Discovery of Weyl Fermions, Topological Fermi Arcs and Topological Nodal-Line States of Matter

Princeton University group (click on the picture to view with higher resolution), From left to right: Guang Bian, M. Zahid Hasan (Principal investigator), Nasser Alidoust, Hao Zheng, Daniel S. Sanchez, Suyang Xu and Ilya Belopolski. 

Author: M. Zahid Hasan

Affiliation: Department of Physics, Princeton University, USA

Link to Hasan Research Group: Laboratory for Topological Quantum Matter & Advanced Spectroscopy >>

The eponymous Dirac equation describes the first synthesis of quantum mechanics and special relativity in describing the nature of electron. Its solutions suggest three distinct forms of relativistic particles - the Dirac, Majorana and Weyl fermions [1-3]. In 1929, Hermann Weyl proposed the simplest version of the equation, whose solution predicted massless fermions with a definite chirality or handedness [3]. Weyl’s equation was intended as a model of elementary articles, but in nearly 86 years, no candidate Weyl fermions have ever been established in high-energy experiments. Neutrinos were once thought to be such particles but later found to possess a small mass. Recently, analogs of the fermion particles have been discovered in certain electronic materials that exhibit strong spin-orbit coupling and topological behavior. Just as Dirac fermions emerge as signatures of topological insulators [4], researchers have shown that electronic excitations in semimetals such as tantalum or niobium arsenides (TaAs and NbAs) behave like Weyl fermions [5-7]. And such a behavior is consistent with their topological semimetal bandstructures [8,9].

Past 2Physics article by M. Zahid Hasan:
July 18, 2009: "Topological Insulators : A New State of Quantum Matter"

In 1937 physicist Conyers Herring considered under what conditions electronic bands in solids have the same energy by accident in crystals that lack certain symmetries [10]. Near these accidental band touching points, the low-energy excitations, or electronic quasiparticles can be described by an equation that is essentially identical to the 1929 Weyl equation. In recent times, these touching points have been theoretically studied in the context of topological materials and are referred to as Weyl points and the quasiparticles near them are the emergent Weyl fermions [11]. In these solids, the electrons’ quantum-mechanical wave functions acquire a phase, as though they were moving in a superficial magnetic field that is defined in momentum space. In contrast to a real magnetic field, this fictional field (known as a Berry curvature) admits excitations that behave like magnetic monopoles. These monopoles are topological defects or singularities that locate at the Weyl points. So the real space Weyl points are associated with chiral fermions and in momentum space they behave like magnetic monopoles [11-17]. The fact that Weyl nodes are related to magnetic monopoles suggests they will be found in topological materials that are in the vicinity of a topological phase transition [14,15]. The surface of a topological insulator has a Fermi surface that forms a closed loop in momentum space; in a Weyl semimetal, these loops become non-closed arcs as some symmetry is lifted [11,12]. These Fermi arcs terminate at the location of the bulk Weyl points ensuring their topological nature [12]. Theory had suggested that Weyl semimetals should occur in proximity to topological insulators in which inversion or time-reversal symmetry was broken [12,14,16].

Building on these ideas, researchers, including the Princeton University group, used ab initio calculations to predict candidate materials [8,9] and perform angle-resolved photoemission spectroscopy to detect the Fermi arcs, characteristic of Weyl nodes, on the surface of TaAs and NbAs [5-7]. ARPES is an ideal tool for studying such a topological material as known from the extensive body of works on topological insulators [4]. The ARPES technique involves shooting high-energy photons on a material and measuring the energy, momentum and spin of the ejected electrons both from the surface and the bulk. This allows for the explicit determination of both bulk Weyl nodes and the Fermi-arc surface states (Figure 1).

Figure 1: (click on the image to view with high resolution) Weyl fermion and Fermi arcs (a) Schematic of the band structure of a Weyl fermion semimetal. (b) Correspondence of the bulk Weyl fermions to surface Fermi arc states. (c) ARPES mapping of TaAs Fermi surface. (d) Fermi arc surface states and Weyl nodes on the (001) surface of TaAs. (e) Linear dispersion of Weyl quasi-particles in TaAs. (Adapted form Ref. [5])

In the absence of spin-orbit coupling, the tantalum arsenide material is a nodal-line semimetal in which the bulk Fermi surface is a closed loop in momentum space [8,17,18]. With spin-orbit coupling turned on, the loop-shaped nodal line condenses into discrete Weyl points in momentum space [8]. In this sense the topological nodal-line semimetal can be thought of as a state where the Weyl semimetals originate from by further symmetry breaking (Figure 2). Such a state has been considered in theory previously [17] but it lacked concrete experimental realizations. Very recently, the first example of a topological nodal-line semimetal in the lead tantalum selenide (PbTaSe₂) materials has been reported experimentally [18]. Even though many predictions existed, no concrete experimentally realizable material was found. These findings suggest that Weyl semimetals [5-7] and nodal-line semimetals [17-18] are the first two examples of topological materials that are intrinsically gapless in contrast to topological insulators [4].

Figure 2: (click on the image to view with high resolution) Topological nodal-line semimetals (a) Schematic of a Weyl semimetal and a topological nodal-line semimetal. (b) ARPES mapping and theoretical simulation of (001)-surface band structure of PbTaSe₂ showing the loop-shaped bulk Fermi surface. (c) ARPES spectrum and theoretical band structure along some momentum space directions. (e) Calculated iso-energy band contour showing the nodal line and topological surface states. (Adapted from Ref. [18])

In the 1980s, Nielsen and Ninomiya suggested that exotic effects, like the ABJ (Adler-Bell-Jackiw) chiral anomaly—in which the combination of an applied electric and magnetic fields generates an excess of quasiparticles with a particular chirality—were associated with Weyl fermions and could be observable in 3D crystals [13]. A further correspondence has been established more recently with the increased understanding of materials with band structures that are topologically protected [11-17]. Unusual transport properties that are associated with Weyl fermions, such as a reduction of the electrical resistance in the presence of an applied magnetic field, have already been reported in the TaAs class of materials [19,20] (Figure 3). Weyl materials can also act as a novel platform for topological superconductivity leading to the realization of Weyl-Majorana modes potentially opening a new pathway for investigating qubit possibilities [21]. Weyl particles have also been observed in photonic (bosonic) crystals. In these systems the number of optical modes has an unusual scaling with the volume of the photonic crystal, which may allow for the construction of large-volume single-mode lasers [22]. Development in the last few months seems to suggest that Weyl particles are indeed associated with a number of unexpected quantum phenomena and these findings may lead to applications in next-generation photonics and electronics.

Figure 3: (click on the image to view with high resolution) Signature of the chiral anomaly in the Weyl fermion semimetal TaAs. (a) Magneto-resistance (MR) data of the Weyl semimetal TaAs in the presence of parallel electric and magnetic fields at T = 2 K. The MR decreases as one increases the magnetic field. (b) MR as a function of angle between the electric and the magnetic fields. The negative magneto-resistance is quickly suppressed as one varies the direction of the magnetic ~B field away from that of the electric ~E field. The observed negative MR and its angular dependence serve as the key signature of the chiral anomaly. (c,d) Landau energy spectra of the left- and right-handed Weyl fermions in the presence of parallel electric and magnetic fields. (Adapted from Ref. [20])

References:
[1] Frank Wilczek “Why are there analogies between condensed matter and particle theory?” Physics Today, 51, 11–13 (1998). Abstract.
[2] Palash B. Pal, “Dirac, Majorana and Weyl fermions”, American Journal of Physics, 79, 485–498 (2011). Abstract.
[3] Hermann Weyl, “Elektron und Gravitation. I”, Zeitschrift für Physik, 56, 330 (1929). Abstract.
[4] M. Z. Hasan and C.L. Kane “Topological Insulators”, Review of Modern Physics, 82, 3045 (2010). Abstract.
[5] Su-Yang Xu, Ilya Belopolski, Nasser Alidoust, Madhab Neupane, Guang Bian, Chenglong Zhang, Raman Sankar, Guoqing Chang, Zhujun Yuan, Chi-Cheng Lee, Shin-Ming Huang, Hao Zheng, Jie Ma, Daniel S. Sanchez, BaoKai Wang, Arun Bansil, Fangcheng Chou, Pavel P. Shibayev, Hsin Lin, Shuang Jia, M. Zahid Hasan, “Discovery of a Weyl Fermion Semimetal and Topological Fermi Arcs in TaAs”,  Science, 349, 613 (2015). Abstract.
[6] Su-Yang Xu, Nasser Alidoust, Ilya Belopolski, Zhujun Yuan, Guang Bian, Tay-Rong Chang, Hao Zheng, Vladimir N. Strocov, Daniel S. Sanchez, Guoqing Chang, Chenglong Zhang, Daixiang Mou, Yun Wu, Lunan Huang, Chi-Cheng Lee, Shin-Ming Huang, BaoKai Wang, Arun Bansil, Horng-Tay Jeng, Titus Neupert, Adam Kaminski, Hsin Lin, Shuang Jia, M. Zahid Hasan, “Discovery of a Weyl Fermion state with Fermi arcs in NbAs”, Nature Physics, 11, 748 (2015). Abstract.
[7] B.Q. Lv, H.M. Weng, B.B. Fu, X.P. Wang, H. Miao, J. Ma, P. Richard, X.C. Huang, L.X. Zhao, G.F. Chen, Z. Fang, X. Dai, T. Qian, H. Ding, “Experimental Discovery of Weyl Semimetal TaAs”, Physical Review X, 5, 031013 (2015). Abstract; B.Q. Lv, N. Xu, H.M. Weng, J.Z. Ma, P. Richard, X.C. Huang, L.X. Zhao, G.F. Chen, C.E. Matt, F. Bisti, V.N. Strocov, J. Mesot, Z. Fang, X. Dai, T. Qian, M. Shi, H. Ding, "Observation of Weyl nodes in TaAs", Nature Physics, 11, 724 (2015). Abstract.
[8] Shin-Ming Huang, Su-Yang Xu, Ilya Belopolski, Chi-Cheng Lee, Guoqing Chang, BaoKai Wang, Nasser Alidoust, Guang Bian, Madhab Neupane, Chenglong Zhang, Shuang Jia, Arun Bansil, Hsin Lin, M. Zahid Hasan, “A Weyl Fermion Semimetal with Surface Fermi Arcs in the Transition Metal Monopnictide TaAs Class”, Nature Communications, 6, 7373 (2015). Abstract.
[9] Hongming Weng, Chen Fang, Zhong Fang, B. Andrei Bernevig, Xi Dai, “Weyl Semimetal Phase in Noncentrosymmetric Transition-Metal Monophosphides”, Physical Review X, 5, 011029 (2015). Abstract.
[10] Conyers Herring, “Accidental Degeneracy in the Energy Bands of Crystals”, Physical Review, 52, 365-373 (1937). Abstract.
[11] Ashvin Vishwanath, “Viewpoint: Where the Weyl Things Are”, Physics, 8, 84 (2015). Full Text.
[12] Xiangang Wan, Ari M. Turner, Ashvin Vishwanath, Sergey Y. Savrasov, “Topological Semimetal and Fermi-Arc Surface States in the Electronic Structure of Pyrochlore Iridates”, Physical Review B, 83, 205101 (2011). Abstract.
[13] H. B. Nielsen, Masao Ninomiya, “The Adler-Bell-Jackiw Anomaly and Weyl Fermions in a Crystal”, Physics Letters B, 130, 389 (1983). Abstract.
[14] Shuichi Murakami, “Phase Transition Between the Quantum Spin Hall and Insulator Phases in 3D: Emergence of a Topological Gapless Phase”, New Journal of Physics, 9, 356 (2007). Full Text.
[15] Grigory E. Volovik, "The Universe in a Helium Droplet", Oxford University Press (2003).
[16] A.A. Burkov, Leon Balents, "Weyl semimetal in a Topological Insulator multilayer", Physical Review Letters, 107, 127205 (2011). Abstract.
[17] A. A. Burkov, M. D. Hook, Leon Balents, "Topological Nodal Semimetals", Physical Review B, 84, 235126 (2011). Abstract.
[18] Guang Bian, Tay-Rong Chang, Raman Sankar, Su-Yang Xu, Hao Zheng, Titus Neupert, Ching-Kai Chiu, Shin-Ming Huang, Guoqing Chang, Ilya Belopolski, Daniel S. Sanchez, Madhab Neupane, Nasser Alidoust, Chang Liu, BaoKai Wang, Chi-Cheng Lee, Horng-Tay Jeng, Chenglong Zhang, Zhujun Yuan, Shuang Jia, Arun Bansil, Fangcheng Chou, Hsin Lin, M. Zahid Hasan , "Topological Nodal-Line Fermions in Spin-Orbit Metal PbTaSe₂", Nature Communications", 7:10556 (2016). Abstract.
[19] Xiaochun Huang, Lingxiao Zhao, Yujia Long, Peipei Wang, Dong Chen, Zhanhai Yang, Hui Liang, Mianqi Xue, Hongming Weng, Zhong Fang, Xi Dai, Genfu Chen, "Observation of the chiral anomaly induced negative magneto-resistance in 3D Weyl semi-metal TaAs", Physical Review X, 5, 031023 (2015). Abstract.
[20] Chenglong Zhang, Su-Yang Xu, Ilya Belopolski, Zhujun Yuan, Ziquan Lin, Bingbing Tong, Nasser Alidoust, Chi-Cheng Lee, Shin-Ming Huang, Hsin Lin, Madhab Neupane, Daniel S. Sanchez, Hao Zheng, Guang Bian, Junfeng Wang, Chi Zhang, Titus Neupert, M. Zahid Hasan, Shuang Jia, "Observation of the Adler-Bell-Jackiw chiral anomaly in a Weyl semimetal", arXiv:1503.02630 [cond-mat.mes-hall] (2015). [To appear in Nature Communications].
[21] Anffany Chen, M. Franz, "Superconducting proximity effect and Majorana flat bands in the surface of a Weyl semimetal", arXiv:1601.01727 [cond-mat.supr-con] (2016).
[22] Ling Lu, Zhiyu Wang, Dexin Ye, Lixin Ran, Liang Fu, John D. Joannopoulos, Marin Soljačić, “Experimental Observation of Weyl Points”, Science, 349, 622 (2015). Abstract.

Physics Nobel Prize 2015: Neutrino Oscillations

Takaaki Kajita (left) and Arthur B. McDonald

The Nobel Prize in Physics 2015 is awarded jointly to Takaaki Kajita (of Super-Kamiokande Collaboration, University of Tokyo, Japan) and Arthur B. McDonald (Sudbury Neutrino Observatory Collaboration, Queen’s University, Canada) "for the discovery of neutrino oscillations, which shows that neutrinos have mass".

The Nobel Prize in Physics 2015 recognises Takaaki Kajita and Arthur B. McDonald  for their key contributions to the experiments which demonstrated that neutrinos change identities. This metamorphosis requires that neutrinos have mass. The discovery has changed our understanding of the innermost workings of matter and can prove crucial to our view of the universe.

Around the turn of the millennium, Takaaki Kajita presented the discovery that neutrinos from the atmosphere switch between two identities on their way to the Super-Kamiokande detector in Japan.

Meanwhile, the research group in Canada led by Arthur B. McDonald could demonstrate that the neutrinos from the Sun were not disappearing on their way to Earth. Instead they were captured with a different identity when arriving to the Sudbury Neutrino Observatory.

A neutrino puzzle that physicists had wrestled with for decades had been resolved. Compared to theoretical calculations of the number of neutrinos, up to two thirds of the neutrinos were missing in measurements performed on Earth. Now, the two experiments discovered that the neutrinos had changed identities.

The discovery led to the far-reaching conclusion that neutrinos, which for a long time were considered massless, must have some mass, however small.

For particle physics this was a historic discovery. Its Standard Model of the innermost workings of matter had been incredibly successful, having resisted all experimental challenges for more than twenty years. However, as itrequires neutrinos to be massless, the new observations had clearly showed that the Standard Model cannot be the complete theory of the fundamental constituents of the universe.

The discovery rewarded with this year’s Nobel Prize in Physics have yielded crucial insights into the all but hidden world of neutrinos. After photons, the particles of light, neutrinos are the most numerous in the entire cosmos. The Earth is constantly bombarded by them.

Many neutrinos are created in reactions between cosmic radiation and the Earth’s atmosphere. Others are produced in nuclear reactions inside the Sun. Thousands of billions of neutrinos are streaming through our bodies each second. Hardly anything can stop them passing; neutrinos are nature’s most elusive elementary particles.

Now the experiments continue and intense activity is underway worldwide in order to capture neutrinos and examine their properties. New discoveries about their deepest secrets are expected to change our current understanding of the history, structure and future fate of the universe.

Homepage of Takaaki Kajita >>
Homepage of Arthur B. McDonald >>

"Secrets of the Universe"

2Physics.com is partnering with K2 Communications, a global leader in the production and distribution of IMAX films, which is currently working on the production of a IMAX 3D documentary film titled "Secrets of the Universe". K2 Communications has been commissioned by the National Science Foundation (NSF) by way of a substantial grant to promote the pursuit of an education and/or career in STEM (Science, Technology, Engineering & Mathematics) by inspiring an appreciation for science through the amazing discoveries in the world of particle physics.

The plan is to do this through a spectacular IMAX 3D experience titled "Secrets of the Universe" that will explore some of the most elusive and fascinating phenomena in the cosmos under investigation at the Large Hadron Collider (LHC) in Geneva, Switzerland, and explain today’s advance scientific discoveries in layman's terms. With greater understanding and enthusiasm from the general public, we can expect greater support and progress for STEM.

The film will address, more specifically, the exciting possibilities for discovery during the second run currently under way at the LHC: research on dark matter, antimatter, and parallel universes that has the potential to turn science fiction into science fact. Perhaps most importantly, it will feature the science and engineering feat that is the Large Hadron Collider - arguably humankind’s greatest machine - as a monument to how technology and research build off each other to create perpetual progress.

Multiple award-winning Director Stephen Low – a veteran of more than 15 giant screen documentaries – will lead the film team that includes the highly acclaimed IMAX cinematographer Sean Phillips.



Here is the Link to the "Secrets of the Universe" campaign >>

A Quantum Gas Microscope for Fermionic Atoms

The Fermi gas microscope group: (from left) graduate students Katherine Lawrence and Melih Okan, postdoc Thomas Lompe, graduate student Matt Nichols, Professor Martin Zwierlein, and graduate student Lawrence Cheuk. Photo credit: Jose-Luis Olivares/MIT.

Authors: Lawrence Cheuk and Martin Zwierlein

Affiliation: 
Department of Physics, MIT-Harvard Center for Ultracold Atoms, and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA.

Link to Ultracold Quantum Gases Group >>

What do electrons, protons, neutrons and even quarks have in common? They all are fermions, particles with half-integer spin. Unlike their bosonic counterparts, integer spin particles, fermions cannot occupy one and the same quantum state. This simple fact leads to the structure of our elements, where electrons have to avoid each other and occupy different orbits around the atomic nucleus, or at least differ in their spin orientation.

When many fermions interact strongly with each other, they can form complex matter with exotic properties, from atomic nuclei to solid state materials, to distant neutron stars. Their collective behavior leads to diverse phenomena such as the structure of the elements, high-temperature superconductivity and colossal magneto-resistance.

Yet our understanding of strongly-interacting Fermi systems is limited. In recent years, ultracold atomic Fermi gases have emerged as a pristine platform to study many-fermion systems. In particular, fermionic atoms trapped in an optical lattice formed by standing waves of light can simulate the physics of electrons in a crystalline solid, shedding light on novel physical phenomena in materials with strong electron correlations.

Yet our understanding of strongly-interacting Fermi systems is limited. In recent years, ultracold atomic Fermi gases have emerged as a pristine platform to study many-fermion systems. In particular, fermionic atoms trapped in an optical lattice formed by standing waves of light can simulate the physics of electrons in a crystalline solid, shedding light on novel physical phenomena in materials with strong electron correlations.

In the present work, recently published in Physical Review Letters [3], we have realized quantum gas microscope that images ultracold fermionic ⁴⁰K atoms with single-lattice-site resolution. Similar results have also been achieved at about the same time by researchers at University of Strathclyde and Harvard University [4,5].

Figure Caption: Fermionic ⁴⁰K atoms in a 2D optical lattice with 541nm spacing imaged using Raman sideband cooling. Image taken from [3].

In our experiment, we prepare a two-dimensional layer of ⁴⁰K atoms via laser cooling and forced evaporation. The atoms are then trapped in an optical lattice formed by retro-reflected laser beams, which form a standing wave with 541nm spacing. In order to resolve atoms with single-lattice-site resolution, we utilize a novel setup that incorporates a solid immersion lens into the vacuum window. This allows an enhancement in the numerical aperture, leading to higher resolution and enhanced light collection. In addition, optical aberrations that arise from a planar window are minimized in this setup.

In order to detect the atoms, we perform fluorescence imaging while simultaneously cooling the atoms. To make the atoms fluoresce, they are illuminated with near-resonant light. However, as the atoms emit photons, they experience heating from the recoil of photons. As the atoms are heated up, they hop between lattice sites and can even hop out of the lattice. In order to faithfully measure the occupation of the lattice sites, one must therefore eliminate the heating that arises when atoms fluoresce. We accomplish this via a technique known as Raman sideband cooling.

Raman sideband cooling, a technique first demonstrated in the 1990s, selectively transfers atoms from high-energy states to lower energy states via a two-photon Raman process. Atoms that are already in the lowest energy state, however, remain “dark” to the Raman light. By collecting photons that are scattered during this cooling process, we extract the position of the atoms while cooling the atoms. Hopping and atom loss are thus avoided. Furthermore, we have found that even after imaging the atoms with Raman sideband cooling, the atoms are predominantly in the lowest energy state. This invites the possibility of assembling low-entropy many-fermion states atom by atom.

The advent of fermion microscope will allow new studies of many-fermion systems in optical lattices, such as measurement of high order correlations and detection of magnetic ordering. Such studies could shed light on the behavior of other fermions, in particular, electrons. This may one day advance our understanding of the diverse phenomena that arise in complex solid-state systems.

References:
[1] Waseem S. Bakr, Jonathon I. Gillen, Amy Peng, Simon Fölling, Markus Greiner, "A quantum gas microscope for detecting single atoms in a Hubbard-regime optical lattice", Nature, 462, 74 (2009). Abstract.
[2] Jacob F. Sherson, Christof Weitenberg, Manuel Endres, Marc Cheneau, Immanuel Bloch, Stefan Kuhr, "Single-atom-resolved fluorescence imaging of an atomic Mott insulator", Nature, 467, 68 (2010). Abstract.
[3] Lawrence W. Cheuk, Matthew A. Nichols, Melih Okan, Thomas Gersdorf, Vinay V. Ramasesh, Waseem S. Bakr, Thomas Lompe, Martin W. Zwierlein, "Quantum-Gas Microscope for Fermionic Atoms", Physical Review Letters, 114, 193001 (2015). Abstract.
[4] Maxwell F. Parsons, Florian Huber, Anton Mazurenko, Christie S. Chiu, Widagdo Setiawan, Katherine Wooley-Brown, Sebastian Blatt, Markus Greiner, "Site-Resolved Imaging of Fermionic ⁶Li in an Optical Lattice", Physical Review Letters, 114, 213002 (2015). Abstract.
[5] Elmar Haller, James Hudson, Andrew Kelly, Dylan A. Cotta, Bruno Peaudecerf, Graham D. Bruce, Stefan Kuhr, "Single-atom imaging of fermions in a quantum-gas microscope", arXiv:1503.02005v2 [cond-mat.quant-gas] (2015).

Finding Optical Transitions for Testing a Fundamental Constant’s Constancy

From left to right: José, Alexander and Hendrik  discuss the spectral analysis -- standing next to the Heidelberg electron beam ion trap, where the results were obtained.

Authors: Alexander Windberger, Hendrik Bekker, José R. Crespo López-Urrutia

Affiliation: Max-Planck-Institut für Kernphysik, Heidelberg, Germany.

We studied the uncharted optical spectra of the highly charged ions W¹⁴⁺, Re¹⁵⁺, Os¹⁶⁺, Ir¹⁷⁺, and Pt¹⁸⁺, and demonstrated generally applicable methods to identify the measured spectral lines. That allowed us to infer the transition energies for proposed ultra-stable frequency standards using Hf¹²⁺ and W¹⁴⁺ ions. In Ir¹⁷⁺, optical transitions with the highest sensitivity to a potential variation of the fine structure constant α ever predicted for a stable atomic system were determined. Highly advanced atomic structure calculations were benchmarked in the extreme regime of a triple level crossing.

Fundamental constants are taken as given by Nature. Our understanding of the origin of these constants is, however, rather poor: Their values are not set within the Standard Model but have to be determined empirically. Alternative theories, such as string or coupled dark energy theories, assume that fundamental constants emerge from dynamical fields and can vary at different times or places in the universe (see [1] for a review). Therefore, probing the stability of these constants allows us to search for physics beyond the Standard Model.

Our work focusses on testing a possible variation of the fine structure constant α, which characterizes the strength of interaction between charged particles and photons. Very small variations of α would lead to a detectable shift of wavelength, or color, of light which is emitted or absorbed by atoms. Following this approach the group of Webb et al. obtained the absorption spectra of interstellar clouds billions of light years away from us and in an extensive analysis found wavelength shifts for spectra observed at different angles [2]. This was interpreted as a spatial dipole-like variation of α.

We aim to test this extraordinary claim under well-defined laboratory conditions, preventing systematic uncertainties that the astrophysical observations might suffer from. Since the Earth, the Solar System, and our galaxy all move, a spatial variation translates into an effective temporal variation which was estimated at 10^-19/year [3]. Such a minuscule drift could be measured by monitoring the frequency ratio of two highly accurate optical atomic clocks. The clock transitions should be very sensitive to an α variation, but to nothing else. Highly charged ions fulfill these requirements. With an increasing ionic charge, the wavelengths of electronic transitions decrease and leave the range accessible to lasers. Systems with level crossings are an exception. When two or more configurations are almost equal in energy, optical transitions are possible. The level crossing of the 5s and 4f subshells predicted for Ir¹⁷⁺ should enable the highest sensitivity to the sought-after α variation in a stable atomic system [4].

No detailed knowledge of the electronic structure of these ion species existed. Most heavy highly charged ions, as Ir¹⁷⁺, are experimentally unexplored, and calculations are not sufficiently accurate for these complex systems. For our studies, we used the Heidelberg electron beam ion trap, which produces and traps the ions of interest. The continuously excited ions decay by emitting radiation, of which we analyzed the optical spectrum. An exemplary measurement can be seen in Fig. 1, showing the optical spectra of W¹⁴⁺, Re¹⁵⁺, Os¹⁶⁺, Ir¹⁷⁺, and Pt¹⁸⁺ (atomic numbers Z=74-78). These ions encompass the whole predicted 5s-4f level crossing region.

Figure 1. (Click on the figure to view with higher resolution) Typical spectral map of Ir ions measured using the Heidelberg electron beam ion trap. For this measurement we acquired spectra at 10 V intervals of the electron beam acceleration potential. New groups of fluorescence lines start to appear when the electron beam energy reaches the ionization potential of an ionic charge state. The new charge state is produced more efficiently as the electron beam energy further increases, and the fluorescence lines become stronger until the ionization threshold of the next higher charge state is reached. At this point the ion population is transferred to the next charge state, which starts to fluoresce, while the former one disappears. This dependence of the fluorescence intensity on the acceleration potential is depicted in the right graph. It is notable that this section of the optical spectrum assigned to Ir¹⁷⁺ already shows a dense manifold of spectral lines. In order to derive the level structure from the spectrum, sophisticated identification schemes had to be applied.

Subsequently, we assigned the measured spectral lines to their corresponding electronic transitions to establish the level scheme [5]. Given the large theoretical uncertainties, a direct comparison of calculated and measured spectra is futile. Instead, we used three alternative methods to identify the spectral lines.

First, we exploited the fact that these ions are isoelectronic, since they have the same number of electrons, and thus similar atomic structures. Over a limited range of atomic numbers, the transition energies depend on the respective nuclear charge with a simple polynomial scaling. By comparison between the measured scaling functions and theoretical predictions we were able to reliably identify all underlying transitions as can be seen in Fig. 2.

Figure 2. (Click on the figure to view with higher resolution) Identification of isoelectronic transitions using their characteristic energy scaling. (a) Measured spectra of W¹⁴⁺, Re¹⁵⁺, Os¹⁶⁺, Ir¹⁷⁺, and Pt¹⁸⁺ (black lines). An algorithm found nine isoelectronic transition energies that obey simple quadratic scaling laws (colored lines) as expected from theoretical considerations. (b) By comparing the experimentally determined constant offset A and the linear term B (full symbols) to the calculated ones (open symbols) an unambiguous identification of the underlying transitions could be achieved.

This method could be independently confirmed by measuring the identified transitions in Ir¹⁷⁺ with increased resolution and accuracy. The spectral lines revealed a characteristic line shape caused by the 8 T magnetic field present at the position of the trapped ions. The observed line shapes were individually modelled according to the Zeeman effect, leading to an independent verification in perfect agreement with the scaling method.

The identified transitions allowed us to test advanced atomic structure calculations for the first time in systems with such a complex level crossing of 4f ¹² 5s², 4f¹³ 5s, and 4f ¹⁴ configurations. We found that only relativistic multi-reference Fock-space coupled cluster calculations consistently showed a fair agreement with most of the observed lines.

A direct application is the determination of the transition energies of two proposed optical clock transitions with a potential relative frequency uncertainty of less than 10^-19 in W¹⁴⁺ and Hf¹²⁺ [6], another isoelectronic ion. Although we did not measure the spectrum of Hf¹²⁺, we were able to extrapolate the transition energy by applying the established energy scaling. Our experimental uncertainty is at least one order of magnitude smaller than that of predictions.

These clock transitions are exceptionally stable. However, they are not sensitive to a variation of the fine structure constant. For that, Ir¹⁷⁺ is ideal. By searching our data, we found closed transition cycles (Rydberg-Ritz principle) combining the identified with unidentified transitions. This enabled us to find two possible, but mutually excluding, candidates for the proposed α-sensitive transitions. We are currently performing more accurate measurements to remove this ambiguity.

Our method, line assignments by isoelectronic scaling of transitions (LINE ASSIST) is a straight-forward and general tool for exploring unknown spectra of highly charged ions. With the recent successful application of sympathetic cooling to highly charged ions [7], much higher accuracy can be achieved in future work: the ion temperature was reduced by nearly six orders of magnitude and the Doppler width accordingly. The experimental values for the transition energies obtained in the present work are needed for follow-up laser spectroscopy studies, applications as optical clock transitions, and testing the constancy of fundamental constants.

References:
[1] Jean-Philippe Uzan, "The fundamental constants and their variation: observational and theoretical status". Review of Modern Physics, 75, 403–455 (2003). Abstract.
[2] J. K. Webb, J. A. King, M. T. Murphy, V. V. Flambaum, R. F. Carswell, M. B. Bainbridge, "Indications of a Spatial Variation of the Fine Structure Constant". Physical Review Letters, 107, 191101 (2011). Abstract.
[3] J.C. Berengut, V.V. Flambaum, "Manifestations of a spatial variation of fundamental constants in atomic and nuclear clocks, Oklo, meteorites, and cosmological phenomena". Europhysics Letters, 97, 20006 (2012). Abstract.
[4] J.C. Berengut, V.A. Dzuba, V.V. Flambaum, A. Ong, "Electron-Hole Transitions in Multiply Charged Ions for Precision Laser Spectroscopy and Searching for Variations in α". Physical Review Letters, 106, 210802 (2011). Abstract.
[5] A. Windberger, J.R. Crespo López-Urrutia, H. Bekker, N.S. Oreshkina, J.C. Berengut, V. Bock, A. Borschevsky, V.A. Dzuba, E. Eliav, Z. Harman, U. Kaldor, S. Kaul, U.I. Safronova, V.V. Flambaum, C.H. Keitel, P.O. Schmidt, J. Ullrich, O.O. Versolato, "Identification of the Predicted 5s−4f  Level Crossing Optical Lines with Applications to Metrology and Searches for the Variation of Fundamental Constants". Physical Review Letters, 114, 150801 (2015). Abstract.
[6] V. A. Dzuba, A. Derevianko, V.V. Flambaum, "High-precision atomic clocks with highly charged ions: Nuclear-spin-zero f ¹²-shell ions". Physical Review A, 86, 054501 (2012). Abstract.
[7] L. Schmöger, O.O. Versolato, M. Schwarz, M. Kohnen, A. Windberger, B. Piest, S. Feuchtenbeiner, J. Pedregosa-Gutierrez, T. Leopold, P. Micke, A.K. Hansen, T.M. Baumann, M. Drewsen, J. Ullrich, P.O. Schmidt, J.R. Crespo López-Urrutia, "Coulomb crystallization of highly charged ions". Science, 347, 1233 (2015). Abstract.

Sound Velocity Bound and Neutron Stars

Paulo Bedaque (left) and Andrew W. Steiner (right)

Authors: Paulo Bedaque¹, Andrew W. Steiner^2,3,4 

Affiliation: 
¹Department of Physics, University of Maryland, College Park, USA 
²Institute for Nuclear Theory, University of Washington, Seattle, USA
³Department of Physics and Astronomy, University of Tennessee, Knoxville, USA 
⁴Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA. 

Neutron stars are the final stage in the evolution of a star, the remnants of supernova explosion marking the end of the star’s life. They are incredibly compact objects: masses comparable to the Sun’s are compressed in a region of about 10 miles radius. At these densities, most matter is composed of neutrons. The repulsion between neutrons balances precariously against the strong gravitational fields generated by this high matter concentration: a little less repulsion or a little more mass leads to the collapse of the star into a black hole [1].

It has been possible to measure the mass of several neutron stars, and until recently, all accurate mass measurements were near 1.4 times the mass of our sun. However, within the past few years, two neutron stars have been discovered to have a mass around twice that of our sun [2]. What this discovery means is that the neutron matter composing the star is stiffer than previously expected.

The speed of sound in air is about 346 meters per second, and it tends to increase with either the density or the temperature of the medium in which it travels. Since neutron stars contain the most dense matter in the universe one might wonder how fast the speed of sound is inside neutron stars.

Everywhere else in the universe [3], the speed of sound seems to be limited to the speed of light divided by the square root of 3, that is, v < 0.577 c (see, for example, the figures here: Link to plots >> ). At high enough densities or temperatures, the speed of sound approaches this limiting value. This result comes from quantum chromodynamics (QCD) [4] - the physical theory which describes how neutrons and protons (made of quarks) interact. At high enough densities and temperatures, QCD exhibits "asymptotic freedom", meaning that the interaction becomes weaker [5]. Unfortunately, neutron star densities are not large enough so that quarks are weakly interacting.

In a paper published in Physical Review Letters (as an 'Editor's suggestion') on January 21st [6], we showed that the speed of sound in neutron stars must exceed this value at some point inside a neutron star. The reason is that models where the speed of sound is smaller than the limiting value at all densities (those like the black lines in the figure) are too soft to produce neutron stars with masses twice the mass of the sun. Thus, the only alternative is that the speed of sound must look something like either the blue dotted or red dashed lines.

This result is important because it tells us more about how neutrons and protons interact, not only in neutron stars, but also here on earth [7]. It gives us more insight into how QCD behaves at high densities. Finally, it also helps us understand some of the more extreme neutron star-related processes like core-collapse supernovae, magnetar flares, and neutron star mergers.

Notes & References:
[1] See a diagram of stellar evolution from the Chandra X-ray observatory, their neutron star page, or the wikpedia entry on neutron stars.
[2] P.B. Demorest, T. Pennucci, S.M. Ransom, M.S.E. Roberts, J.W.T. Hessels, "A two-solar-mass neutron star measured using Shapiro delay". Nature, 467, 1081–1083 (2010). Abstract; John Antoniadis, Paulo C. C. Freire, Norbert Wex, Thomas M. Tauris, Ryan S. Lynch, Marten H. van Kerkwijk, Michael Kramer, Cees Bassa, Vik S. Dhillon, Thomas Driebe, Jason W. T. Hessels, Victoria M. Kaspi, Vladislav I. Kondratiev, Norbert Langer, Thomas R. Marsh, Maura A. McLaughlin, Timothy T. Pennucci, Scott M. Ransom, Ingrid H. Stairs, Joeri van Leeuwen, Joris P. W. Verbiest, David G. Whelan, "A Massive Pulsar in a Compact Relativistic Binary". Science, 340, 6131 (2013). Abstract.
[3] The only possible exception is matter inside the event horizon of a black hole, which is not causally connected with the rest of the universe anyway.
[4] See the Wikipedia article on Quantum Chromodynamics.
[5] This finding led to 2004 Nobel prize in physics for David J. Gross, H. David Politzer and Frank Wilczek.
[6] Paulo Bedaque, Andrew W. Steiner, "Sound Velocity Bound and Neutron Stars". Physical Review Letters, 114, 031103 (2015). Abstract. Also available at: arXiv:1408.5116 [nucl-th].
[7] Neutrons and protons are the basic building blocks of all atomic nuclei.

Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor

From Left to Right: (top row) Stevan Nadj-Perge, Ilya K. Drozdov, Jian Li, Hua Chen ; (bottom row) Sangjun Jeon, Allan H. MacDonald, B. Andrei Bernevig, Ali Yazdani.

Authors: Stevan Nadj-Perge¹, Ilya K. Drozdov¹, Jian Li¹, Hua Chen², Sangjun Jeon¹, Jungpil Seo¹, Allan H. MacDonald², B. Andrei Bernevig¹, Ali Yazdani¹.

Affiliation
¹Joseph Henry Laboratories and Dept of Physics, Princeton University, USA.
²Department of Physics, University of Texas at Austin, USA.

Link to Yazdani Lab >>
Link to Allan H. MacDonald's Group >>

In 1937 Italian scientist Ettore Majorana, one of the most promising theoretical physicists at that time, proposed a hypothetical fermionic excitation, now called Majorana fermion, which has a property that it is its own anti-particle [1]. Ever since significant efforts were invested in finding an elementary particle described by Majorana. While present for many years in particle physics community, it was only in 2001 that Alexei Kitaev suggested an intriguing possibility that a type of a quasi-particle, a condensed matter analog of the Majorana fermion could exist [2]. Such quasi-particle would emerge as a zero energy excitation localized at the boundary of a one dimensional topological superconductor. Following his seminal work various systems were proposed as a potential platform for realization of Majorana quasi-particles. Apart from fundamental scientific interest, the motivation for investigating Majorana bound states partly relies on their potential for use for quantum computing [3,4].

Past 2Physics article by Ali Yazdani :
August 25, 2013: "Visualizing Nodal Heavy Fermion Superconductivity"
by Brian Zhou, Shashank Misra, and Ali Yazdani.

Previous to our experiments, the most promising experimental route to realize these elusive bound states was based on semiconductor-superconductor interfaces in which Majorana fermions would appear as conductance peaks at zero energy [5,6]. Indeed experiments in 2012 reported zero energy conductance peaks suggesting presence of Majorana modes in these type of systems [7,8], however, alternative explanations related to disorder and Kondo phenomena proposed latter could not be fully ruled out. It is worth noting that in these interfaces spatial information about localized excitations is very hard to obtain.

Fig. 1: (A) Schematic of the proposal for realization and detection of Majorana states: A ferromagnetic atomic chain is placed on the surface of strongly spin-orbit–coupled superconductor and studied using STM. (B) Band structure of a linear suspended Fe chain before introducing spin-orbit coupling or superconductivity. The majority spin-up (red) and minority spin-down (blue) d-bands labeled by azimuthal angular momentum m are split by the exchange interaction J (degeneracy of each band is noted by the number of arrows). a, interatomic distance. (C) Regimes for trivial and topological superconducting phases are identified for the band structure shown in (B) as a function of exchange interaction in presence of SO coupling. The value J for Fe chains based on density functional calculations is noted. μ is the chemical potential.

Building upon previous proposal to realize Majorana modes in an array of magnetic nanoparticles [9], we proposed to use a chain of magnetic atoms coupled to a superconductor [10]. The key advantage of this platform is that the experimentally properties of this system can easily be studied using standard scanning tunneling microscopy (STM) technique. While ours and other follow-up initial proposals [11-16] consider specific orientation of the magnetic moments, the approach works also for ferromagnetic atomic chains as long as it is coupled to a superconductor with strong spin-orbit coupling (Fig. 1A) [17]. In this case, the large exchange interaction results in a band structure of the chains such that majority spin band is fully occupied while the Fermi level is in the minority spin bands. For example the electronic structure of a linear Iron (Fe) ferromagnetic atomic chain is shown in Fig. 1B. Considering only d-orbitals which are spin-polarized it is easy to show that many of the bandstructure degeneracies are lifted and that for large range of parameters, chemical potential and the exchange energy, such chains are in topologically non-trivial regime characterized by the odd number of crossing at the Fermi level (Fig 1C). When placed on the superconducting substrate with strong-spin orbit coupling the resulting superconductivity on the chain will necessarily be topological in nature resulting in zero energy Majorana bound states located at the chain ends.

Fig. 2: (A) Topograph of the Pb(110) surface after growth of Fe, showing Fe islands and chains indicated by white arrows and atomically clean terraces of Pb (regions with the same color) with size exceeding 1000 Å. (Lower-right inset) Anisotropic atomic structure of the Pb(110) surface (Upper-left insets) images of several atomic Fe chains and the islands from which they grow (scale bars, 50 Å). (B) Topography of the chain colorized by the conductance at H= ±1 T from low (dark blue) to high conductance (dark red). (C) Difference between conductance on and off the chain showing hysteresis behavior. (D and E) Atomic structure of the zigzag chain, as calculated using density functional theory. The Fe chain structure that has the lowest energy in the calculations matches the structural features in the STM measurements, a_B is the Bohr radius.

We have developed a way to grow iron atomic chains on the surface of lead (Pb) which, due to heavy atomic mass, is expected to have strong spin-orbit coupling. For this purpose we used Pb(110) crystallographic surface orientation which has characteristic anisotropy (Fig. 2(A) lower left inset). When a sub-monolayer of Fe is evaporated and slight annealing, the anisotropy of the substrate could trigger growth of one-dimensional atomic chains. We investigated the resulting structures by using STM at cryogenic temperatures (temperature was 1.4K in the experiment). On relatively large atomically ordered regions of the Pb(110) surface we observed self-assembled islands as well as single atom wide chains of Fe. Depending on growth conditions, we find Fe chains as long as 500 Å with ordered regions approaching 200 Å. In order to confirm ferromagnetic order on the chain we have performed spin-polarized measurements using bulk antiferromagnetic Chromium STM tips. Tunneling conductance (dI/dV) at a low bias voltage as a function of the out-of-plane magnetic field shows contrast for opposite fields (Fig. 2B) and a hysteresis behavior (Fig. 2C, note that no hysteresis is observed on the Pb substrate). The observed hysteresis loop corresponds to the tunneling of electrons between two magnets with the field switching only one of them at around 0.25 T.

We also observed the variation of the spin-polarized STM signal along the chain which is likely due to its electronic and structural properties. Indeed, both topographic features and periodicity of signal variation could be very well explained by our theory collaborators who performed density functional theory modeling. Their calculations suggested that our chains have zig-zag structure which explains both topographic information obtained using STM and matches well with our spin-polarized measurements (Fig. 2D and 2E).

Fig. 3: (A) STM spectra measured on the atomic chain at locations corresponding to those indicated in (B) and (C). For clarity, the spectra are offset by 100 nS. The red spectrum shows the zero-bias peak at one end of the chain. The gray trace measured on the Pb substrate can be fitted using thermally broadened BCS superconducting density of states (dashed gray line, fit parameters Δs = 1.36 meV, T = 1.45 K). (B and C) Zoom-in topography of the upper (B) and lower end (C) of the chain and corresponding locations for spectra marked (1 to 7). Scale bars, 25 Å. (D and E) Spectra measured at marked locations, as in (B) and (C). (F) Spatial and energy-resolved conductance maps of another atomic chain close to its end, which shows similar features in point spectra as in (A). The conductance map at zero bias (middle panel) shows increased conductance close to the end of the chain. Scale bar, 10 Å.

After establishing basic properties of our chains we investigated low-energy excitations using spatial spectroscopic mapping, see Fig 3. While on the surface of bare Pb(110), there is clear structure of the superconducting gap on the Fe atomic chain, the presence of the in-gap states is predominant (Fig. 3A). Most notably a peak close to zero bias voltage is observed near the chain end together with asymmetric less-developed gap-like structure in the middle of the chain (Fig. 3D and Fig. 3E). Both spatially resolved spectra and the spectroscopic maps at low bias voltage show signatures expected from Majorana bound states (Fig. 3F). The ability to correlate the location of the zero bias conductance peak with the end of the atomic chains is one of the main experimental results of our work. This is one of the basic requirements for interpreting that this feature is associated with the predicted Majorana bound state of a topological superconductor. In addition to robust observation of the zero bias peaks in many chains, we have performed several control experiments to eliminate other potential effects which may give similar looking signatures. For example, when superconductivity is suppressed by applying small magnetic field, the spectrum on the chain becomes featureless in contrast to what would be expected for Kondo effect. Also for very short chains zero biased peaks were not observed, ruling out trivial effects related to the chain ends. Furthermore, in order to increase experimental resolution we took measurements with superconducting tip which also confirm the over picture consistent with Majorana bound states in this system.

The observed spectroscopic signatures are consistent with the existence of Majorana bound states in our system. An obvious extension of our experiments is to create two dimensional islands and search for propagating Majorana modes or, for example, investigate other systems with both even and odd number of band crossing at Fermi level in order to further test the concept behind our study. Ultimately the future experiments will focus on manipulation of Majorana bound states in this system [18].

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] A. Yu. Kitaev, "Fault-tolerant quantum computation by anyons". Annals of Physics. 303, 2 (2003). Abstract.
[4] Jason Alicea, Yuval Oreg, Gil Refael, Felix von Oppen, Matthew P. A. Fisher, "Non-Abelian statistics and topological quantum information processing in 1D wire networks". Nature Physics, 7, 412 (2011). 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] Roman M. Lutchyn, Jay D. Sau, S. Das Sarma, "Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures". Physical Review Letters, 105, 077001 (2010). Abstract.
[7] 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.
[8] Anindya Das, Yuval Ronen, Yonatan Most, Yuval Oreg, Moty Heiblum, Hadas Shtrikman, "Zero-bias peaks and splitting in an Al-InAs nanowire topological superconductor as a signature of Majorana fermions". Nature Physics, 8, 887 (2012). Abstract. 2Physics Article.
[9] T. P. Choy, J. M. Edge, A. R. Akhmerov, C. W. J. Beenakker, "Majorana fermions emerging from magnetic nanoparticles on a superconductor without spin-orbit coupling". Physical Review B, 84, 195442 (2011). Abstract.
[10] S. Nadj-Perge, I. K. Drozdov, B. A. Bernevig, Ali Yazdani, "Proposal for realizing Majorana fermions in chains of magnetic atoms on a superconductor". Physical Review B, 88, 020407 (2013). Abstract.
[11] Falko Pientka, Leonid I. Glazman, Felix von Oppen, "Topological superconducting phase in helical Shiba chains". Physical Review B, 88, 155420 (2013). Abstract.
[12] Jelena Klinovaja, Peter Stano, Ali Yazdani, Daniel Loss, "Topological Superconductivity and Majorana Fermions in RKKY Systems". Physical Review Letters, 111, 186805 (2013). Abstract.
[13] Bernd Braunecker, Pascal Simon, "Interplay between Classical Magnetic Moments and Superconductivity in Quantum One-Dimensional Conductors: Toward a Self-Sustained Topological Majorana Phase". Physical Review Letters, 111, 147202 (2013). Abstract.
[14] M. M. Vazifeh, M. Franz, "Self-Organized Topological State with Majorana Fermions". Physical Review Letters, 111, 206802 (2013). Abstract.
[15] Sho Nakosai, Yukio Tanaka, Naoto Nagaosa, "Two-dimensional superconducting states with magnetic moments on a conventional superconductor". Physical Review B, 88, 180503 (2013). Abstract.
[16] Younghyun Kim, Meng Cheng, Bela Bauer, Roman M. Lutchyn, S. Das Sarma, "Helical order in one-dimensional magnetic atom chains and possible emergence of Majorana bound states". Physical Review B, 90, 060401 (2014). Abstract.
[17] Stevan Nadj-Perge, Ilya K. Drozdov, Jian Li, Hua Chen, Sangjun Jeon, Jungpil Seo, Allan H. MacDonald, B. Andrei Bernevig, Ali Yazdani, "Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor". Science 346, 602-607 (2014). Abstract.
[18] Jian Li, Titus Neupert, B. Andrei Bernevig, Ali Yazdani, "Majorana zero modes on a necklace". arXiv:1404.4058 [cond-mat] (2014).

Antineutrino Monitoring for the Iranian Heavy Water Reactor

[From Left to Right] Eric Christensen, Patrick Huber, Patrick Jaffke, Thomas E. Shea

Authors: Eric Christensen¹, Patrick Huber¹, Patrick Jaffke¹, Thomas E. Shea²

Affiliation:
¹Center for Neutrino Physics, Virginia Tech, Blacksburg, Virginia, USA
²TomSheaNuclear Consulting Services, Gorgengasse 10/25, 1190 Vienna, Austria

Antineutrino reactor monitoring has been proposed in the 1970s; steady progress in detector technology will make this technology practically feasible within 1-2 years. In this contribution we investigate how this decades-old idea can be applied to the recent situation in Iran, more specifically we discuss the benefits of using antineutrinos to monitor the heavy water reactor at Arak, the IR-40. One of the key findings is that a detector situated outside the reactor building would meet the verification goals identified by the International Atomic Energy Agency for plutonium production or diversion from declared inventories.

All nuclear reactors produce plutonium during operation, however only very specific types of reactors are suitable for the production of weapons-grade plutonium. Historically, all plutonium used in nuclear weapons has been obtained from either heavy water or graphite moderated reactors fueled with natural uranium. At the beginning of their respective weapons programs these reactors typically had a thermal power output in the 20-250 MW_th range, which is considerably less than typical commercial power reactors. As shown in previous work [1,2] reactors with a power output in this range represent a particularly suitable target for antineutrino reactor monitoring.

Iran is constructing a 40 MW_th heavy water moderated, natural uranium fueled reactor at Arak, the so-called IR-40. Given its design characteristics, this reactor is ideally suited to make weapons-usable plutonium with an annual output of about 10 kg. It is estimated that about 4 kg of plutonium are sufficient to make a simple explosive device with a yield upwards of several kilotons of TNT equivalent [3]. Iran states that the IR-40 will be used exclusively for peaceful purposes, in particular isotope production for medical applications. Nonetheless, the IR-40 is, after the uranium enrichment program, one of the key issues in the ongoing negotiations between Iran and the P5+1 countries (i.e., these are the five permanent members of the UN Security Council: United States, Russia, China, United Kingdom, France plus Germany). A possible solution could be the conversion of the reactor to operate with enriched uranium reducing its plutonium output significantly without limiting its ability to provide isotopes for civilian applications [4].

Any agreement reached about the the future of the IR-40 will present a challenge for effectively monitoring its implementation. The historic example of the first nuclear crisis in the Democratic People's Republic of Korea (DPRK) in the 1990's serves as a stark reminder that providing reliable safeguards and timely warning of possible breaches is very difficult in a host country which is not deterred by international isolation. In the DPRK example the consequences were intermittent, but critically timed, denials of inspector access at the required level and ultimately, this allowed the DPRK to further its nuclear weapons capabilities while negotiating for an end of the plutonium program [5].

Antineutrino monitoring was proposed in the late 1970s by Borovoi and Mikaelyan [6]. The number of antineutrinos produced and their energy spectrum depends in a well-defined manner on the reactor power and on the relative contribution to fission from the various fissile isotopes. Thus a careful measurement of both the number of antineutrinos and their energy distribution allows, in principle, to infer the reactor power and the amount of plutonium in the core. Plutonium production is an inevitable result of reactor operation and thus in itself not indicative of any malfeasance. A quantitative indicator for a diversion of plutonium is a mismatch between the amount of plutonium produced by a reactor core and the amount of plutonium residing in the reactor core. Neither of these two quantities is easily measured directly and thus, suitable proxies are used: the reactor's power history provides a means to compute the amount of plutonium produced whereas a detailed history of reactor fueling allows to track the in-core plutonium content. Both indicators rely on a complete, uninterrupted data record -- should there be any loss of this so-called continuity of knowledge (CoK), the ability to determine any mismatch between produced and in-core plutonium is lost; any recovery is difficult and may be only partial. We argue that antineutrino monitoring could provide a robust and non-intrusive method to recover from a loss of the CoK.

Specifically, we consider a hypothetical IR-40 case which to some extent draws on the experience with the DPRK: There is full safeguards access for N-1 months. The reactor is shut down in the N^th month and at the same time the CoK is lost. The reasons for loss of the CoK can span a wide range from merely technical issues, to a diplomatic standoff, to an attempt at proliferation. The basic question arising in this scenario is: Was the reactor refueled or not? Obviously, finding an answer in a timely fashion would be of prime interest to the international community and in many cases also be in the best of Iran's interests.

In our earlier work [1] we demonstrated quantitatively that a measurement of the energy spectrum of antineutrinos emitted from a reactor makes it possible to determine the burn-up and, thus, the plutonium content with good accuracy and in a timely manner. Here, we make the same assumptions as in Refs.[1,2] about the detection system, we assume that product of efficiency and number of target protons is 4.3 X 10²⁹, which for a realistic detector translates to a detector mass in the 5-15 ton range. This is still light enough to envisage a detector system which fits inside a standard 20 feet intermodal shipping container. Furthermore, we assume sufficient background rejection capabilities to allow for surface operation.

For a long time this was considered not possible for antineutrino detectors, but recently a Japanese group succeeded in the detection of reactor antineutrinos from the back of a van [7]. Nonetheless, we have to point out that at this point in time no detector system with all the required characteristics exists. At the same time, there are about a dozen collaborations world-wide attempting to produce suitable detectors (for a different purpose) and it seems very likely that fully functional prototypes will demonstrate feasibility within 12 months. In our estimate, a detector inside its shipping container can be deployed outside the reactor containment building of the IR-40 at a distance of 19 m from the center of the reactor core.

Figure 1: In the upper panel, data points show the event rate spectrum obtained in a 90 day data taking period for a core of average age of 45 days. The error bars indicate the statistical error in each bin. The blue line indicates the corresponding expected event rate spectrum for a core of average age of 315 days. The lower panel shows the difference in event rates between the 45 day core and the 315 day core and the corresponding statistical error bars. Figure and caption from Ref.[2].

Our analysis of the IR-40 is using standard reactor physics calculations made using commercially available software and the details are given in Ref.[2]. This calculation establishes the relationship between the fission rates and the content of the fissile isotopes in the core. In Fig.1 we show the resulting event rate spectrum for a core of 45 day average age (data points with statistical error bars) and for comparison the expected event rates for a core of 315 days of age (blue line). It can be seen clearly, that the older core emits neutrinos with a lower mean energy corresponding to 7 kg of plutonium, whereas the fresh core has no plutonium. This difference remains statistically significant even in the presence of realistic systematic uncertainties.

Figure 2: Shown is the 1σ accuracy for the determination of the plutonium content of the reactor as a function of time in the reactor cycle. The data-taking period is 90 days each. Dashed error bars indicate the accuracy from a fit to the plutonium fission rate f_Pu, whereas the solid error bars show the result of a fit constrained by a burn-up model. The blue line indicates operation without refueling and the orange line indicates operation with a refueling after 270 days. Figure and caption from Ref.[2].

The quantitative sensitivity to the plutonium content is shown in Fig.2, where the vertical axis shows the amount of plutonium in the reactor core as a function of time. The blue curve shows the change of plutonium content for the case of no refueling, whereas the orange curve assumes that the irradiated core, containing 8\,kg of plutonium, was replaced with a fresh core after 270 days of irradiation. 270 days is the time at which the isotopic content of plutonium-239 [8] drops to 93% of all plutonium and thus formally ceases to be considered weapons-grade. Within the first 90 days after the IR-40 shutdown (shown as gray vertical band) the two cases can be clearly distinguished by the antineutrino monitoring data. Even partial core refuelings corresponding to as little as 2 kg of removed plutonium could be detected at 90% confidence level. Alternatively, a full core refueling would be detected within about 9 days at 90% confidence level.

To summarize, in this note, based on the results of Ref.[2] we demonstrate that antineutrino monitoring of the IR-40 would provide a high-level tool to assess the amount of in-core plutonium as well as the amount of produced plutonium. Both tasks can be accomplished withing the 90 day period set by the International Atomic Energy Agency (IAEA) and with a quantitative accuracy greatly exceeding 1 significant quantity (8 kg) as required by the IAEA. This technique is non-intrusive and independent from any other safeguards information, in particular the CoK is not required. This combination of features appears to be a considerable and practically valuable characteristic not offered by any other known method. Needless to say, these advantages would not only arise for antineutrino monitoring of the IR-40 but for any reactor with a power output in the 20-250 MW_th range, which are the most likely candidates for being an entry point for a plutonium-based nuclear weapons program. Antineutrino reactor monitoring would not replace other techniques but in combination with those techniques can enhance the overall effectiveness and reliability of non-proliferation safeguards. A practical system appears feasible on a timescale of 1-2 years and the next step would be an actual antineutrino reactor monitoring experiment.

This work was supported by the U.S. Department of Energy under contract DE-SC0003915 and by a Global Issues Initiative grant by the Institute for Society, Culture and Environment at Virginia Tech.

References:
[1] Eric Christensen, Patrick Huber, Patrick Jaffke, "Antineutrino reactor safeguards - a case study". arXiv:1312.1959v2 [physics.ins-det] (2013).
[2] Eric Christensen, Patrick Huber, Patrick Jaffke, Thomas E. Shea, "Antineutrino Monitoring for Heavy Water Reactors". Physical Review Letters, 113, 042503 (2014). Abstract.
[3] T. B. Cochran and C. E. Paine, Technical Report, Natural Resources Defense Council, Inc. (1995).
[4] O. Heinonen, "Can the Nuclear Talks With Iran Be Saved?" Foreign Policy, 1 (January 27, 2011). Full Article.
[5] J. S. Wit, D. Poneman, and R. L. Gallucci, "Going Critical: The First North Korean Nuclear Crisis" (Brookings Institution Press, 2007).
[6] A. A. Borovoi, L. A. Mikaélyan, "Possibilities of the practical use of neutrinos". Soviet Atomic Energy, 44, 589 (1978). Link.
[7] S. Oguri, Y. Kuroda, Y. Kato, R. Nakata, Y. Inoue, C. Ito, M. Minowa, "Reactor antineutrino monitoring with a plastic scintillator array as a new safeguards method". Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 757, 33 (2014). Abstract.
[8] Thomas Mo Willig, Cecilia Futsaether, Halvor Kippe, "Converting the Iranian Heavy Water Reactor IR-40 to a More Proliferation-Resistant Reactor". Science and Global Security, 20, 97 (2012). Full Article.

Quantum Information in the Service of Metrology

The spin-spin measurement team at Weizmann Institute of Science, Israel. From left-to-right: Nir Navon, Nitzan Akerman, Roee Ozeri, Shlomi Kotler and Yinnon Glickman

Authors: Roee Ozeri¹, Shlomi Kotler^1,2

Affiliation:
¹Department of Physics of Complex Systems, Weizmann Institute of Science, Israel.
²Current address: Physical measurement Laboratory, National Institute of Standards and Technology, Boulder, USA.

Quantum systems have been extensively studied in the past few years as possible ultra-efficient computers. Such systems have to be as isolated as possible from their environment in order to prevent it from “measuring” the state of the quantum computer, a process which would render the computer classical. Candidate systems that were experimentally studied thus had to be sufficiently isolated from their environment while allowing for a high degree of controllability.

In addition, active methods were developed, in which special quantum states and control techniques were engineered and helped mitigate the effect of noise. Many such techniques, such as dynamic-decoupling or decoherence-free subspaces, were experimentally implemented with great success, increasing the coherence times of quantum systems by many orders of magnitude. Other methods, such as Quantum error-correction codes, have had proof-of principle demonstrations but hold the promise of being able to reject noise in a way where quantum super-positions of very large systems will be maintained coherent for as long as necessary – one of the key requirement from a quantum computer.

A different quantum technology which has seen great progress in recent years is that of quantum metrology. At face value, quantum sensors seem to be exactly antipodal to quantum computers. Here, quantum systems do have to couple to their environment in order to sense some aspect of it. However, as in many seemingly contradicting concepts there can also be a lot of common ground. For example, environmental noise (i.e. that part of the environment which you don’t want to measure!) is a foe of both quantum sensors and quantum computers. Can we therefore use the techniques that were developed to help quantum computers overcome the harmful effects of noise to improve on the measurement precision of quantum sensors? The answer is yes, and with great success! Along these lines, different dynamic modulations schemes, originally used in dynamic decoupling were used for the measurement of alternating signals. This way quantum lock-in amplifiers as well as quantum noise spectrum analyzers were demonstrated. In a recent experiment in our lab at the Weizmann Institute of Science, we used the powerful technique of decoherence-free subspaces in order to measure the very weak magnetic interaction between two electrons that were separated by more than two microns [1].

Figure 1: An artist impression of the spin-spin experiment. Two electrons are placed two microns away from each other. The magnetic field emanating from one electron interacts with the spin of the other electron, resulting in a change of the spin-orientations.

Electrons, like many fundamental particles have an intrinsic magnetic dipole moment which is aligned with their spin. These tiny magnets have a magnetic field that decays as the cube of the distance from the electron. To illustrate, the magnetic field of a single electron two microns away from it, is as small as the earths’ magnetic field at 10 times the distance to the moon. When two electrons feel each other’s magnetic fields their spins interact as magnets do: their opposite poles will attract, their identical poles repel in a way that torques will be applied and the two spins will respectively rotate due to this interaction.

The magnetic interaction between two electrons was never directly observed before. At short atomic distances, such as that between the two electrons of a Helium atom, the magnetic interaction is large enough to be easily measured. Unfortunately, at these distances, it is overwhelmed by the much larger exchange interaction between them which is the result of the interplay between the strong Coulomb interaction between the electron charges and Fermi’s exclusion principle. At large distances, where the exchange interaction is negligible, the magnetic interaction between the electrons is also very small. At a distance of two microns for example, the rotation rate the two spins impose on each other is on the order of one rotation every four minutes. This interaction is way too small to be measured due to typical magnetic noise in labs.

Figure 2: An image of the trap in which the ions were trapped for the duration of the measurement. The image is taken through one of the ultra-high vacuum chamber view-ports.

This is where techniques, borrowed from quantum computing science come to the rescue. We have placed the spins of two trapped Sr+ ions in a decoherence-free subspace that was completely immune to the effect of magnetic field noise. While being immune to noise, this subspace still allowed for the slow and gentle two-spin correlated dance to be performed without interference. Under the protection provided by this technique we could allow the electronic spins to rotate coherently for 15 seconds, after which we measured their collective rotation of more than 20^◦. We also changed the distance between the electrons and verified that the interaction between them varies inverse cubical with their separation. Thus, almost a 100 years after the discovery of the electronic spin, we were able to cleanly observe the interaction between two such tiny magnets.

This measurement bears importance that reaches beyond its demonstrative nature. This is because some hypothetical anomalous spin forces are speculated to modify the interaction between electronic spins at large distances. The motivation for the introduction of these anomalous forces is due to their ability to explain the weakness with which certain symmetries are broken in nature. The experimental bound on the strength and range of these hypothetical fields is therefore important.

The use of quantum error-suppression schemes for the benefit of precision measurements is a fast developing area of research. With the advent of experimental quantum error-correction codes, another opportunity will emerge to apply these codes towards the detection of small and highly correlated signals [2-5].

References:
[1] Shlomi Kotler, Nitzan Akerman, Nir Navon, Yinnon Glickman, Roee Ozeri, "Measurement of the magnetic interaction between two bound electrons of two separate ions". Nature, 510, 376 (2014). Abstract.
[2] Roee Ozeri, "Heisenberg limited metrology using Quantum Error-Correction Codes". arXiv:1310.3432 [quant-ph].
[3] G. Arrad, Y. Vinkler, D. Aharonov, A. Retzker, "Increasing Sensing Resolution with Error Correction". Physical Review Letters, 112, 150801 (2014). Abstract.
[4] E. M. Kessler, I. Lovchinsky, A. O. Sushkov, M. D. Lukin, "Quantum Error Correction for Metrology". Physical Review Letters, 112, 150802 (2014). Abstract.
[5] W. Dür, M. Skotiniotis, F. Fröwis, B. Kraus, "Improved Quantum Metrology Using Quantum Error Correction". Physical Review Letters, 112, 080801 (2014). Abstract.