.comment-link {margin-left:.6em;}


2Physics Quote:
"Perfect transparency has never been realized in natural transparent solid materials such as glass because of the impedance mismatch with free space or air. As a consequence, there generally exist unwanted reflected waves at the surface of a glass slab. It is well known that non-reflection only occurs at a particular incident angle for a specific polarization, which is known as the Brewster angle effect. Our question is: is it possible to extend the Brewster angle from a particular angle to a wide range of or all angles, so that there is no reflection for any incident angle."
-- Jie Luo, Yuting Yang, Zhongqi Yao, Weixin Lu, Bo Hou, Zhi Hong Hang, Che Ting Chan, Yun Lai

(Read Full Article: "Ultratransparent Media: Towards the Ultimate Transparency"

Sunday, June 25, 2017

Solving Linear Equations on Scalable Superconducting Quantum Computing Chip

From left to right: Chao-Yang Lu, Jian-Wei Pan, Xiaobo Zhu, H. Wang, Ming-Cheng Chen

Authors: Ming-Cheng Chen1, H. Wang2, Xiaobo Zhu1,3, Chao-Yang Lu1, Jian-Wei Pan1

1Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China,
2Department of Physics, Zhejiang University, Hangzhou, Zhejiang 310027, China,
3Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China.

One-sentence summary:
Quantum solver of linear system is achieved on scalable superconducting quantum computing chip.

The most ambitious target of quantum computing is to provide both high-efficiency and useful quantum software for killer applications. After decades of intense research on quantum computing, several quantum algorithms are found to demonstrate speedup over their classical counterparts, such as quantum simulation of molecular or condensed system [1], Grover search on unstructured database [2], Shor's period finding to crack RSA cryptography [3], matrix inversion to solve linear systems [4] and sampling from a hard distribution [5, 6]. Among them, sampling from a hard distribution is the most radical example to show the pure quantum computing power beyond the reach of any modern conventional computer and achieve "quantum supremacy" in the near-term [7].

However, the high-efficiency quantum supremacy algorithms have not been found to have practical applications yet. And the Grover search and Shor's period finding algorithms are limited to specific applications. On the contrary, the linear equations quantum algorithm can be applied to almost all areas of science and engineering and recently it finds fascinating applications in data science as a basic subroutine, for instance, in quantum data fitting [8] and quantum support vector machine [9].

Matrix inversion quantum algorithm to solve linear systems [4] is proposed by Harrow, Hassidim and Lloyd (HHL) in 2009 to estimate some features of the solution with exponential speedup. The algorithm uses the celebrated quantum phase estimation technology to force the computation to work at the eigen-basis of system matrix and reduce the matrix inversion to simple eigenvalue reciprocal. A compiled version of the HHL algorithm was previously demonstrated with linear optics [10, 11] and liquid NMR [12] quantum computing platforms, however, both of which are considered not easily scalable to a large number of qubits. Recently, we report the new implementation of the HHL algorithm on solid superconducting quantum circuit system, which is deterministic and easy scalable to large scale.

We run a nontrivial instance of smallest 2×2 system on superconducting circuit chip with four X-shape transmon qubits [13] and tens of one- and two-qubit quantum gates. The chip was fabricated on a sapphire substrate and used aluminum material to define superconducting qubits, resonators and transmission lines. With careful calibration, the single-qubit rotating gates were estimated to be of 98% fidelity and two-qubit entangling gates were of above 95% fidelity. Figure 1 and Figure 2 illustrate the quantum chip and the working quantum circuits, respectively.
Fig. 1: False color photomicrograph of the superconducting quantum circuit for solving 2×2 linear equations. Shown are the four X-shape transmon qubits, marked from Q1 to Q4, and their corresponding readout resonators.
Fig. 2: (click on image to view with higher resolution) Compiled quantum circuits for solving 2×2 linear equations with four qubits. There are three subroutines and more than 15 gates as indicated.

The quantum solver was tested by 18 different input vectors and the corresponding output solution vectors were characterized using quantum state tomography. In our 2*2 instance, the output qubit was measured along X, Y and Z axes of the Bloch sphere, respectively. The estimated quantum state fidelities ranged from 84.0% to 92.3%. The collected data was further used to infer the quantum process matrix of the solver and yielded the process fidelity of 83.7%. Figure 3 and Figure 4 show the experimental quantum state fidelity distribution and the quantum process matrix, respectively.
Fig. 3: Experimental quantum state fidelity distribution of the output states corresponding to the 18 input states.
Fig. 4: The real parts of the experimental quantum process matrix (bars with color) and the ideal quantum process matrix (black frames). All imaginary components (data not shown) of quantum process are measured to be no higher than 0.015 in magnitude.

These experimental results indicate that our superconducting quantum linear solver for 2*2 system have successfully operated. To scale the solver for more complicated instance with high solution accuracy, further improvement of device design and fabrication to increase quantum bit coherent time and optimization of quantum control pulses to reduce the operating time and error rate are necessary. In superconducting quantum circuit platform, there have been vast efforts devoted to scale the circuit complexity and quality, which have extended the qubit coherent time 5~6 orders of magnitude [14] manipulated up to 10 qubits [15] in the past decades, and we can expect the continuous progress in next decade to reach a mature level.

[1] I. M. Georgescu, S. Ashhab, Franco Nori, "Quantum simulation". Reviews of Modern Physics, 86, 153 (2014). Abstract.
[2] P. Shor, “Algorithms for quantum computation: discrete logarithms and factoring” in Proc. 35th Annu. Symp. on the Foundations of Computer Science, edited by S. Goldwasser (IEEE Computer Society Press, Los Alamitos, California, 1994), p. 124–134. Abstract.
[3] Lov K. Grover, "A Fast Quantum Mechanical Algorithm for Database Search", Proceedings of 28th Annual ACM Symposium on Theory of Computing, pp. 212-219 (1996). Abstract.
[4]  Aram W. Harrow, Avinatan Hassidim, Seth Lloyd, “Quantum algorithm for linear systems of equations”. Physical Review Letters, 103, 150502 (2009). Abstract.
[5] A. P. Lund, Michael J. Bremner, T. C. Ralph, "Quantum sampling problems, BosonSampling and quantum supremacy." NPJ Quantum Information, 3:15 (2017). Abstract.
[6] Hui Wang, Yu He, Yu-Huai Li, Zu-En Su, Bo Li, He-Liang Huang, Xing Ding, Ming-Cheng Chen, Chang Liu, Jian Qin, Jin-Peng Li, Yu-Ming He, Christian Schneider, Martin Kamp, Cheng-Zhi Peng, Sven Höfling, Chao-Yang Lu, Jian-Wei Pan, "High-efficiency multiphoton boson sampling". Nature Photonics 11, 361 (2017). Abstract.
[7] John Preskill, "Quantum computing and the entanglement frontier". arXiv:1203.5813 (2012).
[8] Nathan Wiebe, Daniel Braun, Seth Lloyd, "Quantum algorithm for data fitting". Physical review letters 109, 050505 (2012). Abstract.
[9] Patrick Rebentrost, Masoud Mohseni, Seth Lloyd, "Quantum support vector machine for big data classification". Physical review letters 113, 130503 (2014). Abstract.
[10] X.-D. Cai, C. Weedbrook, Z.-E. Su, M.-C. Chen, Mile Gu, M.-J. Zhu, Li Li, Nai-Le Liu, Chao-Yang Lu, Jian-Wei Pan, "Experimental quantum computing to solve systems of linear equations". Physical review letters 110, 230501 (2013). Abstract.
[11] Stefanie Barz, Ivan Kassal, Martin Ringbauer, Yannick Ole Lipp, Borivoje Dakić, Alán Aspuru-Guzik, Philip Walther, "A two-qubit photonic quantum processor and its application to solving systems of linear equations". Scientific reports 4, 6115 (2014). Abstract.
[12] Jian Pan, Yudong Cao, Xiwei Yao, Zhaokai Li, Chenyong Ju, Hongwei Chen, Xinhua Peng, Sabre Kais, Jiangfeng Du, "Experimental realization of quantum algorithm for solving linear systems of equations". Physical Review A 89, 022313 (2004). Abstract.
[13] Jens Koch, Terri M. Yu, Jay Gambetta, A. A. Houck, D. I. Schuster, J. Majer, Alexandre Blais, M. H. Devoret, S. M. Girvin, R. J. Schoelkopf, "Charge-insensitive qubit design derived from the Cooper pair box". Physical Review A 76, 042319 (2007). Abstract.
[14] M. H. Devoret, R. J. Schoelkopf1, "Superconducting circuits for quantum information: an outlook". Science, 339, 1169 (2013). Abstract.
[15] Chao Song, Kai Xu, Wuxin Liu, Chuiping Yang, Shi-Biao Zheng, Hui Deng, Qiwei Xie, Keqiang Huang, Qiujiang Guo, Libo Zhang, Pengfei Zhang, Da Xu, Dongning Zheng, Xiaobo Zhu, H. Wang, Y.-A. Chen, C.-Y. Lu, Siyuan Han, J.-W. Pan, "10-qubit entanglement and parallel logic operations with a superconducting circuit". arXiv:1703.10302 (2017). 


Sunday, May 21, 2017

Schmidt Decomposition Made Universal to Unveil the Entanglement of Identical Particles

From left to right: Stefania Sciara, Rosario Lo Franco, Giuseppe Compagno

Authors: Stefania Sciara1,2, Rosario Lo Franco2,3, Giuseppe Compagno2

1INRS-EMT, Varennes, Québec J3X 1S2, Canada,
2Dipartimento di Fisica e Chimica, Università di Palermo, Italy,
3Dipartimento di Energia, Ingegneria dell'Informazione e Modelli Matematici, Università di Palermo,  Italy.

The Schmidt decomposition is an important mathematical tool which has been already utilized during the early stages of quantum theory by Schrödinger in the context of quantum measurements [1-3]. This tool allows to determine the set of measurements on one part of the system such that the measurement outcome on the other part is determined, in the sense that to each outcome of the first measurement it corresponds a unique outcome for the second measurement. Schmidt decomposition has been shown to be at the heart of quantum information theory, quantifying entanglement in bipartite systems. It has been also widely employed in the context of Einstein-Podolski-Rosen (EPR) paradox, Bell non-locality and black-hole physics [2-4].

Every element of this decomposition consists unavoidably of two independent subsystems. Application of the Schmidt decomposition to identical particles is therefore hindered by the fact that overlapping particles can never be considered independent. In fact, despite its wide utilization in systems of distinguishable particles, the Schmidt decomposition has remained debated for identical particles [5,6]. For instance, it is well known that for distinguishable particles this tool assesses the entanglement of the system by the von Neumann entropy of the reduced density matrix, whose eigenvalues are the squares of the Schmidt coefficients appearing in the decomposition [3]. Differently, in the case of identical particles, it has been claimed that the relationship between the Schmidt coefficients and the eigenvalues of the reduced density matrix breaks down [6]. In strict connection with this issue, the partial trace operation to get the reduced state has not been considered suitable for quantifying the entanglement of pure states of identical particles [6-8].

We recall that, in Nature, particles are of different types, all particles of each type (electrons, protons, photons and so on) being identical. In the quantum world, the identity of particles gives rise to a new characteristic with respect to the classical world, that is the indistinguishability among particles of the same type [9,10]. This exclusive quantum trait leads to fundamental properties of matter such that particles can be of two classes, named bosons and fermions. Moreover, at variance with the case of distinguishable particles, when identical particles have wave functions that spatially overlap, they can never be taken as independent of each other [11,12].

The latter behavior is an essential requisite in determining features like quantum correlations (e.g., entanglement) among the particles themselves and in the theory of measurement [1]. Nevertheless, identical particles constitute the building blocks of quantum information and computation theory, being present in Bose-Einstein condensates [13,14], quantum dots [15,16], superconducting circuits [17] and optical setups [18,19]. It is thus important to have trustable methods and tools to characterize the quantum features of composite systems of identical particles under these general conditions.

A first step towards this goal has been provided by a recent non-standard approach [12] which deals with systems of identical particles within a particle-based description (that is, in terms of particle states) without resorting to the usual practice to assign fictitious labels to the particles [9,10], which render the latter distinguishable removing their indistinguishability. In this way, the ambiguity arising from the introduction of these labels in evaluating quantum correlations in identical particle systems is avoided. This method has, in fact, provided a way to calculate partial trace and von Neumann entropy for identical particles. Using this new approach, in a recent work [20] we have been able to demonstrate that the Schmidt decomposition is universal, meaning that it is also obtainable for an arbitrary state of indistinguishable particles (bosons or fermions) under general conditions of spatial overlap. Thanks to this achievement, the amount of entanglement present in identical particle systems in pure states can be evaluated by the von Neumann entropy of the reduced density matrix, as occurs in the case of distinguishable particles.

We have used the Schmidt decomposition to analyze some paradigmatic states of two identical particles to find the suitable measurement basis for unveiling their entanglement properties. These systems are illustrated in Figure 1 and represent simple yet effective examples which make it emerge the effect of particle identity. The first one is the well-known condition of two identical qubits with opposite pseudospins in spatially separated locations, denoted with left (L) and right (R) (see Fig. 1a).
Figure 1. (a) Two identical qubits in two spatially separated places with opposite pseudospins. (b) Two identical qubits in the same spatial mode with arbitrary pseudospins. (c) Two identical qutrits (three-level quantum systems) in the same spatial mode. The shaded ellipses indicate that the particles are entangled. Figure from Ref. [20].

Indeed, we have found that the Schmidt decomposition and the corresponding von Neumann entropy supply the results which are physically expected in this situation, such as zero entanglement for a product (separable) state of the two particles and maximal entanglement for a Bell state. We have also explicitly shown that nonlocal measurements induce entanglement in a state of distant identical particles. This means that, in principle, identical particles cannot be considered completely independent even when they are spatially separated. Application of the Schmidt decomposition to a system of two boson qubits in the same site (see Fig. 1b) has evidenced that the entanglement increases as the two internal states tend to be orthogonal, as displayed in the plot of Fig. 2. This finding is a generalization of a previous result obtained only for two identical qubits in the same spatial mode with orthogonal internal states (or pseudospins, that is θ = π in the plot of Fig. 2) [12].

Figure 2. Entanglement between the pseudospins of two identical particles in the same site, quantified by the von Neumann entropy, as a function of the angle θ between the directions of the two pseudospins (internal states). Figure from Ref. [20].

Two identical (boson) qutrits, that is three-level quantum systems, constitute a system of interest being promising candidates for quantum processors thanks to their good capacity to store quantum information [21,22]. We consider the qutrits in the same site, that is under the condition of complete spatial overlap, as depicted in Fig. 1c. Our method easily determines the two-qutrit entanglement for given combinations of their internal states and provides a physical interpretation. We remark that the entanglement found for the two qutrits is different from that obtained for the same system by an alternative approach, based on a so-called subalgebra technique [8]. The origin of this difference in the entanglement measure requires further investigation, for instance by comparing the two theoretical approaches or by experimental verifications.

We now briefly discuss the practical aspect concerning the possibility to exploit the entanglement of identical particles, as identified by the Schmidt decomposition we have introduced. In the context of quantum information processing with distinguishable particles, a well-established resource theory is based on local operations and classical communication (LOCC), where each particle is individually addressed [1-3]. On the other hand, a peculiar trait of indistinguishable particles is that it is not possible to operate on a given individual particle. This characteristic in general hinders the manipulation of composite systems of identical particles for desired tasks of quantum information and computation. Nevertheless, it is known that the entanglement quantified by the von Neumann entropy can be extracted from the state of identical particles and then utilized in a conditional way by LOCC [23].

In conclusion, the universal character of the Schmidt decomposition shown in our work allows a faithful treatment of the entanglement of composite systems of identical particles and opens the way to more general investigations of collective properties of such systems.

[1] Ryszard Horodecki, Paweł Horodecki, Michał Horodecki, Karol Horodecki, “Quantum entanglement”, Review of Modern Physics, 81, 865 (2009). Abstract.
[2] John Preskill, “Lectures notes for physics 229: Quantum information and computation” (1998) Link.
[3] Michael A. Nielsen and Isaac L. Chuang, “Quantum Computation and Quantum Information” (Cambridge University Press, Cambridge, 2000).
[4] E.D. Belokolos, M.V. Teslyk, “Scalar field entanglement entropy of a Schwarzschild black hole from the Schmidt decomposition viewpoint”, Classical and Quantum Gravity, 26, 235008 (2009). Abstract.
[5] R. Paškauskas, L. You, “Quantum correlations in two-boson wave functions”, Physical Review A, 64, 042310 (2001). Abstract.
[6] Malte C Tichy, Florian Mintert, Andreas Buchleitner, “Essential entanglement for atomic and molecular physics”, Journal of Physics B: Atomic, Molecular and Optical Physics. 44, 192001 (2011). Abstract.
[7] GianCarlo Ghirardi, Luca Marinatto, Tullio Weber, “Entanglement and properties of composite quantum systems: a conceptual and mathematical analysis”, Journal of Statistical Physics 108, 49 (2002). Abstract.
[8] A. Balachandran, T. Govindarajan, Amilcar R. de Queiroz, A. Reyes-Lega, “Entanglement and particle identity: A unifying approach”, Physical Review Letters, 110, 080503 (2013). Abstract.
[9] Asher Peres, “Quantum Theory: Concepts and Methods” (Springer, Dordrecht, The Netherlands, 1995).
[10] Claude Cohen-Tannoudji, Bernard Diu, Franck Laloe, “Quantum mechanics, Vol. 2” (Wiley-VCH, Paris, France, 2005).
[11] John Schliemann, J. Ignacio Cirac, Marek Kuś, Maciej Lewenstein, Daniel Loss, “Quantum correlations in two-fermion systems”, Physical Review A, 64, 022303 (2001). Abstract.
[12] Rosario Lo Franco, Giuseppe Compagno, “Quantum entanglement of identical particles by standard information-theoretic notions”, Scientific  Reports, 6, 20603 (2016). Abstract.
[13] Immanuel Bloch, Jean Dalibard, Wilhelm Zwerger, “Many-body physics with ultracold gases”, Review of Modern Physics, 80, 885 (2008). Abstract.
[14] Marco Anderlini, Patricia J. Lee, Benjamin L. Brown, Jennifer Sebby-Strabley, William D. Phillips,  J. V. Porto, “Controlled exchange interaction between pairs of neutral atoms in an optical lattice”, Nature 448, 452 (2007). Abstract.
[15] Michael H. Kolodrubetz, Jason R. Petta, “Coherent holes in a semiconductor quantum dot”, Science 325, 42–43 (2009). Abstract.
[16] Frederico Martins, Filip K. Malinowski, Peter D. Nissen, Edwin Barnes, Saeed Fallahi, Geoffrey C. Gardner, Michael J. Manfra, Charles M. Marcus, Ferdinand Kuemmeth, “Noise suppression using symmetric exchange gates in spin qubits”, Physical Review Letters, 116, 116801 (2016). Abstract.
[17] R. Barends, L. Lamata, J. Kelly, L. García-Álvarez, A. G. Fowler, A Megrant, E Jeffrey, T. C. White, D. Sank, J. Y. Mutus, B. Campbell, Yu Chen, Z. Chen, B. Chiaro, A. Dunsworth, I.-C. Hoi, C. Neill,  P. J. J. O’Malley,  C. Quintana,  P. Roushan, A. Vainsencher, J. Wenner, E. Solano, John M. Martinis, “Digital quantum simulation of fermionic models with a superconducting circuit”, Nature Communications, 6, 7654 (2015). Abstract.
[18] Andrea Crespi, Linda Sansoni, Giuseppe Della Valle, Alessio Ciamei, Roberta Ramponi, Fabio Sciarrino, Paolo Mataloni, Stefano Longhi, Roberto Osellame, “Particle statistics affects quantum decay and Fano interference”, Physical Review Letters, 114, 090201 (2015). Abstract.
[19] Christian Reimer, Michael Kues, Piotr Roztocki, Benjamin Wetzel, Fabio Grazioso, Brent E. Little, Sai T. Chu, Tudor Johnston, Yaron Bromberg, Lucia Caspani, David J. Moss, Roberto Morandotti, “Generation of multiphoton entangled quantum states by means of integrated fre-quency combs”, Science 351, 1176 (2016). Abstract.
[20] Stefania Sciara, Rosario Lo Franco, Giuseppe Compagno, “Universality of Schmidt decomposition and particle identity”, Scientific Reports, 7, 44675 (2017). Abstract.
[21] B.P. Lanyon, T.J. Weinhold, N.K. Langford, J.L. O’Brien, K.J. Resch, A. Gilchrist, A.G. White, “Manipulating biphotonic qutrits”, Physical Review Letters, 100, 060504 (2008). Abstract.
[22] K. S. Kumar, A. Vepsalainen, S. Danilin,  G.S. Paraoanu, “Stimulated Raman adiabatic passage in a three-level superconducting circuit”, Nature Communications, 7, 10628 (2016). Abstract.
[23] N. Killoran, M. Cramer, M. B. Plenio, “Extracting entanglement from identical particles”, Physical Review Letters, 112, 150501 (2014). Abstract.

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Sunday, May 14, 2017

A Step Towards The Realization of A Quantum Network

Ataç Imamoglu (left) and Aymeric Delteil (right)

Authors : Aymeric Delteil, Zhe Sun, Stefan Fält, Atac Imamoglu

Affiliation: Institute of Quantum Electronics, ETH Zurich, Switzerland.

Quantum network architectures consist of local nodes comprising quantum memories that are interconnected using single photons propagating in photonic channels. In such networks, the ability to transfer a quantum bit of information (qubit) from one node to another plays a central role. In a practical implementation, the photonic qubits are generated through spontaneous emission from a matter qubit – embodied for instance by a single atom or ion, a point defect or a quantum dot in a solid-state matrix. The generated photons are then collected in a fiber and sent to another matter qubit using a photonic channel.

Since photonic channels are subject to imperfect collection efficiencies and photon losses, there is a finite probability that such a state transfer based on a single photonic qubit fails. It is therefore suitable to have a heralding signal testifying that the transfer has been successful. Although some basic elements towards such heralded quantum state transfer have already been demonstrated in previous work using various physical systems [1-4], a full node-to-node heralded transfer using single photon qubits has not been achieved to date, mainly due to the dominant role of photon losses.

Using self-assembled semiconductor quantum dots (QDs), we have demonstrated heralded absorption of a neutral (source) QD generated single photonic qubit, by a single-electron charged (target) QD that is located 5 m away [5]. The photonic qubit is thereby transferred and stored in the spin degree of freedom of the single host electron. A successful process is heralded by detection of a subsequent photon that carries no information about the qubit state, which is essential to preserve the coherent quantum superposition.

The principle of our experiment is depicted in fig. 1. The source QD (QD1) is neutral and can be prepared in an arbitrary superposition of two exciton states using a two-color laser beam. This quantum state is encoded in the color of a single photon (flying qubit) generated upon radiative recombination of the QD1 exciton. This flying qubit is collected into a fiber and transferred to the target QD. Amongst the wide variety of QDs that are randomly formed during the growth of the sample, the target QD has been carefully selected to have a specific energy level scheme presenting two transitions of identical energies, such that photons emitted after absorption of the photonic qubit carry no information about the decay path. As a consequence, if the spin state is initially prepared in the superposition state |up> + |down>, upon absorption of the photonic qubit and detection of the subsequent photon, the electron spin ends in the qubit state generated by the laser excitation of the source QD.
Figure 1 : (Click on the image to view with higher resolution) Principle of the state transfer protocol based on heralded absorption of a single photon qubit.

Implementing such an experiment is particularly challenging due to finite collection efficiencies and losses in the optical elements along the chain. One of the key elements that have allowed our realization is the use of a photonic structure enabling efficient extraction of the emitted photons. More specifically, the QDs are embedded in a planar cavity and the cavity output is collected using a solid immersion lens placed on top of the sample, ensuring that about 20% of the photons from each QD are collected by the first lens. The use of sensitive superconducting single photon detector with very low dark counts as well as crossed-polarization detection to suppress the strong pump laser light and background scattering have allowed us to demonstrate heralded absorption where we detected up to about 100 successful events per second. We demonstrated that the final state of the destination quantum dot spin is correlated with the initial state of the photon (or the target QD exciton) by measuring time-resolved photon coincidences.

Our scheme can be extended to realize spin-to-spin state transfer, or to generate heralded distant entanglement between two QD spins [6]. It can also be used to connect dissimilar physical systems in the context of hybrid quantum networks [7].


[1] Stephan Ritter, Christian Nölleke, Carolin Hahn, Andreas Reiserer, Andreas Neuzner, Manuel Uphoff, Martin Mücke, Eden Figueroa, Joerg Bochmann, Gerhard Rempe, “An elementary quantum network of single atoms in optical cavities”, Nature, 484, 195 (2012). Abstract.
[2] Christoph Kurz, Michael Schug, Pascal Eich, Jan Huwer, Philipp Müller, Jürgen Eschner, “Experimental protocol for high-fidelity heralded photon-to-atom quantum state transfer”, Nature Communications, 5, 5527 (2014). Abstract.
[3] Norbert Kalb, Andreas Reiserer, Stephan Ritter, Gerhard Rempe, “Heralded Storage of a Photonic Quantum Bit in a Single Atom”, Physical Review Letters, 114, 220501 (2015). Abstract.
[4] Sen Yang, Ya Wang, D. D. Bhaktavatsala Rao, Thai Hien Tran, Ali S. Momenzadeh, M. Markham, D. J. Twitchen, Ping Wang, Wen Yang, Rainer Stöhr, Philipp Neumann, Hideo Kosaka, Jörg Wrachtrup, “High-fidelity transfer and storage of photon states in a single nuclear spin”, Nature Photonics, 10, 507 (2016). Abstract.
[5] Aymeric Delteil, Zhe Sun, Stefan Fält, Atac Imamoğlu, “Realization of a Cascaded Quantum System: Heralded Absorption of a Single Photon Qubit by a Single-Electron Charged Quantum Dot”, Physical Review Letters, 118, 177401 (2017). Abstract.
[6] D. Pinotsi and A. Imamoglu, “Single Photon Absorption by a Single Quantum Emitter”, Physical Review Letters, 100, 093603 (2008). Abstract.
[7] H. M. Meyer, R. Stockill, M. Steiner, C. Le Gall, C. Matthiesen, E. Clarke, A. Ludwig, J. Reichel, M. Atatüre, M. Köhl, “Direct Photonic Coupling of a Semiconductor Quantum Dot and a Trapped Ion”,  Physical Review Letters, 114, 123001 (2015). Abstract.

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Sunday, March 05, 2017

Ultrafast Quantum Simulator

Photos of some of the authors -- From Left to Right: (top row) Nobuyuki Takei,  Christian Sommer,  Claudiu Genes, Guido Pupillo; (bottom row)  Hisashi Chiba,  Matthias Weidemüller,  Kenji Ohmori.

Authors: Nobuyuki Takei1,2, Christian Sommer1,2,3, Claudiu Genes3, Guido Pupillo4, Haruka Goto1, Kuniaki Koyasu1,2, Hisashi Chiba1,5, Matthias Weidemüller6,7,8, Kenji Ohmori1,2

1Department of Photo-Molecular Science, Institute for Molecular Science, National Institutes of Natural Sciences, Okazaki, Japan,
2SOKENDAI (The Graduate University for Advanced Studies), Okazaki, Japan,
3Max Planck Institute for the Science of Light, Erlangen, Germany,
4IPCMS (UMR 7504) and ISIS (UMR 7006), University of Strasbourg and CNRS, Strasbourg, France,
5Faculty of Engineering, Iwate University, Morioka, Japan,
6Physikalisches Institut, Universität Heidelberg, Heidelberg, Germany,
7Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, China,
8CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, China.

Link to Ohmori Group in Okazaki >>

The dynamics of interactions among large numbers of electrons govern a variety of important physical and chemical phenomena such as superconductivity, magnetism, and chemical reactions. An ensemble of many particles thus interacting with each other is referred to as a “strongly correlated system”. Understanding quantum mechanical behavior of a strongly correlated system is thus one of the central goals of modern sciences. It is extremely difficult, however, to predict theoretically the properties of a strongly correlated system even using the Japanese post-K supercomputer, which is expected to be one of the world’s fastest supercomputers planned to be completed by the year 2020. For example, the post-K cannot calculate even the ground-state energy by exact diagonalization, when the number of particles in the system is more than 30. It is in general more demanding to calculate the dynamics of the strongly correlated system.

Instead of calculating with a classical computer such as the post-K, an alternative concept has been proposed by Richard Feynman in 1980’s [1] and is now referred to as a “quantum simulator”, in which quantum mechanical particles such as atoms are assembled into an artificial strongly correlated system, whose properties are known and controllable [2,3]. It is then used to simulate and understand the properties of another strongly correlated system whose properties are not known. A quantum simulator could quickly simulate quantum mechanical behavior of a large number of particles that cannot be handled even by the post-K supercomputer, expected to become a next-generation simulation platform.

We have developed a completely new quantum simulator that can simulate the quantum mechanical dynamics of a strongly correlated system of more than 40 atoms within one nanosecond [4-6]. This has been realized by introducing a novel approach in which an ultrashort laser pulse whose pulse width is only 10 picoseconds is employed to control a high-density ensemble of atoms cooled to temperatures close to absolute zero. Furthermore we have succeeded in simulating the motion of electrons of this strongly correlated system that is modulated by changing the strength of interactions among many atoms in the ensemble.

In order to generate a strongly correlated system in which a large number of particles interact simultaneously with each other, it should be effective to assemble a quantum simulator with particles whose forces could reach as far as possible. A “Rydberg atom” is expected as the most promising candidate for that [7,8]. An atom usually has a diameter of about sub-nanometer, but can be irradiated with laser light to bring an electron that moves near its atom core to a high-energy orbital called a “Rydberg orbital”, whose diameter could be more than hundreds of nanometers. The atom thus generated is referred to as a Rydberg atom. Due to its long distance between the atom core with a positive charge and the Rydberg electron with a negative charge, a Rydberg atom generates an electric field that reaches a long distance. If one could build up an ensemble of Rydberg atoms, it should become a strongly correlated system in which those many Rydberg atoms interact simultaneously with each other. However, the strong electric field induced by a Rydberg atom shifts the energies of the Rydberg orbitals of its surrounding atoms as shown schematically in Fig. 1, so that conventional laser light cannot bring electrons of those surrounding atoms to their Rydberg orbitals. Accordingly there can be only one Rydberg atom within a sphere of a certain radius. This phenomenon is referred to as “Rydberg blockade” [7,8] and needs to be circumvented to generate a strongly correlated system of Rydberg atoms.
Figure 1: Mechanism of Rydberg blockade

Moreover there is another problem to be solved to realize such a Rydberg quantum simulator. Even if one could generate a strongly correlated system, the strong interaction among the Rydberg atoms would induce the temporal evolution of their quantum states on the timescale of 100 picoseconds, which is faster by a factor of more than hundred thousand than the timescale of a quantum simulator that has so far been considered.

In order to create a Rydberg quantum simulator that can simulate a strongly correlated system, therefore, a totally new concept and technique have been needed to solve those two essential problems: (1) how to circumvent Rydberg blockade?; (2) how to observe the system on the timescale faster by a factor of hundred thousand than the one considered for a quantum simulator so far?

We have succeeded in solving those two essential problems for the first time. Figure 2a schematically shows a property of laser light that has so far been used typically for the development of a quantum simulator. It shines continuously as shown in Fig. 2(a-1) and is produced by a so-called “continuous wave laser”. This laser light has an extremely narrow range of wavelength (energy) as shown in Fig. 2(a-2). Therefore it cannot bring an electron to the Rydberg orbital that is shifted energetically in the surrounding atom as shown in Fig. 1. Instead of using this continuous wave laser, therefore, we has introduced a pulsed laser light that shines only during ~ 10 picoseconds as shown in Fig. 2(b-1). This pulsed laser light has its wavelength range broader than that of the continuous wave laser by a factor of more than one million as shown in Fig. 2(b-2). It can therefore bring an electron to the Rydberg orbital even if its energy is shifted in the surrounding atom. Moreover the temporal width of the laser pulse is one tenth of the timescale expected for the temporal evolution of the system, so that the evolution should be able to be observed in real time.
Figure 2: Properties of conventional laser light that has so far been used for the development of a quantum simulator (a-1, a-2) and of the one newly introduced in our work (b-1, b-2).

The experiment was performed with rubidium atoms. Figure 3 shows a schematic of the experiment. An ensemble of ~ 106 rubidium atoms was cooled down to an ultralow temperature around 70 microK with laser cooling techniques and trapped in a laser tweezer. These atoms were irradiated with an “ultrashort laser pulse 1” whose pulse width was ~ 10 picoseconds, and its wavelength range was appropriately manipulated with a special technique. The temporal evolution of the atoms after laser pulse 1 was observed with another “ultrashort laser pulse 2”. The delay of laser pulse 2 from laser pulse 1 was controlled ultra-precisely on the 10 attosecond timescale with a special device, so that the evolution was observed on this timescale. It was then observed in real time that the electrons of many Rydberg atoms, which were generated with laser pulse 1 that circumvented Rydberg blockade, oscillated with a period of one femtosecond, and the timing of those oscillations was gradually shifted on the timescale of 10 attoseconds due to the simultaneous interactions among more than 40 Rydberg atoms. Furthermore this timing shift has successfully been accelerated by enlarging the Rydberg orbitals or by decreasing the distances among Rydberg atoms to increase the strength of the interactions.
Figure 3: Schematic of the experimental setup.

We have thus introduced ultrashort laser pulses into a quantum simulator for the first time and succeeded in developing a totally new quantum simulator. This ultrafast quantum simulator can simulate the dynamics of a large number of particles interacting with each other that cannot be handled by even a world’s fastest supercomputer such as the post-K. The simulation has been completed in 1 nanosecond.

It has been demonstrated that our ultrafast quantum simulator can quickly simulate the dynamics of a strongly correlated system of a large number of particles interacting with each other, which cannot be handled by even the post-K supercomputer. The ultrafast quantum simulator is expected to develop into a future simulation platform that could contribute to designing superconducting and magnetic materials and drug molecules, whose functionalities are governed by strongly correlated electrons. It is also expected to serve as a fundamental tool to investigate the origins of physical properties of matter such as superconductivity and magnetism as well as the mechanism of a chemical reaction that proceeds in a complex environment such as a liquid.

[1] Richard P. Feynman, “Simulating physics with computers”, International Journal of Theoretical Physics 21, 467 (1982). Abstract.
[2] Immanuel Bloch, Jean Dalibard, Wilhelm Zwerger, “Many-body physics with ultracold gases”, Reviews of Modern Physics 80, 885 (2008). Abstract.
[3] I. M. Georgescu, S. Ashhab, Franco Nori, “Quantum simulation”, Reviews of Modern Physics 86, 153 (2014). Abstract.
[4] Nobuyuki Takei, Christian Sommer, Claudiu Genes, Guido Pupillo, Haruka Goto, Kuniaki Koyasu, Hisashi Chiba, Matthias Weidemüller,  Kenji Ohmori, “Direct observation of ultrafast many-body electron dynamics in an ultracold Rydberg gas”, Nature Communications 7, 13449 (2016). Abstract.
[5] Christian Sommer, Guido Pupillo, Nobuyuki Takei, Shuntaro Takeda, Akira Tanaka, Kenji Ohmori, Claudiu Genes, “Time-domain Ramsey interferometry with interacting Rydberg atoms”, Physical Review A 94, 053607 (2016). Abstract.
[6] Kenji Ohmori, “Optically Engineered Quantum States in Ultrafast and Ultracold Systems”, Foundations of Physics, 44, 813 (2014). Abstract.
[7] M. Saffman, T. G. Walker, and K. Mølmer, “Quantum information with Rydberg atoms”, Reviews of Modern Physics, 82, 2313 (2010). Abstract.
[8] Daniel Comparat, Pierre Pillet, “Dipole blockade in a cold Rydberg atomic sample”, Journal of the Optical Society of America, B 27, A208 (2010). Abstract.

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Sunday, January 22, 2017

Glycine, an Amino Acid and Other Prebiotic Molecules in Comet 67P/Churyumov-Gerasimenko

Kathrin Altwegg 

Author: Kathrin Altwegg and the ROSINA Team 

Affiliation: Physikalisches Institut, University of Bern, Switzerland.

By now it is an established fact that comets contain the most primitive material of all solar system bodies. In situ results from the Giotto flyby at comet Halley in 1986 and remote sensing in various wavelength ranges established the presence of many organic molecules in the coma of comets. The importance of comets for the origin of life on Earth has been the topic of many discussions in the past [1]. Among the key ingredients for life as we know it are amino acids and phosphorous. Many primitive meteorites contain amino acids. However most of them are formed by aqueous alterations [2,3]. Traces of amino acids were detected in samples from the Stardust mission to comet Wild 2 [4]. However, there always remained some doubts that these amino acids were actually cometary as the extraction and analysis of the material from the aerogel and aluminium frame always involves either hot water or even acids, which could then readily form amino acid on Earth.

In order to investigate the composition of the organics and to assess the importance of comets for the origin of terrestrial life the European Space Agency ESA launched in 2004 the spacecraft Rosetta towards comet 67P/ Churyumov-Gerasimenko . This comet belongs to the Jupiter family with an aphelion at 5.5 AU and a perihelion at 1.25 AU. Its orbital period is 6.5 y. In order to match the comet’s orbit Rosetta had to flyby three times the Earth and once Mars to arrive at the comet more than 10 years after launch in August 2014. Subsequently, Rosetta flew with the comet around the Sun from 3.6 AU to perihelion and out again to 3.8 AU, sometimes as close as 10 km from the comet centre. This allowed a thorough investigation of the comet from up close during the different phases of its orbit.

On board Rosetta was the ROSINA (Rosetta Orbiter Sensor for Ion and Neutral Analysis) suite consisting of two mass spectrometers (DFMS and RTOF) and the cometary pressure sensor COPS [5]. These sensors were built to analyse the composition of the cometary atmosphere along its path around the Sun, encountering very low densities for large heliocentric distances to much more violent outgassing during perihelion.

ROSINA measured almost continuously during more than two years. Most of the time, water was the dominant component of the cometary coma. However, due to its peculiar shape and the tilted rotation axis of the comet, the coma was very heterogeneous and varying along the orbit. Apart from water, ROSINA identified many more simple molecules like CO, CO2, HCN, CH4 and NH3. But it detected also many complex organics like aliphatic carbon chains, alcohols with up to five C atoms and amines [6]. Most surprisingly it detected abundant O2 [7]. O2 is very reactive and was believed to have been non-existent in the protosolar nebula. Very few detections of O2 outside the Earth have been made so far. The very good correlation with water led to the finding, that O2 was most probably formed in the presolar stage due to radiolysis of water ice and that the water ice survived the solar system formation unchanged.

In March 2015 Rosetta performed a close flyby over the comet surface of just 15 km from the comet centre. During this flyby, dust production was high. In the mass spectra of ROSINA DFMS from this flyby an analysis of the mass spectrometry data of ROSINA DFMS revealed two mass peaks at mass 75 Da, one of which was identified as coming from the amino acid glycine. The exact mass of glycine is 75.0315 Da. There are several isomers on the exact same mass. In mass spectrometry, where ionization of the neutrals is done by electron impact, isomers can be distinguished by their fragmentation pattern as molecules are not only ionized to yield the parent ion, but also dissociate into ionized fragments according to the structure of a molecule. All of the isomers of glycine could be ruled out by looking at the specific fragmentation pattern from the electron impact ionisation in the ion source of DFMS.
Figure 1: (click on the image to view with higher resolution) a mass spectrum of mass 75 Da, taken by ROSINA/DFMS on March 28, 2015, integrated over 160 s at a distance of ~20 km from the comet.

Figure 1 shows a sample mass spectrum at 75 Da. The number of ionized particles registered on the detector is given as a function of the position on the detector which corresponds to m/z. The mass resolution of DFMS m/Δm is ~9000 at FWHM for mass 28 and decreases with increasing mass. Also on mass 75 Da we find C3H7O2 (75.0441 Da) which might be a fragment of propylene glycol (C3H8O2) or any of its isomers or/and of even heavier species like butanediol (C4H10O2). Only a thorough analysis of all fragments can identify the parent of C3H7O2. Details on the data analysis for ROSINA DFMS can be found in Ref.[6].

To detect glycine in the coma of 67P was quite surprising as glycine has a sublimation temperature of 140°C (8), a lot higher than the comet surface (9). Analysis of the flyby revealed that the density of glycine did not follow the expected 1/r2 behaviour, which led to the conclusion that glycine sublimated from dust grains in the coma, which can become much hotter due to their small sizes of a few μm and their low albedo of a few % [10].

The way to form glycine on dust grains has been investigated by [11-13]. It can be formed from the precursor molecule methylamine which was also found in the mass spectra of DFMS together with CO2. It is up to now the only amino acid where a path for formation is known without involving liquid water. It is therefore not surprising that a search for other amino acids like e.g. alanine was unsuccessful, as the comet most probably never had liquid water.

As glycine is probably mostly on dust grains and its sublimation temperature is high, it is not possible to determine the glycine abundance in the nucleus. The abundance in the coma varies relative to water between 0 and 0.0025. Glycine is not always detected in the spectra of DFMS. We preferentially see a signal from glycine during the perihelion passage between spring 2015 and September 2015 and only if the spacecraft was close enough to the comet.

The precursor molecules methylamine and ethylamine are seen in the mass spectra only when glycine also is detected. The three molecules seem to be closely related which is not surprising. Chemical models show that glycine could form on dust grains via three radical-addition mechanisms at temperatures from 40-120 K [11] which is compatible with temperatures in hot cores. Glycine can also be formed involving photochemistry and CO2 [13]. In both cases methylamine is part of the process.

Another important species for living organisms is phosphorous found in adenosine triphosphate (ATP), in the backbone of DNA and RNA, and in cell membranes. The phosphorous atom with a mass of 30.9732 Da was detected by DFMS already in October 2014. However, the search for the parent (PH3, PO, PN or HCP) was unsuccessful although these species have been detected in the interstellar medium [14-17]. This is mostly due to overlaps in the mass spectra with other species, very often with abundant sulphur bearing species.

Many of the molecules found by ROSINA DFMS in the coma of comet 67P are compatible with the idea that comets delivered key molecules for prebiotic chemistry throughout the solar system and in particular to the early Earth [18] increasing drastically the concentration of life-related chemicals by impact on a closed water body. The fact that glycine was most probably formed on dust grains in the presolar stage also makes these molecules somehow universal, which means that what happened in the solar system could probably happen elsewhere in the Universe.

This article is based on our work published in 'Science Advances', 2016 [19].

[1] Alyssa K. Cobb, Ralph E. Pudritz, and Ben K. D. Pearce, "Nature's Starships. II. Simulating the Synthesis of Amino Acids in Meteorite Parent Bodies", Astrophysical Journal, 809, 6 (2015). Abstract.
[2] Alyssa K. Cobb, Ralph E. Pudritz, "Nature's Starships. I. Observed Abundances and Relative Frequencies of Amino Acids in Meteorites", Astrophysical Journal, 783, 140 (2014). Abstract.
[3] Aaron S. Burton, Jennifer C. Stern, Jamie E. Elsila, Daniel P. Glavin, Jason P. Dworkin, "Understanding prebiotic chemistry through the analysis of extraterrestrial amino acids and nucleobases in meteorites", Chemical Society Reviews, 41, 5459-5472 (2012). Abstract.
[4] Jamie E. Elsila, Daniel P. Glavin, Jason P. Dworkin, "Cometary glycine detected in samples returned by Stardust", Meteoritics & Planetary Science, 44, 9, 1323–1330 (2009). Abstract.
[5] H. Balsiger, K. Altwegg, P. Bochsler, et al., SSR, 128, 745 (2007).
[6] Léna Le Roy, Kathrin Altwegg, Hans Balsiger, Jean-Jacques Berthelier, Andre Bieler, Christelle Briois, Ursina Calmonte, Michael R. Combi, Johan De Keyser, Frederik Dhooghe, Björn Fiethe, Stephen A. Fuselier, Sébastien Gasc, Tamas I. Gombosi, Myrtha Hässig, Annette Jäckel, Martin Rubin, Chia-Yu Tzou, "Inventory of the volatiles on comet 67P/Churyumov-Gerasimenko from Rosetta/ROSINA", Astronomy & Astrophysics, 583, A1 (2015). Abstract.
[7] A. Bieler, K. Altwegg, H. Balsiger, A. Bar-Nun, J.-J. Berthelier, P. Bochsler, C. Briois, U. Calmonte, M. Combi, J. De Keyser, E. F. van Dishoeck, B. Fiethe, S. A. Fuselier, S. Gasc, T. I. Gombosi, K. C. Hansen, M. Hässig, A. Jäckel, E. Kopp, A. Korth, L. Le Roy, U. Mall, R. Maggiolo, B. Marty, O. Mousis, T. Owen, H. Rème, M. Rubin, T. Sémon, C.-Y. Tzou, J. H. Waite, C. Walsh, P. Wurz, "Abundant molecular oxygen in the coma of comet 67P/Churyumov–Gerasimenko", Nature, 526, 678-681. (2015). Abstract.
[8] D. Gross, G. Grodsky, "On the Sublimation of Amino Acids and Peptides", Journal of the American Chemical Society, 77, 1678 (1955). Abstract.
[9] F. Peter Schloerb, Stephen Keihm, Paul von Allmen, Mathieu Choukroun, Emmanuel Lellouch, Cedric Leyrat, Gerard Beaudin, Nicolas Biver, Dominique Bockelée-Morvan, Jacques Crovisier, Pierre Encrenaz, Robert Gaskell, Samuel Gulkis, Paul Hartogh, Mark Hofstadter, Wing-Huen Ip, Michael Janssen, Christopher Jarchow, Laurent Jorda, Horst Uwe Keller, Seungwon Lee, Ladislav Rezac, Holger Sierks, "MIRO observations of subsurface temperatures of the nucleus of 67P/Churyumov-Gerasimenko", Astronomy & Astrophysics, 583, A29 (2015). Abstract.
[10] D.J. Lien, "Dust in comets. I - Thermal properties of homogeneous and heterogeneous grains", Astrophysical Journal, 355, 680-692 (1990). Abstract.
[11] Robin T. Garrod, "A Three phase chemical model of hot cores: The formation of Glycine", Astrophysical Journal, 765, 60 (2013). Abstract.
[12] Uwe J. Meierhenrich, Guillermo M. Muñoz Caro, Willem A. Schutte, Wolfram H.-P. Thiemann, Bernard Barbier, André Brack, "Precursors of Biological Cofactors from Ultraviolet Irradiation of Circumstellar/Interstellar Ice Analogues", Chemistry – A European Journal, 11(17), 4895-4900 (2005). Abstract.
[13] Jean-Baptiste Bossa, Fabien Borget, Fabrice Duvernay, Patrice Theulé, Thierry Chiavassa, Journal of Physical Organic Chemistry, 23, 333–339 (2010). Abstract.
[14] L.M. Ziurys, "Detection of interstellar PN - The first phosphorus-bearing species observed in molecular clouds", ApJ, 321, L81, (1987). Abstract.
[15] M.Guélin, J. Cernicharo, G.Paubert, B.E. Turner, "Free CP in IRC +10216", Astronomy & Astrophysics, 230, L9 (1990). Abstract.
[16] Marcelino Agúndez, José Cernicharo, Michel Guélin, "Discovery of Phosphaethyne (HCP) in Space: Phosphorus Chemistry in Circumstellar Envelopes", Astrophysical Journal, 662, L91 (2007). Abstract.
[17] E. D. Tenenbaum, N. J. Woolf, L. M. Ziurys, "Identification of Phosphorus Monoxide (X2Πr) in VY Canis Majoris: Detection of the First P-O Bond in Space", Astrophysical Journal, 666, L29 (2007). Abstract.
[18] J. Oró, "Comets and the Formation of Biochemical Compounds on the Primitive Earth", Nature, 190, 389-390 (1961). Abstract.
[19] Kathrin Altwegg, Hans Balsiger, Akiva Bar-Nun, Jean-Jacques Berthelier, Andre Bieler, Peter Bochsler, Christelle Briois, Ursina Calmonte, Michael R. Combi, Hervé Cottin, Johan De Keyser, Frederik Dhooghe, Bjorn Fiethe, Stephen A. Fuselier, Sébastien Gasc, Tamas I. Gombosi, Kenneth C. Hansen, Myrtha Haessig, Annette Jäckel, Ernest Kopp, Axel Korth, Lena Le Roy, Urs Mall, Bernard Marty, Olivier Mousis, Tobias Owen, Henri Rème, Martin Rubin, Thierry Sémon, Chia-Yu Tzou, James Hunter Waite, Peter Wurz, "Prebiotic chemicals—amino acid and phosphorus—in the coma of comet 67P/Churyumov-Gerasimenko", Science Advances, 2(5), e1600285 (2016). Abstract.

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Sunday, January 15, 2017

On The Quest of Superconductivity at Room Temperature

Authors: Christian E. Precker1, Pablo D Esquinazi1, Ana Champi2, José Barzola-Quiquia1, Mahsa Zoraghi1, Santiago Muiños-Landin1, Annette Setzer1, Winfried Böhlmann1, Daniel Spemann3,6, Jan Meijer3, Tom Muenster4, Oliver Baehre4, Gert Kloess4, Henning Beth5

1Division of Superconductivity and Magnetism, Institut für Experimentelle Physik II, Universität Leipzig, Germany,
2Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, Santo André, São Paulo, Brazil,
3Division of Nuclear Solid State Physics, Institut für Experimentelle Physik II, Universität Leipzig, Germany,
4Institut für Mineralogie, Kristallographie und Materialwissenschaft, Fakultät für Chemie und Mineralogie, Universität Leipzig, Germany,
5Golden Bowerbird Pty Ltd., Mullumbimby, NSW, Australia,
6Present address: Leibniz Institute of Surface Modification, Physical Department, Leipzig, Germany.

Superconductivity is the phenomenon in nature where the electrical resistance of a conducting sample vanishes completely below a certain temperature which is known as “critical temperature (Tc)”. For low enough applied magnetic fields upon sample geometry, the phenomenon of flux expulsion (the Meissner effect) is observable, an effect of special importance for the physics of superconductivity. Due to its interesting characteristics, the phenomenon of superconductivity discovered by Kammerlingh Onnes in Leiden in 1911, is one of the most studied phenomena in experimental and theoretical solid state physics. It has important applications, like the generation of high magnetic fields using superconducting solenoids cooled at liquid He (4K) up to liquid nitrogen (77K) temperatures, or the use of extremely sensitive magnetic field sensors via the so-called Josephson effect. The higher the critical temperature, the easier is the use of superconducting devices, especially in microelectronic. The critical temperature of superconducting materials ranges between a few tens of mK to ~200K, this last critical temperature found recently in SxHy under very high pressures [1].

Among experts in low-temperature physics, in particular those with solid backgrounds on superconductivity, there exists a kind of unproven law regarding the (im)possibility to have superconductivity at room temperature, which means having a material with a critical temperature above 300K. In short, for most of the experts it is extremely difficult to accept that a room temperature superconductor would be possible at all, although there is actually no clear theoretical upper limit for Tc. This general (over)skepticism is probably the reason why, for more than 35 years, the work of Kazimierz Antonowicz [2] (on the superconducting-like behavior he observed on annealed graphite/amorphous carbon powders at room temperature [3]) was not taken seriously by the scientific community. Probably, the lack of easy reproducibility of the observed superconducting-like behavior and the vanishing of the amplitude of the signals within a few days [3] (added to the (over)skepticism of scientists) did not encourage them to look more carefully at those results. The work of Antonowicz on the room temperature superconductivity in carbon powders [3] was not cited in reviews discussing the possibility to reach superconductivity at room temperature, see, e.g., [4].

In the last 16 years, however, different measurements done in highly oriented pyrolytic graphite samples and graphite powders, see [5,6] for reviews, suggest that some kind of interfaces in the graphite structure may quite possibly be the origin for some of the measured signals. This may explain several aspects of this hidden superconductivity, like low reproducibility, time instability, small amount of superconducting mass and the difficulty to localize the superconducting phase(s).

Assuming that somewhere in graphite samples the room temperature superconductivity exists, the question arises: which is actually the critical temperature? This was the main question the work of Precker et al. [7] wanted to answer. For that purpose, the authors took natural crystals from Brazil and Sri Lanka mines. A reader would perhaps be surprised that in these days someone selects natural graphite crystals instead of highly pure and ordered pyrolytic graphite, so called HOPG, for research. The main reason to start with ordered natural crystals is that their several microns long interfaces are very well defined, see Fig. 1. The team in [7] also performed measurements with HOPG samples, whose results support those found in natural graphite crystals. Highly ordered natural graphite crystals of good quality were created during the earth's early evolution at temperature and pressure conditions unreachable in laboratories nowadays. Therefore, the well-defined stacking order phases (hexagonal and rhombohedral) and their interfaces shown in Fig.1 may contribute substantially to the metallic-like behavior of graphite [5,6].
Fig.1: (Click on the image to view with higher resolution) Scanning Transmission electron microscopy (STEM) pictures taken from three ~100nm thick lamellae from three different regions of a natural crystal from Brazil. The e-beam points always parallel to the graphene layers. The different colors mean different stacking ordered regions or regions with the same stacking order but rotated a certain angle around the c-axis. The c-axis is always normal to the graphene planes and interfaces. The picture (c) shows that there are regions in the same sample with no or much less interfaces density. The scale bars at the right bottom denotes 1 µm.

Detailed X-ray diffraction studies done in Ref.[7] show that in all samples a mixture of hexagonal (ABAB…, the majority phase) and rhombohedral (ABCABCA…) stacking orders exist in bulk graphite samples, independently of the sample origin. These two phases as well as their twist around the c-axis are the reason for the different colors in the STEM pictures of Fig.1. There are experimental [5,6] as well as theoretical reasons [8] that indicate that the origin for the metallic, and also most probably the superconducting behavior of graphite, is localized at some of those interfaces. One of the reasons why one expects superconductivity at certain interfaces, e.g. between rhombohedral and hexagonal stacking order, is that the relation between energy and wave-vector for conduction electrons becomes dispersionless. In this case and following the common BCS theory of superconductivity, the superconducting critical temperature is proportional to the Cooper pairs interaction strength. Therefore, it is expected that Tc is much higher than in the case of a quadratic dispersion relation [8].

Coming back to the main question, i.e. the critical temperature of the hidden superconductivity in graphite samples with interfaces, two results obtained in Ref.[7] and shown in Fig.2 resume the main evidence suggesting the existence of granular superconductivity below 350K in the measured crystal.

Figure 2(a) shows the temperature dependence of the resistance (a linear in temperature background is subtracted from the original data) around the transition. It is accompanied by the difference between the field cooled and zero field cooled magnetic moment that starts to increase at the lowest temperature onset of the transition in the resistance. Figure 2(b) shows the change in resistance for the same sample at 325K and after cooling it from 390K at zero field. The relatively large response of the resistance with field and the irreversibility are compatible with granular superconductivity; see also other results in [5,6].
Fig.2: (Click on the image to view with higher resolution) (a) The difference (left y-axis, red points) between the measured field cooled magnetic moment mFC and the zero field cooled mZFC vs. temperature at a field of 50 mT applied at 250K for a natural graphite crystal from Brazil. Right y-axis: Difference between the measured resistance and a linear in temperature background vs. temperature -- for a sample from the same batch at zero field. (b) Change of the resistance with field at a temperature of 325K after cooling it from 390K at zero field. The field was applied normal to the interfaces.

The observed remanence in the resistance indicates that magnetic flux remains trapped within certain regions of the graphite samples. The origin and characteristics of this trapped flux and its non-monotonous temperature behavior [7] have to be clarified in the future and using other experimental techniques. One should also clarify to what extent a magnetically ordered state could have some influence on the observed phenomena. The observed phenomenology in Ref.[7] (see Fig.2) as well as in different studies done on graphite in the past [5,6] strongly suggest the existence of superconductivity. Although several details of the phenomenology, especially the large magnetic anisotropy of the effects in resistance, do not support magnetic order as a possible origin, one should not rule out yet the existence of unusual magnetic states at the graphite embedded interfaces, which are partially being studied theoretically nowadays, see, e.g., Ref.[9].

[1] A. P. Drozdov, M. I. Eremets, I. A. Troyan, V. Ksenofontov, S. I. Shylin, "Conventional superconductivity at 203 kelvin at high pressures in the sulfur hydride system", Nature, 525, 73–6. Abstract.
[2] Kazimierz Antonowicz (1914–2003) started in the 60s the carbon research at Nicolas Copernicus University (Torum, Poland) investigating the structural and electronic properties of different forms of carbon.
[3] K. Antonowicz, "Possible superconductivity at room temperature", Nature, 247, 358–60 (1974). Abstract;   "The effect of microwaves on DC current in an Al–carbon–Al sandwich", Physica Status Solidi (a), 28, 497–502 (1975). Abstract.
[4] Arthur W. Sleight, "Room Temperature Superconductors", Accounts of Chemical Research, 28, 103-108 (1995). Abstract.
[5] Pablo Esquinazi, "Invited review: Graphite and its hidden superconductivity", Papers in Physics, 5, 050007 (2013). Abstract.
[6] P. Esquinazi, Y.V. Lysogorsky, "Experimental evidence for the existence of interfaces in graphite and their relation to the observed metallic and superconducting behavior", ed. P Esquinazi (Switzerland: Springer) pp 145-179 (2016), and refs. therein.
[7] Christian E Precker, Pablo D Esquinazi, Ana Champi, José Barzola-Quiquia, Mahsa Zoraghi, Santiago Muiños-Landin, Annette Setzer, Winfried Böhlmann, Daniel Spemann, Jan Meijer, Tom Muenster, Oliver Baehre, Gert Kloess, Henning Beth, "Identification of a possible superconducting transition above room temperature in natural graphite crystals", New Journal of Physics, 18, 113041 (2016). Abstract.
[8] T.T Heikkilä, G.E. Volovik, "Flat bands as a route to high-temperature superconductivity in graphite", ed. P Esquinazi (Switzerland: Springer) pp 123-143 (2016), and refs. therein.
[9] Betül Pamuk, Jacopo Baima, Francesco Mauri, Matteo Calandra, "Magnetic gap opening in rhombohedral stacked multilayer graphene from first principles", arXiv:1610.03445 [cond-mat.mtrl-sci].

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Sunday, January 08, 2017

Indications of an Influence of Solar Neutrinos on Beta Decays

From left to right: Peter A. Sturrock, Ephraim Fischbach, Jeffrey D. Scargle

Authors: Peter A. Sturrock1, Ephraim Fischbach2, Jeffrey D. Scargle3

1Kavli Institute for Particle Astrophysics and Cosmology and the Center for Space Science and Astrophysics, Stanford University, California, USA,
2Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana, USA,
3NASA/Ames Research Center, Moffett Field, California, USA.

Eckhard D. Falkenberg, who found evidence of an annual oscillation in the beta-decay rate of tritium, was either the first or one of the first to propose that some beta-decay rates may be variable [1]. He suggested that the beta-decay process may be influenced by neutrinos, and attributed the annual variation to the varying Earth-Sun distance that leads to a corresponding variation in the flux of solar neutrinos as detected on Earth. Supporting evidence for the variability of beta-decay rates could be found in the results of an experiment carried out at the Brookhaven National Laboratory. Alburger et al. had measured the decay rates of 36Cl and of 32Si from 1982.13 to 1986.13 (later extended to 1989.93), and reported finding “small periodic annual deviations of the data points from an exponential decay … of uncertain origin” [2].

In 2006, Fischbach and Jenkins of Purdue University set up an experiment to track the decay rate of 54Mn as part of a project to determine whether or not beta decays are strictly random. They found, as had Falkenberg, that the decay rate appeared to be variable. This led them to examine the publication of Alburger et al. [2] and an article by Siegert et al. [3] concerning measurements of the decay rates of 226Ra acquired at the Physikalisch Technische Bundesanstalt in Germany. Jenkins and Fischbach proposed, as had Falkenberg, that the beta decay process may be influenced by solar neutrinos, and that the annual variation may be due to the varying Earth-Sun distance [4]. They also found evidence of a notable variation in the decay rate at the time of a solar flare on December 13, 2006, which led them to suggest that the beta decay process may somehow influence or be influenced by solar activity [5]. Although these two suggestions (that an annual oscillation in beta decays is due to the varying Earth-Sun distance and that beta decays are somehow correlated with solar activity) have not been substantiated by subsequent investigations, their articles were effective in drawing attention to the possibility of decay-rate variability.

Contrary to what one might hope for, but in line with reality, their suggestions quickly led to several nay-saying articles [6,7,8], to which Fischbach and his colleagues responded [9,10,11]. More recently, Kossert and Nahle have claimed to have evidence that beta-decay rates are constant [12], but their claims have been refuted [13]. The latest such article is one by Pomme et al. [14], who have published data concerning 67 measurements of a variety of decay processes, examining the measurements only for evidence of an Earth-Sun-Distance effect (which is known to be an inadequate test of variability) and claim to establish that there is no such effect. Their data have not yet been subjected to an independent analysis.

Although the first evidence for variability was the discovery of annual oscillations in decay rates, this approach to the problem has the obvious defect that an annual variation may be caused by any one of several experimental or environmental influences, which led us to seek evidence for an influence of solar rotation. We have learned from helioseismology that the synodic rotation rate (as seen from Earth) of the radiative zone is in the range 12.5 to 12.8 year-1, whereas the synodic rotation rate of the photosphere extends to 13.8 year-1 [15]. Variation of the solar neutrino flux may be attributable to the RSFP (Resonant Spin Flavor Precession) process [16], which can more easily occur in the deep solar interior (where there can be much stronger magnetic field) than in the convection zone [17]. This scenario would not lead one to expect an association between decay-rate variations and flare-like solar activity, which takes place in the outermost layer of the convection zone and in the solar atmosphere.

Power spectrum analysis of BNL data has in fact yielded evidence of oscillations in the frequency range 11 – 13 year-1, supporting our conjecture that there may be a rotational influence on the solar neutrino flux [18,19]. However, these results raised the question of whether one could find corresponding evidence for solar rotation in measurements of the solar neutrino flux made by neutrino observatories such as Super-Kamiokande. An analysis of Super-Kamiokande data that takes account only of the mid-time of each bin, ignores the error estimates, and adopts an unrealistically wide search band, yields inconclusive results [20], but an analysis that takes account of the start and stop time of each measurement bin and of the upper and lower error estimates, and adopts an appropriate search band, yields strong evidence of an oscillation of frequency 9.43 year-1 [21].

A crucial issue is whether or not solar influences are steady or time variable. Our investigations of GALLEX solar neutrino data indicated that the influence of rotation tends to be episodic [22]. This suggested that one should examine neutrino and beta-decay data by means of spectrograms rather than periodograms. These considerations led us to carry out a comparative analysis of spectrograms formed from the BNL data and from Super-Kamiokande data. The results have recently been published in Solar Physics [23].
Figure 1. Spectrogram formed from 36Cl data for the frequency band 8 – 16 year-1.

Figures 1 and 2, taken from that article, show spectrograms formed from BNL 36Cl and 32Si data, respectively. In order to focus on possible evidence of solar rotation, we show spectrograms only for the frequency range 8 to 16 year-1. Figure 1 shows evidence of strong but transient oscillations at frequencies of approximately 11 year-1 and 12.6 year-1. Figure 2 also shows evidence of an oscillation at approximately 12.6 year-1, but only slight evidence of an oscillation at approximately 11 year-1. Evidence of these two oscillations has previously been found in power-spectrum analyses [18,19].
Figure 2. Spectrogram formed from 32Si data for the frequency band 8 – 16 year-1.

Figure 3 shows a spectrogram formed from Super-Kamiokande data, again for the frequency range 8 – 16 year-1. This spectrogram shows evidence of a strong and steady oscillation at approximately 9.5 year-1, as expected from our earlier power-spectrum analysis [21]. However, it also shows evidence of a transient oscillation with a frequency of approximately 12.6 year-1, supporting the proposition that beta-decay variability may be attributed to an influence of solar neutrinos.
Figure 3. Spectrogram formed from Super-Kamiokande data for the frequency band of 8 – 16 year-1.

The schedules of the relevant experiments were such that measurements leading to Figures 1 and 2 and measurements leading to Figure 3 were not acquired at the same time. It would clearly be desirable to compare beta-decay measurements and solar neutrino measurements that are acquired in the same time frame. The most extensive set of beta-decay measurements is the sequence currently (beginning in early 1992) being acquired by Steinitz and his colleagues at the Geological Survey of Israel (GSI) [24, 25]. The Borexino solar neutrino experiment began operation in 2007 and is still operational [26], so it may be possible at some time to compare beta-decay data with contemporaneous solar-neutrino data. It is however important to note that one may not find a perfect match between the two sets of data, even if beta decays are in fact influenced by neutrinos, since beta decays and neutrino detectors may respond to neutrinos of different energies and (since we have no theoretical understanding of beta-decay variability) conceivably of different flavors.

[1] Eckhard Dieter Falkenberg, "Radioactive Decay Caused by Neutrinos?", Apeiron, 8, 32 (2001). Full Article.
[2] D.E. Alburger, G. Harbottle, E.F. Norton, "Half Life of 32Si", Earth and Planetary Science Letters, 78, 168 (1986). Abstract.
[3] Helmut Siegert, Heinrich Schrader, Ulrich Schötzig, "Half-life measurements of Europium radionuclides and the long-term stability of detectors", Applied Radiation and Isotopes, 49, 1397 (1998). Abstract.
[4] Jere H. Jenkins, Ephraim Fischbach, John B. Buncher, John T. Gruenwald, Dennis E. Krause, Joshua J. Mattes, "Evidence of correlations between nuclear decay rates and Earth–Sun distance", Astroparticle Physics, 32, 42 (2009). Abstract.
[5] Jere H. Jenkins, Ephraim Fischbach, "Perturbation of nuclear decay rates during the solar flare of 2006 December 13", Astroparticle Physics, 31, 407 (2009). Abstract.
[6] Peter S. Cooper, "Searching for modifications to the exponential radioactive decay law with the Cassini spacecraft", Astroparticle Physics, 31, 267 (2009). Abstract.
[7] Eric B. Norman, Edgardo Browne, Howard A. Shugart, Tenzing H. Joshi, Richard B. Firestone, "Evidence against correlations between nuclear decay rates and Earth–Sun distance", Astroparticle Physics, 31, 135 (2009). Abstract.
[8] T.M. Semkowa, D.K. Hainesa, S.E. Beacha, B.J. Kilpatricka, A.J. Khana, K. O'Brienb, "Oscillations in radioactive exponential decay", Physics Letters B, 675, 415 (2009). Abstract.
[9] D.E. Krause, B.A. Rogers, E. Fischbach, J.B. Buncher, A. Ging, J.H. Jenkins, J.M. Longuski, N. Strange, P.A. Sturrock, "Searches for solar-influenced radioactive decay anomalies using spacecraft RTGs", Astroparticle Physics, 36, 51 (2012). Abstract.
[10] D. O’Keefe, B.L. Morreale, R.H. LeeJohn, B. Buncher, J.H. Jenkins, Ephraim Fischbach, T. Gruenwald, D. Javorsek II, P.A. Sturrock, "Spectral content of 22Na/44Ti decay data: implications for a solar influence", Astrophysics and Space Science, 344, 297 (2013). Abstract.
[11] Jere H. Jenkins, Daniel W. Mundy, Ephraim Fischbach, "Analysis of environmental influences in nuclear half-life measurements exhibiting time-dependent decay rates", Nuclear Instruments and Methods in Physics Research Section A. 620, 332 (2010). Abstract.
[12] Karsten Kossert, Ole J. Nähle, "Disproof of solar influence on the decay rates of 90Sr/90Y", Astroparticle Physics, 69, 18 (2015). Abstract.
[13] P.A. Sturrock, G. Steinitz, E. Fischbach, A. Parkhomov, J.D. Scargle, "Analysis of beta-decay data acquired at the Physikalisch-Technische Bundesanstalt: Evidence of a solar influence", Astroparticle Physics, 84, 8 (2016). Abstract.
[14] S. Pomméa, H. Stroh, J. Paepen, R. Van Ammel, M. Marouli, T. Altzitzoglou, M. Hult, K. Kossert, O. Nähle, H. Schrader, F. Juget, C. Bailat, Y. Nedjadi, F. Bochud, T. Buchillier, C. Michotte, S. Courte, M.W. van Rooy, M.J. van Staden, J. Lubbe, B.R.S. Simpson, A. Fazio, P. De Felice, T.W. Jackson, W.M. Van Wyngaardt, M.I. Reinhard, J. Golya, S. Bourke, T. Roy, R. Galea, J.D. Keightley, K.M. Ferreira, S.M. Collins, A. Ceccatelli, M. Unterweger, R. Fitzgerald, D.E. Bergeron, L. Pibida, L. Verheyen, M. Bruggeman, B. Vodenik, M. Korun, V. Chisté, M.-N. Amiot, "Evidence against solar influence on nuclear decay constants", Physics Letters B, 761, 281 (2016). Abstract.
[15] J. Schou, R. Howe, S. Basu, J. Christensen-Dalsgaard, T. Corbard, F. Hill, R. Komm, R. M. Larsen, M. C. Rabello-Soares, M. J. Thompson, "A Comparison of Solar p-Mode Parameters from the Michelson Doppler Imager and the Global Oscillation Network Group: Splitting Coefficients and Rotation Inversions", Astrophysical Journal, 567, 1234 (2002). Abstract.
[16] E. Kh. Akhmedov, "Resonant amplification of neutrino spin rotation in matter and the solar-neutrino problem", Physics Letters B, 213, 64 (1988). Abstract.
[17] João Pulido, C R Das, Marco Picariello, "Remaining inconsistencies with solar neutrinos: Can spin flavour precession provide a clue?", Journal of Physics: Conference series, 203, 012086 (2009). Abstract.
[18] P.A. Sturrock, J.B. Buncher, E. Fischbach, J.T. Gruenwald, D. Javorsek II, J.H. Jenkins, R.H. Lee, J.J. Mattes, J.R. Newport, "Power spectrum analysis of BNL decay rate data", Astroparticle Physics, 34, 121 (2010). Abstract.
[19] D. Javorsek II, P.A. Sturrock, R.N. Lasenby, A.N. Lasenby, J.B. Buncher, E. Fischbach, J.T. Gruenwald, A.W. Hoft, T.J. Horan, J.H. Jenkins, J.L. Kerford, f, R.H. Lee, A. Longman, J.J. Mattes, B.L. Morreale, D.B. Morris, R.N. Mudry, J.R. Newport, D. O’Keefe, M.A. Petrelli, M.A. Silver, C.A. Stewart, B. Terry, "Power spectrum analyses of nuclear decay rates", Astroparticle Physics, 34, 173 (2010). Abstract.
[20] J. Yoo et al. (Super-Kamiokande Collaboration), "Search for periodic modulations of the solar neutrino flux in Super-Kamiokande-I", Physical Review D, 68, 092002 (2003). Abstract.
[21] P.A. Sturrock, J.D. Scargle, "Power-Spectrum Analysis of Super-Kamiokande Solar Neutrino Data, Taking into Account Asymmetry in the Error Estimates", Solar Physics, 237, 1 (2006). Abstract.
[22] P.A. Sturrock, "Time–Frequency Analysis of GALLEX and GNO Solar Neutrino Data", Solar Physics, 252, 1 (2008). Abstract.
[23] P.A. Sturrock, E. Fischbach, J.D. Scargle, "Comparative Analyses of Brookhaven National Laboratory Nuclear Decay Measurements and Super-Kamiokande Solar Neutrino Measurements: Neutrinos and Neutrino-Induced Beta-Decays as Probes of the Deep Solar Interior", Solar Physics, 291, 3467 (2016). Abstract.
[24] G. Steinitz, O. Piatibratova, P. Kotlarsky, "Sub-daily periodic radon signals in a confined radon system", Journal of Environmental Radioactivity, 134, 128 (2014). Abstract.
[25] G. Steinitz, P. Kotlarsky, O. Piatibratova, "Observations of the relationship between directionality and decay rate of radon in a confined experiment", European Physical Journal, 224, 731 (2015). Abstract.
[26] S. Davini, G. Bellini, J. Benziger, D. Bick, G. Bonfini, D. Bravo, B. Caccianiga, F. Calaprice, A. Caminata, P. Cavalcante, A. Chepurnov, D. D'Angelo, A. Derbin, A. Etenko, K. Fomenko, D. Franco, C. Galbiati, C. Ghiano, A. Goretti, M. Gromov, Aldo Ianni, Andrea Ianni, V. Kobychev, D. Korablev, G. Korga, D. Kryn, M. Laubenstein, T. Lewke, E. Litvinovich, F. Lombardi, P. Lombardi, L. Ludhova, G. Lukyanchenko, I. Machulin, S. Manecki, W. Maneschg, S. Marcocci E. Meroni, M. Misiaszek, P. Mosteiro, V. Muratova, L. Oberauer, M. Obolensky, F. Ortica, K. Otis, M. Pallavicini, L. Papp, A. Pocar, G. Ranucci, A. Razeto, A. Re, A. Romani, N. Rossi, C. Salvo, S. Schönert, H. Simgen, M. Skorokhvatov, O. Smirnov, A. Sotnikov, S. Sukhotin, Y. Suvorov, R. Tartaglia, G. Testera, D. Vignaud, R. B. Vogelaar, J. Winter, M. Wojcik, M. Wurm, O. Zaimidoroga, S. Zavatarelli, G. Zuzel, "New results of the Borexino experiment: pp solar neutrino detection", Il Nuovo Cimento C, 38, 120 (2015). Abstract.

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