, this process was crucial for the formation of the first cosmic structures, and it turns out that measurements of the CMB can place limits on the masses of each of the relativistic particle species added together. According to ESA’s Planck satellite, this figure is about 0.2 eV, which goes against the existence of a 1 eV sterile neutrino.
But there is another cosmological parameter that might yet go in favour of a new particle. In conjunction with certain other measurements, measurements of the CMB can provide an estimate of the total number of relativistic neutrino species in the early universe, neff. A few years ago this parameter was calculated to be about 4; after the latest analysis from Planck, neff came down to about 3.3. Given its uncertainty of ±0.3, the result is now compatible with three light neutrinos, but optimists see room for hope. “It seems to want to be a value greater than three,” says Jon Link, an experimental neutrino physicist at Virginia Tech in the US.
Well grounded
The most concerted effort to find sterile neutrinos, however, is back on Earth. A white paper authored by sterile-neutrino specialists in 2012 lists more than 20 proposed experiments to search for the particles. These range from accelerator to reactor and radioactive-source experiments; from experiments that search for electron-neutrino disappearance to those that search for muon-neutrino disappearance or muon-to-electron neutrino transitions. But, “realistically, only five or so of these will be pursued, and maybe only two funded”, says Guenette.
Guenette is working on one of those that is being funded – a successor to MiniBooNE, called MicroBooNE. A 150 tonne tank of liquid argon, MicroBooNE ought to be able to rule out the main concern about MiniBooNE’s 2010 result: that the detectors mistook photons – a very normal feature of background noise – for electron antineutrinos. That is because argon is less sensitive to a photon background than the mineral oil used in MiniBooNE.
Commissioning for MicroBooNE begins this autumn, and Guenette expects the data analysis to take three years. True, more evidence for a 1 eV sterile neutrino will not necessarily solve any cosmological mysteries. But Guenette believes a discovery would make the concept of heavier sterile neutrinos more palatable.
Joachim Kopp, a theorist at the Max Planck Institute for Nuclear Physics in Heidelberg, Germany, agrees. “There is no scientific argument for why a sterile neutrino at electronvolt scales would imply the existence of others,” he says. “But I would say it would make theorists more comfortable about the idea.”
Hitting his stride – Robert P Crease in full flow at yesterday’s TEDx talk at CERN after forgetting about the timer, which is the small object at his feet. (Courtesy: Maya Elhalal)
By Robert P Crease in CERN, Geneva
It’s great to go first.
Then you can actually listen to the other performances without fretting about your own. Somewhere near the middle of my TEDxCERN talk yesterday (Wednesday 24 September) I stopped being aware of the timer at my feet, began to have fun and left the stage at the end without even noticing whether I had exceeded my time limit. I made a brief stop backstage to lose my “Madonna” – a microphone that’s not on a neck clip or attached to a headset but extends out from an ear brace – then retook my seat in the front row.
A flaw in how quantum-interference experiments are interpreted has been quantified for the first time by a team of physicists in India. Using the “path integral” formulation of quantum mechanics, the team calculated the interference pattern created when electrons or photons travel through a set of three slits. It found that non-classical paths – in which a particle can weave its way through several slits – must be considered along with the conventional quantum superposition of three direct paths (one through each of the slits). The team says the effect should be measurable in experiments involving microwave photons, and that the work could also provide insights into potential sources of decoherence in some quantum-information systems.
One of the cornerstones of quantum theory is the fact that particles can also behave as waves. This can be demonstrated by the double-slit experiment with electrons, which was once voted as the most beautiful physics experiment of all time by Physics World readers. It involves firing electrons through two adjacent slits and observing the build-up of a wave-like interference pattern on a screen on the other side of the slits. However, each particle is detected as a tiny dot within the pattern, suggesting that the particles are discrete entities too.
Physics students are taught that the double-slit pattern can be explained by treating the system as a superposition of waves that travel through one slit and waves that travel through the other slit. Although this description reproduces the pattern seen in experiments, the Japanese physicist Haruichi Yabuki pointed out in 1986 that this approach is approximate because it ignores the tiny possibility that a particle could take a non-classical path through the slits.
Quantum weaving
These non-classical paths are easier to think of with an arrangement of three slits. A particle could go through, say, the slit on its left, curve around, go back through the centre slit before turning again and emerging from the slit on the right (see figure). Now, Urbasi Sinha and colleagues at the Raman Research Institute and Indian Institute of Science in Bangalore have calculated the effect of these non-classical paths on the resulting interference pattern of such a triple slit. Using the path-integral formulation of quantum mechanics, the team looked at different combinations of slit width and slit separation for both incident photons and electrons.
In the case of electrons, the researchers worked out that the non-classical paths would have a minuscule effect on the observed pattern, which would deviate from a simple superposition by a factor of about 10–8. For visible light, this change increases to about 10–5, but this is still too small to detect. Indeed, the calculations explain why Sinha and colleagues at the University of Waterloo in Canada did not see any deviations in an optical triple-slit experiment done in 2010 (see “Quantum theory survives its latest ordeal”).
Microwaveable deviation
It turns out, however, that the deviation should rise to about 10–3 for microwave photons, and the team believes that it could be measured in an experiment using photons of wavelength 4 cm, a slit width of 120 cm and a slit separation of 400 cm. Indeed, Sinha told physicsworld.com that her team at the Raman Research Institute has already set up a microwave experiment to look for the effect, but could not comment on the preliminary results.
Such an experiment, if carried out, could provide a room-sized demonstration of the path-integral formulation of quantum mechanics – something that is normally associated with sub-atomic processes. Furthermore, understanding the role of non-classical paths in interferometer-based quantum-information systems could help physicists reduce the destructive effects of noise in these systems.
A mathematician is not necessarily the first person that you would associate with speech science. But as Samuli Siltanen demonstrates in this short film, researchers in his field can bring fresh approaches to long-standing challenges relating to the human voice.
Siltanen, who works at the University of Helsinki, explains how vowel sounds are generated in the vocal tract. Never one to shy away from giving a demonstration, Siltanen reveals his own vocal folds in action by visiting a clinic where a laryngoscope attached to a camera is inserted into his throat.
Vowel sounds are produced thanks to two independent processes. First is what Siltanen refers to as the “excitation signal”, which is generated as we push air through our lungs into the vocal folds, causing them to flap. The sound waves then travel up towards the mouth through the vocal tract, and it is this stage where speech generates its “colour” or “texture”.
An inverse approach
Siltanen demonstrates how an electronic larynx can be used to provide the excitation signal in cases where people have had their vocal folds damaged or removed, perhaps following surgery for cancer. His particular expertise is an area of mathematics called “inverse problems”, so he is interested in using available data to work out the missing information in speech generation. What this means in practise is that he is building a clearer picture of the physiology and processes relating to human speech based on available measurements.
Why is this useful? Siltanen explains that it can be the case that a young girl or woman who has lost her voice has to use a computer synthesis device that speaks with a grown man’s voice. The reason is related to so-called glottal inverse filtering, which means it is much more difficult to recreate a realistic female or a child’s voice because of the higher fundamental frequencies involved compared with a mature male voice.
Siltanen will be explaining the challenges of speech synthesis, and how mathematics can help, in a feature he is writing that will appear in a future issue of Physics World.
