Physics Nobel Prize 2013: Higgs Boson

Peter Higgs (left) and François Englert (right)

The Nobel Prize in Physics 2013 was awarded jointly to François Englert and Peter W. Higgs "for the theoretical discovery of a mechanism that contributes to our understanding of the origin of mass of subatomic particles, and which recently was confirmed through the discovery of the predicted fundamental particle, by the ATLAS and CMS experiments at CERN's Large Hadron Collider"

In 1964, they proposed the theory independently of each other (Englert together with his now deceased colleague Robert Brout) [1,2]. In 2012, their ideas were confirmed by the discovery of a so called Higgs particle at the CERN laboratory outside Geneva in Switzerland.

François Englert, Belgian citizen. Born 1932 in Etterbeek, Belgium. Ph.D. 1959 from Université Libre de Bruxelles, Brussels, Belgium. Professor Emeritus at Université Libre de Bruxelles, Brussels, Belgium.

Link to Prof. Englert's homepage >>

Peter W. Higgs, UK citizen. Born 1929 in Newcastle upon Tyne, UK. Ph.D. 1954 from King’s College, University of London, UK. Professor emeritus at University of Edinburgh, UK.

Link to Prof. Higg's homepage >>

The awarded theory is a central part of the Standard Model of particle physics that describes how the world is constructed. According to the Standard Model, everything, from flowers and people to stars and planets, consists of just a few building blocks: matter particles. These particles are governed by forces mediated by force particles that make sure everything works as it should.

The entire Standard Model also rests on the existence of a special kind of particle: the Higgs particle. This particle originates from an invisible field that fills up all space. Even when the universe seems empty this field is there. Without it, we would not exist, because it is from contact with the field that particles acquire mass. The theory proposed by Englert and Higgs describes this process.

On 4 July 2012, at the CERN laboratory for particle physics, the theory was confirmed by the discovery of a Higgs particle. CERN’s particle collider, LHC (Large Hadron Collider), is probably the largest and the most complex machine ever constructed by humans. Two research groups of some 3,000 scientists each, ATLAS and CMS, managed to extract the Higgs particle from billions of particle collisions in the LHC [3,4].

Even though it is a great achievement to have found the Higgs particle — the missing piece in the Standard Model puzzle — the Standard Model is not the final piece in the cosmic puzzle. One of the reasons for this is that the Standard Model treats certain particles, neutrinos, as being virtually massless, whereas recent studies show that they actually do have mass. Another reason is that the model only describes visible matter, which only accounts for one fifth of all matter in the cosmos. To find the mysterious dark matter is one of the objectives as scientists continue the chase of unknown particles at CERN.

References:
[1] F. Englert and R. Brout, “Broken symmetry and the mass of gauge vector mesons”. Physical Review Letters, 13, 321 (1964). Abstract. Read full paper in Google Books.
[2] P. W. Higgs, "Broken symmetries, massless particles and gauge fields". Physics Letters, 12, 132-133 (1964). Abstract. 
[3] ATLAS Collaboration, "Observation of a New Particle in the Search for the Standard Model Higgs Boson with the ATLAS Detector at the LHC", Physics Letters B, 716, 1-29 (2012). Full Paper.
[4] CMS Collaboration, "Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC", Physics Letters B, 716, 30-61 (2012). Full paper.

Relativistic Heavy Ion Collider (RHIC) and the Puzzle of Proton’s “missing” Spin.

Stony Brook University/RHIC physicist Barbara Jacak at RHIC's PHENIX detector [photo courtesy: Brookhaven National Laboratory, USA]

The refrigeration system at the Relativistic Heavy Ion Collider (RHIC) began humming to life last week, beginning cool-down of the magnets in the 2.4-mile-circumference accelerator ring at Brookhaven Lab. Temperatures inside the magnets will ultimately reach a frigid four degrees Kelvin (-452 degrees Fahrenheit) as Run 13 at RHIC gets under way. When collisions begin this Monday, scientists from Brookhaven and around the world will collect data from particles emerging from the particle smashups to try to solve one of the biggest mysteries of the basic building blocks of matter: the puzzle of the proton’s “missing” spin.

“Recent data from RHIC show for the first time that gluons carry some of the proton’s spin; we now want to find out whether the same is true for antiquarks. RHIC has the unique capability for doing this,” said Berndt Mueller, who was recently named the Associate Laboratory Director for Nuclear and Particle Physics.

Run 13 is scheduled to continue for 15 weeks, with funding provided by a continuing resolution set to expire in March. More time may be added, depending on how the next federal budget is resolved.

RHIC is the only particle collider operating in the United States, and the only collider in the world where scientists can collide polarized protons—bunches of 100 billion protons all spinning like gyroscopes with their axes aligned in a particular direction. Collisions between two beams of these polarized protons are key to the quest to understand the subatomic components that make up the proton—quarks and gluons—and how those pieces contribute to the proton’s overall spin. RHIC operators will spend most of Run 13 colliding these polarized protons at 255 billion electron volts (GeV) for proton spin research.

In this picture of a proton-proton collision, the spin of the particles is shown as arrows circling the spherical particles. The red and green particles represent reaction products from the collision which will be "seen" and analyzed by RHIC detectors [image courtesy: Brookhaven National Laboratory, USA]

Budgets permitting, the operators will also spend a few weeks at the end of the run colliding gold ions at energies of about 15 GeV. These relatively low-energy heavy ion collisions will provide a set of data that should be useful in learning more about how ordinary matter changes to quark-gluon plasma—a phase change that may be similar to how water changes from a liquid to ice or steam under certain conditions.

Protons, Quarks and Gluons Spin—But the Numbers Don’t Add Up:

New detector components recently inserted into the heart of STAR will track "heavy flavor" quarks and W bosons to reveal subtle details of conditions created in particle collisions [photo courtesy: Brookhaven National Laboratory, USA]

The early thought that protons get their spin from their three constituent quarks was proved to be over simplistic many years ago when fixed target experiments revealed that these building blocks account for only about 30 percent of total spin. Scientists have been looking for the missing source of proton spin ever since.

“Protons’ quarks, antiquarks, gluons and other pieces all contribute fractions of the proton’s spin,” explained Jamie Dunlop, a deputy spokesperson for the STAR collaboration, one of the two experiments at RHIC. “If you add everything up, including the motion of the quarks, antiquarks, and gluons, they have to add up to the whole of the proton’s spin. But we don’t know what fraction is in the spin of the antiquarks and gluons, and in the internal motion of all these particles inside the proton.”

RHIC’s polarized proton collisions were the first to probe the gluons’ role. From these experiments it appears that gluons make a significant contribution, but still not enough to account for all the missing spin. So the search goes on.

“New detectors at both STAR and PHENIX give us the ability to track particles called W bosons that emerge from collisions,” Dunlop said. “These W bosons can be used as probes to quantify spin contributions from a proton’s antiquarks and from different ‘flavors’ of quarks.”

Teasing apart these subtle contributions is essential to help reveal the complexity that resides within one of the most seemingly simple objects on Earth, explained Dave Morrison, a co-spokesperson for the PHENIX collaboration at RHIC.

“Protons are the most simple of all stable states of QCD matter,” he said, referring to matter made of quarks and gluons whose interactions are described by a theory called quantum chromodynamics (QCD). “The equation for QCD can be written in one line, but it’s taken us 40 years of theory and experimentation to get to the point we’re at today,” he said.

“You, I, and the coffee we drink are all made of protons and the quarks and gluons inside them. QCD is not some distant thing that only happens far off in the cosmos. It just takes an amazingly complex machine like RHIC to enable us to see how these components work together.”

Tracking Particles at STAR and PHENIX:

Using muon detectors contained inside the funnel-shaped sides of the PHENIX experiment, collaborators will study the production of W bosons and learn about how up and down quarks contribute to the spin of the proton [photo courtesy: Brookhaven National Laboratory, USA]

During Run 13, the STAR collaboration will track W bosons with a forward GEM tracker that was tested during Run 12 and is now ready for serious use. GEM stands for gaseous electron multiplier. The state-of-the-art detector relies not on wires, but sheets of plastic film coated with copper with holes punched in it (like Gore-Tex) to amplify the path and charge of collision debris with accuracy of 100-150 microns—about the width of a hair.

Additionally, muon telescope detector trays at STAR will look for lower-momentum muons produced from decays of other subatomic debris—upsilon and J/psi particles, which offer clues about collision conditions in the heart of STAR. And collaborators will also begin commissioning the Heavy Flavor Tracker, a $15 million major upgrade designed to track heavy quarks.

Meanwhile, the PHENIX collaboration will use silicon-based forward vertex detectors, tested during Run 12, to identify short-lived particles that are produced and decay within microns of the primary collision. New electronics were recently installed along with these new detectors to help PHENIX rapidly select those rare collisions that contain muons. Some of these muons come from the decay of W bosons. Using the PHENIX muon detectors, contained inside the funnel-shaped sides of the experiment, collaborators will study the production of W bosons and learn about how up and down quarks contribute to the spin of the proton.

“The new detectors and electronics we tested last year should work extremely well in Run 13,” said Morrison. “The particle signatures we’re looking for are fairly rare, so we have to accumulate a lot of data to do the physics we want to do. With the improvements the Collider-Accelerator Department [C-AD] made last year, we have what we need to take data like crazy from every bit of beam sent our way.”

Collisions, Intensity and Polarization, Courtesy of C-AD:

C-AD made a number of improvements to the RHIC accelerator complex during Run 12, some that led to a new world record and three world firsts. For Run 13, C-AD is again working toward superlative performance: high beam intensity with the most polarized protons crammed into the smallest area possible; high luminosity with the highest rate of particles colliding; and the highest degree of polarization as protons race around the RHIC ring.

“We have only about 12 weeks for collisions, so we must attain high luminosity as quickly as possible,” said C-AD Chair Thomas Roser. “We are always working at the edge of what’s really possible. If we’re not, we didn’t explore enough and need to push harder.”

Anatoli Zelenski of Brookhaven's Collider-Accelerator Department and the new Optically Pumped Polarized Ion Source (OPPIS), which will pump up the production of polarized protons at RHIC for Run 13 [photo courtesy: Brookhaven National Laboratory, USA]

A new Optically Pumped Polarized Ion Source (OPPIS) will make its debut for Run 13. The OPPIS system uses a laser to polarize negatively charged electrons, which are then attached to protons to which their spin is transferred. The new OPPIS source will produce many more polarized protons than the old one. The new system—designed by Anatoli Zelenski and his team from C-AD and the Budker Institute of Nuclear Physics in Russia—took three years to develop and was only commissioned successfully in the weeks leading up to Run 13.

With uncertain federal budgets in the coming years, the future for research at RHIC is unclear. Run 13 is scheduled to begin this Monday, but people who operate RHIC and rely on the data it provides are already thinking about Run 14 and beyond.

Collisions will be put on hold every other Wednesday during the run for accelerator research and development, including testing new technologies such as electron lenses that mitigate the detrimental effects of beam-beam interactions.

“We work constantly to increase luminosity and polarization, so research and development will even continue during the run,” explained C-AD Accelerator Division Head Wolfram Fischer. “There are new, important questions to answer, not to mention records to set and break.”

[The Text is written by Joe Gettler of Brookhaven National Laboratory, USA]

Evidence of Majorana States in an Al Superconductor – InAs Nanowire Device

[From left to right] Moty Heiblum, Yuval Oreg, Anindya Das, Yonathan Most, Hadas Shtrikman, Yuval Ronen

Authors: Yuval Ronen, Anindya Das, Yonatan Most, Yuval Oreg, Moty Heiblum, and Hadas Shtrikman

Affiliation: Dept. of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel

When a bridge between fields in physics is created, exciting physics can emerge. In 1962 Anderson walked on a bridge connecting condensed matter physics with particle physics, by introducing the Anderson mechanism in superconductivity to explain the Meissner effect. A similar idea was used on the other side of the bridge by Higgs in 1964, to explain the mechanism that generates the mass of elementary particles known as the Higgs mechanism. Nowadays, another bridge is formed between these two fields emanating from an idea first originated by Ettore Majorana in 1937 – where spin 1/2 particles can be their own anti-particles[1]. Back then, Majorana suggested the neutrino as a possible candidate for his prediction, and experiments such as double-beta decay are planned to test his prediction.

A link between Majorana’s prediction of new elementary particles and the field of condensed matter physics was formed already more than a decade ago. Quasi-particle excitations, which are equal to their anti-quasi-particle excitations, are predicted to be found in the solid. Specifically, in vortices that live in an esoteric two-dimensional P-wave spinless superconductor. Moreover, these excitations are expected to be inherently different from their cousins the elementary particles: they have non-abelian statistics. The non-abelian statistics is one of the beautiful triumphs of the physics of condensed matter.

This so far unobserved quasi-particle, that has non-abelian statistics, has for a while been a ‘holy grail’ in the fractional quantum Hall effect regime; with filling factor 5/2 being the most promising candidate for its observation. Lately, another realization of Majorana quasi-particles is pursued. It follows a 1D toy model presented by Kitaev in 2001, showing how one can isolate two Majorana states at two widely separated ends of a 1D P-wave spinless superconductor [2]. These two Majorana states are expected to sit in the gap of the superconductor (at the Fermi energy) for a wide range of system parameters. Seven years later, Fu and Kane [3] found that a P-wave spinless superconductor can be induced by an S-wave superconductor in proximity to a topological insulator, occurring in a semiconductor with an inversion gap. It was thus not long before two theoretical groups [4,5] provided a prescription for how to turn a 1D semiconductor nanowire into an effective Kitaev 1D spinless P-wave superconductor.

The prescribed system is a semiconductor nanowire, with strong spin-orbit coupling, coupled to an S-wave superconductor (a trivial superconductor, with Cooper pairs in a singlet state). Electrons from the semiconductor undergo Andreev reflections, a process which induces S-wave superconductivity in the nanowire. The induced superconductivity opens gaps in the nanowire spectrum around the Fermi energy, at momentums k=0 and k=k_F (the Fermi momentum), due to the two spin bands being separated by spin-orbit coupling. An applied magnetic field quenches the gap at k=0 while hardly affecting the gap at k_F (the Zeeman splitting competes with superconductivity at k=0, where spin-orbit coupling, being proportional to k, plays no role), creating an effective gap different from the one induced by superconductivity. A gate voltage is used to tune the chemical potential into the effective gap. When the Zeeman energy is equal to the induced superconducting gap, the effective gap at k=0 closes; it then reopens upon further increase of the magnetic field, bringing the nanowire into a so called ‘topological phase’. Kitaev’s original toy model of a 1D P-wave superconductor is then implemented (Fig. 1).

Figure 1: Energy dispersion of the InAs nanowire excitations (Bogoliubov-de Gennes spectrum), in proximity to the Al superconductor. Heavy lines show electron-like bands and light lines show hole-like bands. Opposite spin directions are denoted in blue and magenta (red and cyan) for the spin-orbit effective field direction (perpendicular direction), where a relative mixture denotes intermediate spin directions. (a) Split electronic spin bands due to spin-orbit coupling in the InAs wire. Spin-orbit energy defined as Δ_so, with the chemical potential μ measured with respect to the spin bands crossing at p=0. (b) With the application of magnetic field, B, perpendicular to the spin-orbit effective magnetic field, B_so a Zeeman gap, E_z= gμ_BB/2, opens at p=0. (c) Light curves for the hole excitations are added, and bringing into close proximity a superconductor opens up superconducting gaps at the crossing of particle and hole curves. The overall gap is determined by the minimum between the gap at p=0 and the gap at p_F, while for μ=0 and E_z close to Δ_ind the gap at p=0 is dominant. (d) As in (c) but E_z is increased so that the gap at p_F is dominant. (e) B is rotated to a direction of 30^o with respect to B_so. The original spin-orbit bands are shifted in opposite vertical directions, and the B component, which is perpendicular to B_so is diminished. (f) The evolution of the energy gap at p=0 (dotted blue), at p_F (dotted yellow), and the overall energy gap (dashed black) with Zeeman energy, E_z, for μ=0. The overall gap is determined by the minimum of the other two, where the p=0 gap is dominant around the phase transition, which occurs at E_z=Δ_ind. At high E_z the p_F gap, which is decreasing with E_z, becomes dominant.

Seventy five years after Majorana’s monumental paper, we may be close to a realization of a quasi-particle that is identical to its anti-quasi-particle, possessing non-abelian statistics. Several experimental groups [6,7,8] follow the prescribed recipe for a 1D P-wave spinless superconductor[4,5], with our group being one of them. A zero energy conductance peak, at a finite Zeeman field, had been seen now in InSb and InAs nanowires in proximity to Nb and Al superconductors, respectively. This peak is considered a signature for the existence of a Majorana quasi-particle, since the Majorana resides at the Fermi energy.

Figure 2: Structure of the Al-InAs structures suspended above p-type silicon covered with 150nm SiO₂. (a) Type I device, the nanowire is supported by three gold pedestals, with a gold ‘normal’ contact at one edge and an aluminum superconducting contact at the center. The conductive Si substrate serves as a global gate (GG), controlling barrier as well as the chemical potential of the nanowire. Two narrow local gates (RG and LG), 50nm wide and 25nm thick, displaced from the superconducting contact by 80nm, also strongly influence the barrier height as well as the chemical potential in the wire. (b) Type II device, similar to type I device, but without the pedestal under the Al superconducting contact. This structure allows control of the chemical potential under the Al contact. (c) SEM micrograph of type II device. A voltage source, with 5 Ohm resistance, provides V_SD, and closes the circuit through the ‘cold ground’ (cold finger) in the dilution refrigerator. Gates are tuned by V_GG and V_RG to the desired conditions. Inset: High resolution TEM image (viewed from the <1120> zone axis) of a stacking faults free, wurtzite structure, InAs nanowire, grown on (011) InAs in the <111> direction. TEM image is courtesy of Ronit Popovitz-Biro. (d) An estimated potential profile along the wire. The two local gates (LG and RG) and global gate (GG) determine the shape of the potential barriers; probably affect the distance between the Majoranas.

Our work, with MBE grown InAs nanowire in proximity to an Al superconductor [8] (Fig 2), demonstrated a zero bias peak and several more interesting features in the parameters' space. First, the closing of the gap at k=0 was clearly visible when the Zeeman energy was equal to the induced gap. Second, splitting of the zero-bias-peak was observed at low and high Zeeman field; likely to result from spatial coupling of the two Majorana states. Third, the zero-bias-peak was found to be robust in a wide range of chemical potential (assumed to be within the k=0 gap). While these observations agree with the presence of a Majorana quasi-particle (though the peak height is much smaller than expected, maybe due to the finite temperature of the experiment), the available data does not exclude other effects that may result with a similar zero bias peak (such as, interference, disorder, multi-bands, Kondo correlation).

Quoting Wilczek: “Whatever the fate of these particular explorations, there is no doubt that Majorana's central idea, which long seemed peripheral, has secured a place at the core of theoretical physics"[9].

References:
[1] Ettore Majorana, "Teoria simmetrica dell’elettrone e del positrone", Il Nuovo Cimento, 171 (1937). Abstract.
[2] A. Yu. Kitaev, "Unpaired Majorana fermions in quantum wires". Physics Uspekhi, 44, 131 (2001). Full Article.
[3] Liang Fu and Charles Kane, "Superconducting Proximity Effect and Majorana Fermions at the Surface of a Topological Insulator", Physical Review Letters 100, 096407 (2008). Abstract.
[4] Roman M. Lutchyn, Jay D. Sau and Sankar Das Sarma, "Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures", Physical Review Letters, 105, 077001 (2010). Abstract.
[5] Yuval Oreg, Gil Refael, and Felix von Oppen, "Helical Liquids and Majorana Bound States in Quantum Wires", Physical Review Letters, 105, 177002 (2010). Abstract.
[6] V. Mourik, K. Zuo, S.M. Frolov, S.R. Plissard, E.P.A.M. Bakkers, L.P. Kouwenhoven, "Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices", Science 336, 1003 (2012). Abstract. 2Physics Article.
[7] M. T. Deng, C. L. Yu, G. Y. Huang, M. Larsson, P. Caroff, H. Q. Xu, "Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device", arXiv: 1204.4130 (2012).
[8] Anindya Das, Yuval Ronen, Yonathan Most, Yuval Oreg, Hadas Shtrikman, Moty Heiblum, "Zero-bias peaks and splitting in an Al–InAs nanowire topological superconductor as a signature of Majorana fermions", Nature Physics, 8, 887–895 (2012). Abstract.
[9] Frank Wilczek, "Majorana Returns", Nature Physics, 5, 614 (2009). Abstract.

Importance of Electron-Electron Interactions in Graphene

Michael Crommie [Photo by Roy Kaltschmidt, Courtesy: Lawrence Berkeley National Laboratory]

 Perhaps no other material is generating as much excitement in the electronics world as graphene, sheets of pure carbon just one atom thick through which electrons can race at nearly the speed of light – 100 times faster than they move through silicon. Superthin, superstrong, superflexible and superfast as an electrical conductor, graphene has been touted as a potential wonder material for a host of electronic applications, starting with ultrafast transistors. For the vast potential of graphene to be fully realized, however, scientists must first learn more about what makes graphene so super. The latest step in this direction has been taken by researchers with the U.S. Department of Energy (DOE)’s Lawrence Berkeley National Laboratory (Berkeley Lab) and the University of California (UC) Berkeley.

Michael Crommie, a physicist who holds joint appointments with Berkeley Lab’s Materials Sciences Division and UC Berkeley’s Physics Department, led a study in which the first direct observations at microscopic lengths were recorded of how electrons and holes respond to a charged impurity – a single Coulomb potential – placed on a gated graphene device. The results provide experimental support to the theory that interactions between electrons are critical to graphene’s extraordinary properties. This work has been published online on July 29th in the journal 'Nature Physics'[1].

“We’ve shown that electrons in graphene behave very differently around charged impurities than electrons in other materials,” Crommie says. “Some researchers have held that electron-electron interactions are not important to intrinsic graphene properties while others have argued they are. Our first-time-ever pictures of how ultra-relativistic electrons re-arrange themselves in response to a Coulomb potential come down on the side of electron-electron interactions being an important factor.”

Graphene sheets are composed of carbon atoms arranged in a two-dimensional hexagonally patterned lattice, like a honeycomb. Electrons moving through this honeycomb lattice perfectly mimic the behavior expected of highly relativistic charged particles with no mass: think of a ray of light that is electrically charged. Because this is the same behavior displayed by highly relativistic free electrons, charge-carriers in graphene are referred to as “Dirac quasiparticles,” after Paul Dirac, the scientist who first described the behavior of relativistic fermions in 1928.

“In graphene, electrons behave as massless Dirac fermions,” Crommie says. “As such, the response of these electrons to a Coulomb potential is predicted to differ significantly from how non-relativistic electrons behave in traditional atomic and impurity systems. However, until now, many key theoretical predictions for this ultra-relativistic system had not been tested.”

Image 1: This zoom-in STM topograph shows one of the cobalt trimers placed on graphene for the creation of Coulomb potentials – charged impurities – to which electrons and holes could respond. (Image courtesy of Crommie group)

Working with a specially equipped scanning tunneling microscope (STM)in ultra-high vacuum, Crommie and his colleagues probed gated devices consisting of a graphene layer deposited atop boron nitride flakes which were themselves placed on a silicon dioxide substrate, the most common of semiconductor substrates.

“The use of boron-nitride significantly reduced the charge inhomogeneity of graphene, thereby allowing us to probe the intrinsic graphene electronic response to individual charged impurities,” Crommie says. In this study, the charged impurities were cobalt trimers constructed on graphene by atomically manipulating cobalt monomers with the tip of an STM.”

Image 2: The response of ultrarelativistic electrons in graphene to Coulomb potentials created by cobalt trimers was observed to be signficantly different the response of non-relativistic electrons in traditional atomic and impurity systems. (Image courtesy of Crommie group)

The STM used to fabricate the cobalt trimers was also used to map (through spatial variation in the electronic structure of the graphene) the response of Dirac quasiparticles – both electron-like and hole-like – to the Coulomb potential created by the trimers. Comparing the observed electron–hole asymmetry to theoretical simulations allowed the research team to not only test theoretical predictions for how Dirac fermions behave near a Coulomb potential, but also to extract graphene’s dielectric constant.

“Theorists have predicted that compared with other materials, electrons in graphene are pulled into a positively-charged impurity either too weakly, the subcritical regime; or too strongly, the supercritical regime,” Crommie says. “In our study, we verified the predictions for the subcritical regime and found the value for the dielectric to be small enough to indicate that electron–electron interactions contribute significantly to graphene properties. This information is fundamental to our understanding of how electrons move through graphene.”

Reference:
[1] Yang Wang, Victor W. Brar, Andrey V. Shytov, Qiong Wu, William Regan, Hsin-Zon Tsai, Alex Zettl, Leonid S. Levitov, Michael F. Crommie, "Mapping Dirac quasiparticles near a single Coulomb impurity on graphene", Nature Physics, doi:10.1038/nphys2379 (Published online July 29, 2012). Abstract.

[This article is written by Lynn Yarris of Lawrence Berkeley National Laboratory]

Signatures of Majorana Fermions in Hybrid Superconductor-Semiconductor Nanowire Devices

Authors: Vincent Mourik¹, Kun Zuo¹, Sergey Frolov¹, Sébastien Plissard², Erik Bakkers^1,2, Leo Kouwenhoven¹

Affiliation:
¹Kavli Institute of Nanoscience, Delft University of Technology, Netherlands.
²Dept of Applied Physics, Eindhoven University of Technology, Netherlands.

Particle Predictors:
Paul Dirac was the very first particle predictor. In 1927, Dirac developed a formula that linked two new theories: Einstein’s special theory of relativity and quantum mechanics. Dirac’s equation, however, had several solutions. The first solution described the familiar electron: a particle with a negative charge holding a certain amount of positive energy. Another solution actually constituted its very opposite: a positively charged particle holding a certain amount of negative energy. Rather than ignoring the contradiction raised by his additional solution, Dirac surmised that there must be a particle in nature with a positive electrical charge and negative energy [1]. This particle therefore has properties that would exactly mirror the properties of an electron. Several years later, this particle was indeed found, and was named positron. Together, the electron and the positron form a particle and antiparticle pair.

A pure genius, Paul Dirac was utterly convinced of the veracity of his formula. If his equation offered a certain solution, then a corresponding particle simply had to exist in nature. Since that time, numerous other particles have been predicted and identified this way. For example, the ongoing search for the Higgs boson is set up just like that, based on a prediction from the Standard Model.

Ettore Majorana was a physicist and a contemporary of Dirac. Majorana had an enigmatic biography that formed the topic of many books and films in Italy. At some point in the 1930s, Majorana was playing around with Dirac’s equation and after slightly modifying it he found a new solution: a particle that is identical to its antiparticle. And something can only be identical to its counterpart if it has properties that are all zero. Ettore Majorana, too, had a firm belief in formulas and in 1937 he published a paper [2] predicting his new particle, which has since become known as the Majorana fermion.

For decades the Majorana particle received little attention, but in the 1970s the search began afresh. Using large accelerators and detectors, scientists started hunting for neutrino particles with Majorana properties. Indeed, these elementary Majorana particles might even solve the mystery of dark matter that fills our Universe. So far, the elementary Majorana particles have remained elusive, but this important quest is still being pursued by CERN in Geneva.

Particle Creators:

In addition to elementary particles, composite or collective particles (see box) also exist in the world of condensed matter physics. We know of heat particles (phonons), electron density waves (plasmons), magnetic waves (magnons) and a long list of other collective particles. These collective particles are particularly convenient for making the physics of materials a lot simpler. Materials hold a distinct place in physics because by combining materials we can create objects that did not exist before. Technology, for instance, abounds with remarkable material combinations, such as silicon and silicon oxide forming the backbone of electronics. But material combinations can also be used in fundamental physics to create something new. This prompted a number of theoretical physicists to reflect on whether we could combine materials in such a way that the collective particles inside them will acquire the properties of Majorana fermions.

The one-dimensional lattice proposed by Alexei Kitaev in 2001 was still highly mathematical and abstract [3]. A number of propositions then followed based on (p-wave superconducting) materials that did not yet exist. In 2008, Liang Fu and Charles Kane’s theory [4] was the first to be based on existing materials, but was still difficult to put into practice. The year 2010 saw the publication, in Physical Review Letters of two similar theories by two groups of theorists, independently of each other, which for the first time looked feasible in practice. One of the publications [5] came from theorists at the University of Maryland (Roman Lutchyn, Jay Sau and Sankar Das Sarma); the other [6] was a collaborative effort between theorists at the Weizmann Institute in Israel, California Institute of Technology of USA and the Free University of Berlin in Germany (Yuval Oreg, Gil Rafael and Felix von Oppen). The importance of the aforementioned theoretical developments was that it shifted the focus from what is found in nature to the artificial creation of Majorana particles.

Prior knowledge: there are particles and then there are particles…

If you blow into your hand, what you will primarily feel are oxygen and nitrogen molecules. Those molecules are minute, subnanometer-scale particles that are composed, in this case, of two atoms each. In turn, each atom is made up of an atomic nucleus encircled by electrons. The electrons cannot be divided into smaller particles - they are ‘elementary’ particles. However, the protons and neutrons inside the nucleus can be shattered to create even smaller particles. This shattering process is generated in accelerators such as the one at CERN in Geneva, where the search for the Higgs particle continues unabated. Other popular particles are the neutrinos (which for a short period were believed to travel even faster than light) and the Majorana fermions. These Majorana fermions have not yet been found at CERN.The Majorana fermions may well be the key to explaining the dark matter mystery. In the universe, there is five times as much dark matter as ordinary matter, and so Majorana fermions could be the most widespread particles in the universe.

CERN are engaged in the study of fundamental particles. Each of these particles are smaller than the smallest atom, hydrogen. Our world of matter is based on atoms and clusters of atoms that form molecules. The glue that binds these atoms to molecules is described by quantum mechanics. Our bodies, for instance, are chemical factories in which atoms are stuck together with quantum glue. Apart from complex biological materials, there are also crystals that frequently hold the same atoms stacked inside a grid. Even the smallest materials may contain large numbers of atoms. For example, a nanowire with a diameter of 100 nm and a length of 1000 nm (1000 nm = 1 micrometer) alone contains some 10 billion atoms.

Next to fundamental particles and atoms there are also collective particles. The ‘wave’ in a stadium is a good example. The ‘wave’ is simply a group of spectators jumping up and down to create a wave. If we wanted to describe this wave in mathematical terms, we might do that by including everyone in a large formula. Then again, we could also approach it more simply by forgetting about all those individuals and only describe their collective behavior, that is, the wave. And for simplicity’s sake we could call the ‘wave’ a particle, in this case, a collective particle. This reduction to collective particles simplifies matters enormously and is often highly successful. An example: heat in a material is not described in terms of a bunch of vibrating atoms but, far more easily, as heat particles that are known as phonons.

You may think that ‘collective particles’ is a rather imprecise way of describing what actually happens. This may be true of the wave but phonons, for example, can in fact provide us with a very exact, realistic description. What is perhaps the most surprising fact is that collective particles can actually behave in accordance with the laws of quantum mechanics. A phonon can find itself in the superposition of both hot and cold. Such a quantum superposition may sound absurd enough for elementary particles, but is really stretching our imagination where collective particles are concerned.

The Majorana fermions in crystals are not only interesting from a fundamental viewpoint, but also have unique properties that can be used to build a quantum computer. Field medalist Michael Freedman works at Microsoft and has been carrying out active research into topological quantum computers with a team of scientists since 2005. This computer works by moving Majorana particles around each other and forming space-time braids.

The proposals put forward by Lutchyn et al [5] and Oreg et al [6] are both based on bringing semiconducting nanowires into contact with a superconducting material. We had already successfully accomplished this combination in Delft, which resulted in publications in Science (2005) and Nature (2006). Combining these specific materials suddenly made us the experimental specialists in the search for Majorana fermions.

Note that the Majorana quest had already been described at an early stage in the journal 'Science' [7].

Majorana in Delft:

How do you create a Majorana fermion? Based on the condition that the particle is identical to its antiparticle, you can do some reverse engineering. It cannot, for instance, have an electrical charge, nor have energy or spin. The theoretical proposals argue that those properties are created by combining materials consisting of a superconductor with a special semiconductor that has strong spin-orbit coupling. This semiconductor should take the form of a one-dimensional nanowire. If a magnetic field is also applied, the Majorana fermion should appear at low temperatures, just above absolute zero temperature. We combined these materials on a microchip. We developed InSb (Indium Antimonide) nanowires for the semiconductor. InSb has strong spin-orbit coupling. We used a Nb alloy as a superconductor. This material will retain its superconductive properties also in the presence of an external magnetic field. For this material we were granted permission to use the technology available in Teun Klapwijk’s group in Delft. Using nanotechnology, we produced an electronic chip that, admittedly, looks rather messy (top right). Zooming down to sub-micrometre scale, we can see the nanowire thread and the electrical contacts (below right).

In this device, the superconductor is larger than the semiconductor. The diameter of the nanowire is so small that it actually becomes a one-dimensional conductor. A portion of the superconductor is covering the nanowire, which causes the superconductivity to leak into the semiconductor, effectively creating a one-dimensional superconductor. These do not exist in nature but can be induced this way. The strong spin-orbit coupling in the InSb nanowire makes this one-dimensional superconductor particularly unique. It has a so-called p-symmetry, which again has also not been found in nature. This p-superconductor extends across the entire section where the nanowire is in contact with the superconductor. At the end points, where the p-superconductor ends, two Majorana fermions appear, one on each end point.

Image: The microchip used with three different Majorana devices. This chip is cooled down to almost absolute zero point (-273 degrees Celsius). The electrical wires are connected to measuring equipment at room temperature.
 
We can measure the Majorana fermions in the electrical conductivity. From the gold contact we send electrons into the nanowire, towards the lower Majorana fermion. Only when we send electrons inside with precisely zero energy can we measure a current. If we add voltage to the electrons to energise them further, they are reflected at the p-superconductor and we measure zero conductivity. The presence of the Majorana fermion in our system is therefore visible as a conductance peak at a voltage that is precisely zero.

In the 'Science' publication [8] we also included various control experiments, which demonstrate that each single ingredient from the original theory is essential for this observation. The results can only be interpreted if we assume the presence of Majorana fermions. The article is published online on 12 April in 'Science Express' [8].

Image: The nanowire, shown vertically in this photo, is lying flat on a substrate. Hidden in the substrate are different gate electrodes (the horizontal ‘stripes’ below the nanowire and the contacts), which can change the conductivity of the nanowire. The lower electrical contact to the nanowire is madefrom gold, a normal conductor. The contact on the top is covering half of the nanowire. This is the superconductor. The total length of the nanowire is three micrometres. The anticipated positions of two Majorana fermions are indicated with red stars. 

We have since been carrying out new experiments. As the title of our article ‘Signatures of …’ suggests, we also want to demonstrate other unique properties of Majorana fermions. And our Majorana fermions are literally one of a kind. Nature has two types of particles: fermions (such as electrons, positrons, neutrons, etc.) and bosons (photons, Higgs particles, phonons, etc.). Our Majorana particles are likely to have other properties than fermions and bosons. In terms of physics, their behaviour is described by non-Abelian statistics. If we can demonstrate these statistics in our new experiments, we add a completely new chapter to the book of physics. This new round of experiments is based on a highly theoretical approach using new concepts that are not yet quite understood. To translate abstract concepts into experiments we are working with Carlo Beenakker’s theory group from Leiden. The non-Abelian statistics also make Majorana particles useful for a topological quantum computer.

References:
[1] P. A. M. Dirac, "The Quantum Theory of the Electron". Proceedings of the Royal Society of London: Series A 117, 610–624 (1928). Full Article.
[2] Ettore Majorana, "Teoria simmetrica dell’elettrone e del positrone", Il Nuovo Cimento, 171 (1937). Abstract. 
[3] A. Yu. Kitaev, "Unpaired Majorana fermions in quantum wires". Physics Uspekhi, 44, 131 (2001). Full Article. 
[4] Liang Fu and Charles Kane, "Superconducting Proximity Effect and Majorana Fermions at the Surface of a Topological Insulator", Phys. Rev. Lett. 100, 096407 (2008). Abstract.   
[5] Roman M. Lutchyn, Jay D. Sau and Sankar Das Sarma, "Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures", Physical Review Letters, 105, 077001 (2010). Abstract.
[6] Yuval Oreg, Gil Refael, and Felix von Oppen, "Helical Liquids and Majorana Bound States in Quantum Wires", Physical Review Letters, 105, 177002 (2010). Abstract.
[7] Robert F. Service, "Search for Majorana Fermions Nearing Success at Last?", Science, 332, 193 (2011). Abstract.
[8] V. Mourik, K. Zuo, S.M. Frolov, S.R. Plissard, E.P.A.M. Bakkers, L.P. Kouwenhoven, "Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices", Science Express, DOI: 10.1126/science.1222360 (Published Online April 12 2012). Abstract.

“Dressing” Atoms with Laser Allows High Angular Momentum Scattering : Could Reveal Ways to Observe Majorana Fermions

Ian Spielman (photo courtesy: Joint Quantum Institute, USA)

Scientists at the Joint Quantum Institute (JQI, a collaborative enterprise of the 'National Institute of Standards and Technology' and the University of Maryland) have for the first time engineered and detected the presence of high angular momentum collisions between atoms at temperatures close to absolute zero. Previous experiments with ultracold atoms featured essentially head-on collisions. The JQI experiment, by contrast, is able to create more complicated collisions between atoms using only lasers that dramatically influences their interactions in specific ways.

Such light-tweaked atoms can be used as proxies to study important phenomena that would be difficult or impossible to study in other contexts. Their most recent work, appearing in Science [1] demonstrates a new class of interactions thought to be important to the physics of superconductors that could be used for quantum computation.

Particle interactions are fundamental to physics, determining, for example, how magnetic materials and high temperature superconductors work. Learning more about these interactions or creating new “effective” interactions will help scientists design materials with specific magnetic or superconducting properties.Because most materials are complicated systems, it is difficult to study or engineer the interactions between the constituent electrons. Researchers at JQI build physically analogous systems using supercooled atoms to learn more about how materials with these properties work.

The key to the JQI approach is to alter the atoms’ environment with laser light. They “dress” rubidium atoms by bathing them in a pair of laser beams, which force the atoms to have one of three discrete values of momentum. In the JQI experiment, rubidium atoms comprise a Bose-Einstein condensate (BEC). BECs have been collided before. But the observation of high-angular-momentum scattering at such low energies is new.

The paper in 'Science Express' [1] includes a variety of technical issues which require some explanation:

Collisons

One of the cardinal principles of quantum science is that matter must be simultaneously thought of as both particles and waves. When the temperature of a gas of atoms is lowered, the wavelike nature of the atom emerges, and the idea of position becomes fuzzier. While an atom at room temperature might spread over a hundredth of a nm, atoms at nano-kelvin temperatures have a typical wavelength of about 100 nm. This is much larger than the range of the force between atoms, only a few nm. Atoms generally collide only when they meet face to face.

However, to study certain interesting quantum phenomena, such as searching for Majorana particles---hypothetical particles that might provide a robust means of encoding quantum information---it is desirable to engineer inter-atomic collisions beyond these low-energy, head-on type. That’s what the new JQI experiment does.

Partial Waves

Scattering experiments date back to the discovery of the atomic nucleus 100 years ago, when Ernest Rutherford shot alpha particles into a foil of gold. Since then other scattering experiments have revealed a wealth of detail about atoms and sub-atomic matter such as the quark substructure of protons.

A convenient way of picturing an interaction between two particles is to view their relative approach in terms of angular momentum. Quantized angular momentum usually refers to the motion of an electron inside an atom, but it necessarily pertains also to the scattering of the two particles, which can be thought of as parts of a single quantum object.

If the value of the relative angular momentum is zero, then the scattering is designated as “s-wave” scattering. If the pair of colliding particles has one unit of angular momentum, the scattering is called p-wave scattering. Still more higher-order scattering scenarios are referred to by more letters: d-wave, f-wave, g-wave, and so on. This model is referred to as the partial waves view.

In high energy scattering, the kind at accelerators, these higher angular-momentum scattering scenarios are important and help to reveal important structure information about the particles. In atomic scattering at low temperatures, the s-wave interactions completely swamp the higher-order scattering modes. For ultralow-temperature s-wave scattering, when two atoms collide, they glance off each other (back to back) at any and all angles equally. This isotropic scattering doesn’t reveal much about the nature of the matter undergoing collision; it’s as if the colliding particles were hard spheres.

This has changed now. The JQI experiment is the first to create conditions in which d-wave and g-wave scattering modes in an ultracold experiment could be seen in otherwise long-lived systems.

Quantum Collider

Ian Spielman and his colleagues at the National Institute for Standards and Technology (NIST) chill Rb atoms to nano-kelvin temperatures. The atoms, around half a million of them, have a density about a millionth that of air at room temperature. Radiofrequency radiation places each atom into a superposition of quantum spin states. Then two (optical light) lasers impart momentum (forward-going and backward-going motion) to the atoms.

Schematic drawing of collision between two BECs (the gray blobs) that have been “dressed” by laser light (brown arrows) and an additional magnetic field (green arrow). The fuzzy halo shows where atoms have been scattered. The non-uniform projection of the scattering halo on the graph beneath shows that some of the scattering has been d-wave and g-wave [image courtesy: JQI]

If this were a particle physics experiment, we would say that these BECs-in-motion were quantum beams, beams with energies that came in multiples of the energy kick delivered by the lasers. The NIST “collider” in Gaithersburg, Maryland is very different for the CERN collider in Geneva, Switzerland. In the NIST atom trap the particles have kinetic energies of a hundred pico-electron-volts rather than the trillion-electron-volt energies used at the Large Hadron Collider.

At JQI, atoms are installed in their special momentum states, and the collisions begin. Outward scattered atoms are detected after the BEC clouds are released by the trap. If the atoms hadn’t been dressed, the collisions would have been s-wave in nature and the observed scattered atoms would have been seen uniformly around the scattering zone.

The effect of the dressing is to screen the atoms from s-wave scattering in the way analogous to that in some solid materials, where the interaction between two electrons is modified by the presence of trillions of other electrons nearby. In other words, the laser dressing effectively increased the range of the inter-atom force such that higher partial wave scattering was possible, even at the lowest energies.

In the JQI experiment, the observed scattering patterns for atoms emerging from the collisions was proof that d-wave and g-wave scattering had taken place. “The way in which the density of scattered atoms is distributed on the shell reflects the partial waves,” said Ian Spielman. “A plot of scattered-density vs. spherical polar angles would give the sort of patterns you are used to seeing for atomic orbitals. In our case, this is a sum of s-, p-, and d- waves.”

Simulating Solids Using Gases

Ultracold atomic physics experiments performed with vapors of atoms are excellent for investigating some of the strongly-interacting quantum phenomena usually considered in the context of condensed matter physics. These subjects include superconductivity, superfluids, the quantum Hall effect, and topological insulators, and some things that haven’t yet been observed, such as the “Majorana” fermions.

Several advantages come with studying these phenomena in the controlled environment of ultracold atoms. Scientists can easily manipulate the landscape in which the atoms reside using knobs that adjust laser power and frequency. For example, impurities that can plague real solids can be controlled and even removed, and because (as in this new JQI experiment) the scattering of atoms can now (with the proper “dressing”) reveal higher-partial-wave effects. This is important because the exotic quantum effects mentioned above often manifest themselves under exactly these higher angular-momentum conditions.

“Our technique is a fundamentally new method for engineering interactions, and we expect this work will stimulate new directions of research and be of broad interest within the physics community, experimental and theoretical,” said Spielman. “We are modifying the very character of the interactions, and not just the strength, by light alone.”

On To Fermions

The JQI team, including Nobel Laureate William Phillips, is truly international, with scientists originating in the United Kingdom (lead author Ross Williams), Canada (Lindsay LeBlanc), Mexico (Karina Jiménez-García), and the US (Matthew Beeler, Abigail Perry, William Phillips and Ian Spielman).

The researchers now will switch from observing bosonic atoms (with a total spin value of 1) to fermion atoms (those with a half-integral spin). Combining the boson techniques demonstrated here with ultracold fermions offers considerable promise for creating systems which are predicted to support the mysterious Majorana fermions. “A lot of people are looking for the Majorana fermion,” says lead author and JQI postdoctoral fellow Ross Williams. “It would be great if our approach helped us to be the first.”

Reference
[1] R. A. Williams, L. J. LeBlanc, K. Jiménez-García, M. C. Beeler,A. R. Perry, W. D. Phillips, I. B. Spielman, "Synthetic partial waves in ultracold atomic collisions”, Science Express, (December 7, 2011). DOI: 10.1126/science.1212652. Abstract.

New Limit on Antimatter Imbalance

Physicists including Pieter Mumm (shown) used the emiT detector they built at NIST to investigate any potential statistical imbalance between the two natural types of neutron decay [image courtesy: emiT team]

Why there is stuff in the universe—more properly, why there is an imbalance between matter and antimatter—is one of the long-standing mysteries of cosmology. A team of researchers working at the National Institute of Standards and Technology (NIST) at Boulder, Colorado has just concluded a 10-year-long study of the fate of neutrons in an attempt to resolve the question, the most sensitive such measurement ever made. The universe, they concede, has managed to keep its secret for the time being, but they’ve succeeded in significantly narrowing the number of possible answers.

Their work is published in a recent issue of Physical Review Letters [1]. The research team also includes scientists from the University of Washington, the University of Michigan, the University of California at Berkeley, Lawrence Berkeley National Laboratory, Tulane University, the University of Notre Dame, Hamilton College and the University of North Carolina at Chapel Hill. Funding was provided by the U.S. Department of Energy and the National Science Foundation.

Though the word itself evokes science fiction, antimatter is an ordinary—if highly uncommon—material that cosmologists believe once made up almost exactly half of the substance of the universe. When particles and their antiparticles come into contact, they instantly annihilate one another in a flash of light. Billions of years ago, most of the matter and all of the antimatter vanished in this fashion, leaving behind a tiny bit of matter awash in cosmic energy. What we see around us today, from stars to rocks to living things, is made up of that excess matter, which survived because a bit more of it existed.

“The question is, why was there an excess of one over the other in the first place?” says Pieter Mumm, a physicist at NIST’s Physical Measurements Lab. “There are lots of theories attempting to explain the imbalance, but there’s no experimental evidence to show that any of them can account for it. It’s a huge mystery on the level of asking why the universe is here. Accepted physics can’t explain it.”

An answer might be found by examining radioactivity in neutrons, which decay in two different ways that can be distinguished by a specially configured detector. Though all observations thus far have invariably shown these two ways occur with equal frequency in nature, finding a slight imbalance between the two would imply that nature favors conditions that would create a bit more matter than antimatter, resulting in the universe we recognize.

Two types of neutron decay produce a proton, an electron and an electron antineutrino but eject them in different configurations, The experiments at NIST detected no imbalance, but the improved sensitivity could help place limits on competing theories about the matter-antimatter imbalance in the universe [Image credit: emiT team]

Mumm and his collaborators from several institutions used a detector at the NIST Center for Neutron Research to explore this aspect of neutron decay with greater sensitivity than was ever possible before. For the moment, the larger answer has eluded them—several years of observation and data analysis once again turned up no imbalance between the two decay paths. But the improved sensitivity of their approach means that they can severely limit some of the numerous theories about the universe’s matter-antimatter imbalance, and with future improvements to the detector, their approach may help constrain the possibilities far more dramatically.

“We have placed very tight constraints on what these theories can say,” Mumm says. “We have given theory something to work with. And if we can modify our detector successfully, we can envision limiting large classes of theories. It will help ensure the physics community avoids traveling down blind alleys.”

Reference
[1] H.P. Mumm, T.E. Chupp, R.L. Cooper, K.P. Coulter, S.J. Freedman, B.K. Fujikawa, A. García, G.L. Jones, J.S. Nico, A.K. Thompson, C.A. Trull, J.F. Wilkerson and F.E. Wietfeldt. "New limit on time-reversal violation in beta decay". Physical Review Letters, Vol. 107, p. 102301 (2011). DOI: 10.1103/PhysRevLett.107.102301. Abstract.

[We thank National Institute of Standards and Technology, Boulder, CO for materials used in this report]

Three-Body Force in Nucleus

David Dean (left) and Hai Ah Nam (right)

The nucleus of an atom, like most everything else, is more complicated than we first thought. Just how much more complicated is the subject of a Petascale Early Science project led by Oak Ridge National Laboratory's David Dean.

According to findings outlined by Dean and his colleagues in a recent paper in the journal Physical Review Letters [1], researchers who want to understand how and why a nucleus hangs together as it does and disintegrates when and how it does have a very tough job ahead of them. Scientists from five institutes have contributed to this project: (from USA) Department of Physics and Astronomy, Iowa State University; Lawrence Livermore National Laboratory; Michigan State University; Oak Ridge National Laboratory; (from Canada) TRIUMF, Vancouver.

Specifically, they must take into account the complex nuclear interactions known as the three-body force.

Nuclear theory to this point has assumed that the two-body force is sufficient to explain the workings of a nucleus. In other words, the half-life or decay path of an unstable nucleus was to be understood through the combined interactions of pairs of protons and neutrons within.

An accurate picture of the carbon-14 nucleus must consider the interactions among protons and neutrons both in pairs (known as the two-body force, left) and in threes (known as the three-body force, right).

Dean's team, however, determined that the two-body force is not enough; researchers must also tackle the far more difficult challenge of calculating combinations of three particles at a time (three protons, three neutrons, or two of one and one of the other). This approach yields results that are both different from and more accurate than those of the two-body force.

Nuclei are held together by the strong force, one of four basic forces that govern the universe (The other three are gravity, which holds planets, solar systems, and galaxies together and pins us to the ground, the electromagnetic force, which holds matter together and keeps us from, for instance, falling through the ground, and the weak force, which drives nuclear decay). The strong force acts primarily to combine elementary particles known as quarks into protons and neutrons through the exchange of force carriers known as gluons. Each proton or neutron has three quarks. The strong force also holds neighboring protons and neutrons together into a nucleus.

It does so imperfectly, however. Many nuclei are unstable and will eventually decay, emitting one or more particles and becoming a smaller nucleus. While we cannot say specifically when an individual nucleus will decay, we can determine the likelihood it will do so within a certain time. Thus an isotope's half-life is the time it takes half the nuclei in a sample to decay. Known half-lives range from an absurdly small fraction of a second for beryllium-8 to more than 2 trillion trillion years for tellurium-128.

One job of nuclear theory, then, is to determine why nuclei have different half-lives and predict what those half-lives are.

"For a long time, nuclear theory assumed that two-body forces were the most important and that higher-body forces were negligible," noted team member and ORNL computational physicist Hai Ah Nam. "You have to start with an assumption: How to capture the physics best with the least complexity?"

Two factors complicate the choice of approaches. First, two-body interactions do accurately describe some nuclei. Second, accurate calculations including three-body forces are very difficult and demand state-of-the-art supercomputers such as ORNL's Jaguar, the most powerful system in the United States. With the ability to churn through as many as 2.33 thousand trillion calculations each second, or 2.33 petaflops, Jaguar gave the team the computing muscle it needed to analyze the carbon-14 nucleus using the three-body force.

Carbon-14, with six protons and eight neutrons, is the isotope behind carbon dating, allowing researchers to determine the age of plant- or animal-based relics going back as far as 60,000 years. It was an ideal choice for this project because studies using only two-body forces dramatically underestimate the isotope's half-life, which is around 5,700 years.

"With Jaguar we are able to do ab initio calculations, using three-body forces, of the half-life for carbon-14," Nam said. "It's an observable that is sensitive to the three-body force. This is the first time that we've demonstrated at this large scale how the three-body force contributes."

The three-body force does not replace the two-body force in these calculations, she noted; rather, the two approaches are combined to present a more refined picture of the structure of the nucleus. In the carbon-14 calculation, the three-body force serves to correct a serious underestimation of the isotope's half-life produced by the two-body force alone.

Dean and his colleagues used an application known as Many Fermion Dynamics, nuclear, or MFDn, which was created by team member James Vary of Iowa State University. With it, they tackled the carbon-14 nucleus using an approach known as the nuclear shell model and performing ab initio calculations—or calculations based on the fundamental forces between protons and neutrons.

Analogous to the atomic shell model that explains how many electrons can be found at any given orbit, the nuclear shell model describes the number of protons and neutrons that can be found at a given energy level. Generally speaking, the nucleons gather at the lowest available energy level until the addition of any more would violate the Pauli exclusion principle, which states that no two particles can be in the same quantum state. At that point, some nucleons bump up to the next higher energy level, and so on. The force between nucleons complicates this picture and creates an enormous computational problem to solve.

The carbon-14 calculation, for instance, involved a billion-by-billion matrix containing a quintillion values. Fortunately, most of those values are zero, leaving about 30 trillion nonzero values to then be multiplied by a billion vector values. As Nam noted, just keeping the problem straight is a phenomenally complex task, even before the calculation is performed; those 30 trillion matrix elements take up 240 terabytes of memory.

"Jaguar is the only system in the world with the capability to store that much information for a single calculation," Nam said. "This is a huge, memory-intensive calculation."

The job is even more daunting with larger nuclei, and researchers will have a long wait for supercomputers powerful enough to compute the nature of the largest nuclei using the three-body force. Even so, if the three-body force gives more accurate results than the two-body force, should researchers be looking at four, five, or more nucleons at a time?

"Higher-body forces are still under investigation, but it will require more computational resources than we currently have available," Nam said.

Reference
[1] P. Maris, J. P. Vary, P. Navráti, W. E. Ormand, H. Nam, and D. J. Dean, "Origin of the Anomalous Long Lifetime of ¹⁴C", Physical Review Letters, 106, 202502 (2011). Abstract.

[The text is written by Leo Williams of Oak Ridge National Laboratory]

Phase Diagram of Quantum Chromodynamics

Nu Xu [Photo courtesy: Lawrence Berkeley National Laboratory]

In its infancy, when the universe was a few millionths of a second old, the elemental constituents of matter moved freely in a hot, dense soup of quarks and gluons. As the universe expanded, this quark–gluon plasma quickly cooled, and protons and neutrons and other forms of normal matter “froze out”: the quarks became bound together by the exchange of gluons, the carriers of the color force.

Nu Xu of the U.S. Department of Energy’s Lawrence Berkeley National Laboratory (Berkeley Lab), the spokesperson for the STAR experiment at the Relativistic Heavy Ion Collider (RHIC) at DOE’s Brookhaven National Laboratory says,“The theory that describes the color force is called quantum chromodynamics, or QCD, which has been extremely successful at explaining interactions of quarks and gluons at short distances, such as high-energy proton and antiproton collisions at Fermi National Accelerator Laboratory. But in bulk collections of matter – including the quark-gluon plasma – at longer distances or smaller momentum transfer, an approach called lattice gauge theory has to be used.”























Image 1: An ordinary proton or neutron (foreground) is formed of three quarks bound together by gluons, carriers of the color force. Above a critical temperature, protons and neutrons and other forms of hadronic matter “melt” into a hot, dense soup of free quarks and gluons (background), the quark-gluon plasma.

Until recently, lattice QCD calculations of hot, dense, bulk matter could not be tested against experiment. Beginning in 2000, however, RHIC was able to recreate the extreme conditions of the early universe in miniature, by colliding massive gold nuclei (heavy ions) at high energies.

Experimentalists at RHIC, working with theorist Sourendu Gupta of India’s Tata Institute of Fundamental Research, have recently compared lattice-theory predictions about the nature of the quark-gluon plasma with certain STAR experimental results for the first time. In so doing they have established the temperature boundary where ordinary matter and quark matter cross over and change phase. Their results appear in the journal `Science' [1].

The authors of the paper are: Sourendu Gupta of Tata Institute of Fundamental Research in Mumbai, India, where the theoretical calculations for this paper were carried out; Bedangadas Mohanty of the Variable Energy Cyclotron Centre in Kolkata, India (He was formerly a postdoctoral fellow at Berkeley Lab); Xiafeng Luo, Hans Georg Ritter, and Nu Xu of Berkeley Lab’s Nuclear Science Division (Luo is also with the University of Science and Technology of China in Hefei, and Xu is also with the Central China Normal University in Wuhan).

Phase diagrams

The aim of both the theoretical and experimental work is to explore and fix key points in the phase diagram for quantum chromodynamics. Phase diagrams are maps, showing, for example, how changes in pressure and temperature determine the phases of water, whether ice, liquid, or vapor. A phase diagram of QCD would map the distribution of ordinary matter (known as hadronic matter), the quark-gluon plasma, and other possible phases of QCD such as color superconductivity.

“Plotting a QCD phase diagram requires both theory calculations and experimental effort with heavy-ion collisions,” says Xu, who is a member of Berkeley Lab’s Nuclear Science Division and an author of the Science paper. Experimental studies require powerful accelerators like RHIC on Long Island or the Large Hadron Collider at CERN in Geneva, while calculations of QCD using lattice gauge theory require the world’s biggest and fastest supercomputers. Direct comparisons can achieve more than either approach alone.

One of the basic requirements of any phase diagram is to establish its scale. A phase diagram of water might be based on the Celsius temperature scale, defined by the boiling point of water under normal pressure (i.e., at sea level). Although the boiling point changes with pressure – at higher altitudes water boils at lower temperatures – these changes are measured against a fixed value.

The scale of the QCD phase diagram is defined by a transition temperature at the zero value of “baryon chemical potential.” Baryon chemical potential measures the imbalance between matter and antimatter, and zero indicates perfect balance.

Through extensive calculations and actual data from the STAR experiment, the team was indeed able to establish the QCD transition temperature. Before they could do so, however, they first had to realize an equally significant result, showing that the highly dynamical systems of RHIC’s gold-gold collisions, in which the quark-gluon plasma winks in and out of existence, in fact achieve thermal equilibrium. Here’s where theory and experiment worked hand in hand.

“The fireballs that result when gold nuclei collide are all different, highly dynamic, and last an extremely short time,” says Hans Georg Ritter, head of the Relativistic Nuclear Collisions program in Berkeley Lab’s Nuclear Science Division and an author of the Science paper. Yet because differences in values of the kind observed by STAR are related to fluctuations in thermodynamic values predicted by lattice gauge theory, says Ritter, “by comparing our results to the predictions of theory, we have shown that what we measure is in fact consistent with the fireballs reaching thermal equilibrium. This is an important achievement.”






















Image 2: The “current conjecture” for the QCD phase diagram. The boundary between the normal (hadronic) low-temperature phase and the high-temperature quark-gluon plasma phase is marked in black. The square box on the solid line indicates the yet-to-be-found critical point where phases can co-exist; RHIC is the only heavy-ion collider whose energy can be tuned across the region where it is likely to lie. Neutrons and protons and other ordinary matter particles (including antimatter particles) are detected after they “freeze out” of fireballs caused by heavy-ion collisions like those at RHIC, indicated by the dotted line. To the right is a possible region of “color superconductivity.”

The scientists were now able to proceed with confidence in establishing the scale of the QCD phase diagram. After a careful comparison between experimental data and the results from the lattice gauge theory calculations, the scientists concluded that the transition temperature (expressed in units of energy) is 175 MeV (175 million electron volts).

Thus the team could develop a “conjectural” phase diagram that showed the boundary between the low-temperature hadronic phase of ordinary matter and the high-temperature quark-gluon phase.

In search of the critical point

Lattice QCD also predicts the existence of a “critical point.” In a QCD phase diagram the critical point marks the end of a line showing where the two phases cross over, one into the other. By changing the energy, for example, the baryon chemical potential (balance of matter and antimatter) can be adjusted.

Among the world’s heavy-ion colliders, only RHIC can tune the energy of the collisions through the region of the QCD phase diagram where the critical point is most likely to be found – from an energy of 200 billion electron volts per pair of nucleons (protons or neutrons) down to 5 billion electron volts per nucleon pair.

Says Ritter, “Establishing the existence of a QCD critical point would be much more significant than setting the scale.” In 2010, RHIC started a program to search for the QCD critical point.

Xu says, “In this paper, we compared experimental data with lattice calculations directly, something never done before. This is a real step forward and allows us to establish the scale of the QCD phase diagram. Thus begins an era of precision measurements for heavy-ion physics.”

Reference
[1] Sourendu Gupta, Xiaofeng Luo, Bedangadas Mohanty, Hans Georg Ritter, Nu Xu, "Scale for the Phase Diagram of Quantum Chromodynamics", Science, vol. 332, pp. 1525-1528 (June 24, 2011). Abstract.

[The text is written by Paul Preuss of Lawrence Berkeley National Laboratory]