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


2Physics Quote:
"Controlling quantum cascade lasers so that they produce tuneable, single frequency light is particularly difficult. In our earlier work we achieved all-electrical tuning in a terahertz laser over a discrete set of frequencies. We did this by integrating a specially designed photonic lattice into the gold waveguide of the laser, which we dubbed an ‘aperiodic lattice laser’. Such lasers are compact (~1 cm2), powerful (~10 mW of power), and capable of working at a range of terahertz frequencies. However, to be a practical THz source, these lasers need to show continuous tuning over a wide range of THz frequencies."
-- Subhasish Chakraborty, Owen Marshall, Thomas Folland, Yong-Jin Kim, Alexander Grigorenko, Konstantin Novoselov (Read Full Article: "Graphene Tuned Terahertz Lasers" )

Sunday, April 24, 2016

Demonstrating One-Way Einstein-Podolsky-Rosen Steering in Two Qubits

Some authors of the PRL paper (Reference 6) published on Thursday. From Left to Right: (top row) Kai Sun, Xiang-Jun Ye, Jin-Shi Xu, (bottom row) Jing-Ling Chen, Chuan-Feng Li, Guang-Can Guo.

Authors: Kai Sun1, Xiang-Jun Ye1, Jin-Shi Xu1, Jing-Ling Chen2, Chuan-Feng Li1, Guang-Can Guo1

1Key Laboratory of Quantum Information, CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, China.
2Chern Institute of Mathematics, Nankai University, Tianjin, China.

Asymmetric Einstein-Podolsky-Rosen (EPR) steering is an important “open question” proposed when EPR steering is reformulated in 2007 [1]. Suppose Alice and Bob share a pair of two-qubit states; it is easy to imagine that if Alice entangles with Bob, then Bob must also entangle with Alice. Such a symmetric feature holds for both entanglement and Bell nonlocality [2]. However, the situation is dramatically changed when one turns to a novel kind of quantum nonlocality, the EPR steering, which stands between entanglement and Bell nonlocality. It may happen that for some asymmetric bipartite quantum states, Alice can steer Bob but Bob cannot steer Alice. This distinguished feature would be useful for the one-way quantum tasks. The first experimental verification of one-way EPR steering was performed by using two entangled continuous variable systems in 2012 [3]. However, the experiments demonstrating one-way EPR steering [3,4] are restricted to Gaussian measurements, and for more general measurements, like projective measurements, there is no experiment realizing the asymmetric feature of EPR steering, even though the theoretical analysis has been proposed [5].

Figure 1: Illustration of one-way EPR steering. In one direction (red), EPR steering is realized and this direction is safe for quantum information. In the other direction (blue), steering task fails and this direction is not safe.

Recently, we for the first time quantified the steerability and demonstrated one-way EPR steering in the simplest entangled system (two qubits) using two-setting projective measurements [6]. The asymmetric two-qubit states in the form of ρAB = η |Ψ(θ)⟩⟨Ψ(θ)| + (1-η) |Φ(θ)⟩⟨Φ(θ)|, where 0 ≤ η≤ 1, |Ψ(θ)⟩ = cos ⁡θ |0A 0B⟩ + sin⁡θ |1A 1B⟩, |Φ(θ)⟩ = cos⁡θ |1A 0B⟩ + sin⁡θ |0A 1B⟩, are prepared in this experiment (see Figure 2(a) ). Based on the steering robustness [7], an intuitive criterion R called as “steering radius” is defined to quantify the steerability (see Figure 2 (c) ). The different values of R on two sides clearly illustrate the asymmetric feature of EPR steering. Furthermore, the one-way steering is demonstrated when R > 1 on one side and R < 1 on the other side (see Figure 2 (b)).
Figure 2:  (click on the figure to view with higher resolution)  Experimental results for asymmetric EPR steering. (a) The distribution of the experimental states. The right column shows the entangled states we prepared, and the left column is a magnification of the corresponding region in the right column. The states located in the yellow (grey) regions are predicted to realize one-way (two-way) steering theoretically in the case of two-setting measurements. The blue points and red squares represent the states realizing one-way and two-way EPR steering, respectively. The black triangles represent the states for which EPR steering task fails for both observers. (b) The values of R for the states are labeled in the left column in (a). The red squares represent the situation where Alice steers Bob's system, and the blue points represent the case where Bob steers Alice's system. (c) Geometric illustration of the strategy for local hidden states (black points) to construct the four normalized conditional states (red points) obtained from the maximally entangled state.

For the failing EPR steering process, the local hidden state model, which provides a direct and convinced contradiction between the nonlocal EPR steering and classical physics, is prepared experimentally to reconstruct the conditional states obtained in the steering process (see Figure 3).
Figure 3. (click on the figure to view with higher resolution) The experimental results of the normalized conditional states and local hidden states shown in the Bloch sphere. The theoretical and experimental results of the normalized conditional states are marked by the black and red points (hollow), respectively. The blue and green points represent the results of the four local hidden states in theory and experiment, respectively. The normalized conditional states constructed by the local hidden states are shown by the brown points. Spheres (a) and (c) are for the case in which Alice steers Bob's system, whereas (b) and (d) show the case in which Bob steers Alice's system. The parameters of the shared state in (a) and (b) are θ = 0.442 and η = 0.658; the parameters of the shared state in (c) and (d) are θ = 0.429 and η = 0.819. The spheres (a), (b) and (d) show that the local hidden state models exist, and the steering tasks fail. The sphere (c) Shows that no local hidden state model exists for the steering process with the constructed hidden states located beyond the Bloch sphere and R = 1.076.

The quantification of EPR steering provides an intuitional and fundamental way to understand the EPR steering and the asymmetric nonlocality. The demonstrated asymmetric EPR steering is significant within quantum foundations and quantum information, and shows the applications in the tasks of one-way quantum key distribution [8] and the quantum sub-channel discrimination [7], even within the frame of two-setting measurements.

[1] H. M. Wiseman, S. J. Jones, and A. C. Doherty, “Steering, entanglement, nonlocality, and the Einstein-Podolsky-Rosen paradox”, Physical Review Letters, 98, 140402 (2007). Abstract.
[2] John S. Bell, “On the Einstein Podolsky Rosen paradox”, Physics, 1, 195 (1964). Full Text.
[3] Vitus Händchen, Tobias Eberle, Sebastian Steinlechner, Aiko Samblowski, Torsten Franz, Reinhard F. Werner, and Roman Schnabel, “Observation of one-way Einstein-Podolsky-Rosen steering”, Nature Photonics, 6, 596 (2012). Abstract.
[4] Seiji Armstrong, Meng Wang, Run Yan Teh, Qihuang Gong, Qiongyi He, Jiri Janousek, Hans-Albert Bachor, Margaret D. Reid, and Ping Koy Lam, “Multipartite Einstein-Podolsky-Rosen steering and genuine tripartite entanglement with optical networks”, Nature Physics, 11, 167 (2015). Abstract.
[5] Joseph Bowles, Tamás Vértesi, Marco Túlio Quintino, and Nicolas Brunner, “One-way Einstein-Podolsky-Rosen steering”, Physical Review Letters, 112, 200402 (2014). Abstract.
[6] Kai Sun, Xiang-Jun Ye, Jin-Shi Xu, Xiao-Ye Xu, Jian-Shun Tang, Yu-Chun Wu, Jing-Ling Chen, Chuan-Feng Li, and Guang-Can Guo, “Experimental quantification of asymmetric Einstein-Podolsky-Rosen steering”, Physical Review Letters, 116, 160404 (2016). Abstract.
[7] Marco Piani, John Watrous, “Necessary and sufficient quantum information characterization of Einstein-Podolsky-Rosen steering”, Physical Review Letters, 114, 060404 (2015). Abstract.
[8] Cyril Branciard, Eric G. Cavalcanti, Stephen P. Walborn, Valerio Scarani, and Howard M. Wiseman, “One-sided device-independent quantum key distribution: security, feasibility, and the connection with steering”, Physical Review A, 85, 010301 (2012). Abstract.


Sunday, March 20, 2016

Efficient Long-Distance Heat Transport by Microwave Photons

Research team behind the original discovery (Reference [11] ) from left to right: Tuomo Tanttu, Joonas Goveenius, Mikko Möttönen, Matti Partanen, and Miika Mäkelä (Missing from the figure: Kuan Yen Tan and Russell Lake). Photo Credit: Vilja Pursiainen/Kaskas Media.

Authors: Matti Partanen and Mikko Möttönen

Affiliation: QCD Labs, Department of Applied Physics, Aalto University, Finland.

Link to the Quantum Computing and Devices (QCD) Group >>

Quantum computers are predicted to vastly speed up the computation for certain problems of great practical interest [1]. One of the most promising architectures for quantum computing is based on superconducting quantum bits [2], or qubits, which are the key ingredients in circuit quantum electrodynamics [3]. In such systems, the control of heat at the quantum level is extremely important, and remote cooling may turn out to be a viable option.

In one dimension, heat transport may be described by individual heat conduction channels -- each corresponding to a certain quantized profile of the heat carriers in the transverse direction. Importantly, the maximum heat power flowing in a single channel between bodies at given temperatures is fundamentally limited by quantum mechanics [4,5]. This quantum limit has previously been observed for phonons [6], sub-wavelength photons [7,8], and electrons [9]. Among these, the longest distance of roughly 50 μm [7,8] was recorded in the photonic channel [10]. Such short distance may be undesirable in cooling quantum devices which are sensitive to spurious dissipation.

In our recent work [11], we observe quantum-limited heat conduction by microwave photons flying in a superconducting transmission line of length 20 cm and 1 m. Thus we were able to extend the maximum distance 10,000 fold compared with the previous experiments.
Figure 1: (click on the figure to view with higher resolution) Sample structure and measurement scheme. The electron temperature of the right resistor is controlled with an external voltage while the temperatures of both resistors are measured. Microwave photons transport heat through the spiraling transmission line.

Our sample is shown in Figure 1. The heat is transferred between two normal-metal resistors functioning as black-body radiators to the transmission line [10,12]. To be able to fabricate the whole sample on a single relatively small chip, the transmission line has a double spiral structure. We have measured such spiraling transmission lines without resistors and confirmed that photons travel along the line; they do not jump through vacuum from one end to the other. Thus for heat transport, the distance should be measured along the line.

We measure the electron temperatures of both normal-metal resistors while we change the temperature of one of them [13]. The obtained temperature data agrees well with our thermal model, according to which the heat conduction is very close to the quantum limit.

In contrast to subwavelength distances employed in References [7,8], we need to match the resistance of the normal-metal parts to the characteristic impedance of the transmission line to reach the quantum limit. Furthermore, the transmission line itself has to be so weakly dissipative that almost no photons are absorbed even over distances of about a meter. However, we managed to develop nanofabrication techniques which enabled us to satisfy these conditions well. In fact, the losses in the transmission line are so weak they allow a further increment of the distance by several orders of magnitude.

We consider that long-distance heat transport through transmission lines may be a useful tool for certain future applications in the quickly developing field of quantum technology. If the coupling of a quantum device to a low-temperature transmission line can be well controlled in situ, the device may be accurately initialized without disturbing its coherence properties when the coupling is turned off [14]. Furthermore, the implementation of such in-situ-tunable environments opens an interesting avenue for the study of the detailed dynamics of open quantum systems and quantum fluctuation relations [15].

Acknowledgements: We thank M. Meschke, J. P. Pekola, D. S. Golubev, J. Kokkala, M. Kaivola and J. C. Cuevas for useful discussions, and L. Grönberg, E. Mykkänen, and A. Kemppinen for technical assistance. We acknowledge the provision of facilities and technical support by Aalto University at Micronova Nanofabrication Centre. We also acknowledge funding by the European Research Council under Starting Independent Researcher Grant No. 278117 (SINGLEOUT), the Academy of Finland through its Centres of Excellence Program (project nos 251748 and 284621) and grants (nos 138903, 135794, 265675, 272806 and 276528), the Emil Aaltonen Foundation, the Jenny and Antti Wihuri Foundation, and the Finnish Cultural Foundation.

[1] T.D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, J.L. O'Brien, “Quantum computers”, Nature, 464, 45 (2010). Abstract.
[2] J. Kelly, R. Barends, 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, A.N. Cleland, John M. Martinis, “State preservation by repetitive error detection in a superconducting quantum circuit”, Nature, 519, 66 (2015). Abstract.
[3] A. Wallraff, D.I. Schuster, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. Kumar, S.M. Girvin, R.J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum Electrodynamics”, Nature, 431, 162 (2004). Abstract.
[4] J.B. Pendry, “Quantum limits to the flow of information and entropy”, Journal of Physics A: Mathematical and General, 16, 2161 (1983). Abstract.
[5] Luis G. C. Rego, George Kirczenow, “Fractional exclusion statistics and the universal quantum of thermal conductance: A unifying approach”, Physical Review B, 59, 13080 (1999). Abstract.
[6] K. Schwab, E.A. Henriksen, J.M.Worlock, M.L. Roukes, “Measurement of the quantum of thermal conductance”, Nature, 404, 974 (2000). Abstract.
[7] Matthias Meschke, Wiebke Guichard, Jukka P. Pekola, “Single-mode heat conduction by photons”, Nature, 444, 187 (2006). Abstract.
[8] Andrey V. Timofeev, Meri Helle, Matthias Meschke, Mikko Möttönen, Jukka P. Pekola, “Electronic refrigeration at the quantum limit”, Physical Review Letters, 102, 200801 (2009). Abstract.
[9] S. Jezouin, F.D. Parmentier, A. Anthore, U. Gennser, A. Cavanna, Y. Jin, and F. Pierre, “Quantum limit of heat flow across a single electronic channel”, Science, 342, 601 (2013). Abstract.
[10] D.R. Schmidt, R.J. Schoelkopf, A.N. Cleland, “Photon-mediated thermal relaxation of electrons in nanostructures”, Physical Review Letters, 93, 045901 (2004). Abstract.
[11] Matti Partanen, Kuan Yen Tan, Joonas Govenius, Russell E. Lake, Miika K. Mäkelä, Tuomo Tanttu, Mikko Möttönen, “Quantum-limited heat conduction over macroscopic distances”, Nature Physics, Advance online publication, DOI:10.1038/nphys3642 (2016). Abstract.
[12] L.M.A. Pascal, H. Courtois, F.W.J. Hekking, “Circuit approach to photonic heat transport”, Physical Review B, 83, 125113 (2011). Abstract.
[13] Francesco Giazotto, Tero T. Heikkilä, Arttu Luukanen, Alexander M. Savin, Jukka P. Pekola, “Opportunities for mesoscopics in thermometry and refrigeration: Physics and applications”, Reviews of Modern Physics, 78, 217 (2006). Abstract.
[14] P. J. Jones, J.A.M. Huhtamäki, J. Salmilehto, K.Y. Tan, M. Möttönen, “Tunable electromagnetic environment for superconducting quantum bits”, Scientific Reports, 3, 1987 (2013). Abstract.
[15] Jukka P. Pekola, “Towards quantum thermodynamics in electronic circuits”, Nature Physics, 11, 118 (2015). Abstract.

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Sunday, March 13, 2016

Why Statistical Physics Should Be A Foundation For Materials Design

Marc Miskin

Author: Marc Miskin

James Franck Institute and Department of Physics, The University of Chicago, USA.

The fact that major epochs in human history have been named after materials like bronze, steel, silicon, and stone expresses both how important materials are for technology and how long it can take before a new material is discovered. Even today, the timespan to convert materials' discoveries into functioning technologies takes upwards of 20 years. In part this is because creating technologically useful materials requires selecting a wide range of parameters to optimize the material’s performance. While tools like statistical physics are useful for describing a material’s behavior given a set of parameters, it remains unknown how to generally invert these relationships to target desired behavior. This task is called materials design and it is a new concept at the forefront of materials research.

Recently, several methods have emerged across disciplines that draw upon optimization and simulation to create computer programs that tailor material responses to specified behaviors. However, so far the methods developed either involve black-box techniques, in which the optimizer operates without explicit knowledge of the physical laws that underpin the material’s behavior, or require carefully tuned algorithms with applicability limited to a narrow subclass of materials.

Our recent publication titled “Turning Statistical Physics Models into Materials Design Engines” [1] presents a new perspective for material design. In contrast to prior approaches, it is broad enough to be applied without modification to any system that is well described by statistical mechanics and also retains much of the key insight that is at the heart of statistical physics. In short, our formalism allows a user to transform the capacity to predict material behavior into an optimizer that tunes it.

We achieved this by examining the fundamental relationship between microstate configurations and material properties. Statistical physics poses the idea that materials are intrinsically statistical objects: the properties a bulk material has are best calculated by averaging over all the possible configurations for the material's microscopic parts. Our insight was that design programs should focus on tailoring materials at the level of micro-states themselves, rather than simply focusing on the bulk emergent properties.

For instance, suppose that the pressure and temperature affect the stiffness of a given material and the goal is to set these two parameters to make the stiffest material. The black-box approach is to view this as an optimization problem with pressure and temperature as inputs and stiffness as an output. Yet this view completely ignores the micro-states. A better perspective is to treat the control parameters as means to alter the likelihood of micro-states. To design the material, an algorithm should tweak the parameters so that the material is more likely to be in micro-states with the target behavior.

This idea is the kernel of our approach: we built a formalism out of this concept and tackle materials' design at the level of micro-state information. This gave us a program that is broad enough to address the range of materials that are well described by statistical physics, and we achieve this with a boost in efficiency, thanks to the extra information extracted from the microstate configurations.

To test our approach, we constructed test problems that a good materials optimization scheme should be able to address by itself. Material scientists need optimizers that can solve problems where the search landscape has little variation between candidate materials, juggle multiple potentially competing physical effects, operate in high dimensional search spaces, tune the processing conditions that a material is subject to, and operate when on real-world scale optimization problems. We then translated these challenges into physical test problems, and compared our approach against optimization schemes that we have used successfully for materials design in the past. Given the criterion that the best optimizer is the one that has to make the fewest guesses to arrive at the material that performs a target function, our optimizer outperformed all of our old standards.

Probably the two most fascinating solutions presented in the paper [1] are the polymer folding problem and the directed self-assembly problem. In the polymer folding problem, we asked our optimizer to tune the interaction strengths between 6 beads attached to each other along a linear chain (Figure 1). Because the interactions are attractive, when they are strong enough the chain will fold itself up into a compact shape. The goal here was to make the chain fold into a specific shape: an octahedron. Its an interesting problem because it's well known that simply making all the interactions large will not produce an octahedral geometry. Instead, the interactions needed to be developed into three separate families to generate octahedron and it took hard work from the colloidal self-assembly community to show that this worked. So it was very exciting for us when our optimizer not only produced a virtually identical motif, but managed to yield the result in the span of hours.
Figure 1: Given a polymer of 6 beads each of different color, how should the strength of each short-ranged interaction be picked so that the polymer self-folds into an octahedron geometry? Each image shows a typical polymer configuration obtained at each stage in an optimization using our new approach. The optimizer essentially starts from random, chain like geometries and after ~200 cycles transforms them into the target shape.

There is a similar story behind our directed self-assembly problem. In this case, the material is a polymer made of two types of beads. The goal is to pattern a substrate with a thin strip that has an affinity for a particular one of those two beads (Figure 2). By setting the strip width and the strength of affinity just right, it is possible to make the polymer self-assemble into stripes containing only one polymer type followed by a stripe of the other polymer type and so on. This idea holds serious promise as a next-generation manufacturing technology for semiconductors because the sizes of these stripes are on the order of nanometers. By using the polymer stripes as stencils or masks, it is possible to make next generation circuits or hard drive media with features significantly smaller than what current processing techniques allow. What we found was that not only can our optimizer produce solutions to the problem of tailoring interaction strengths for this kind of directed self-assembly, but that it does so between 5-130X faster than approaches we had tried in the past. To put this into context, solving a directed self assembly problem in the past took us roughly 1 week. Now we can solve them in just under 12 hours.
Figure 2: Given melt of polymer chains each made from half a-type (red) and half b-type (blue) beads, how should one tune the interactions between the a and b beads and a substrate so that the polymer melt self-assembles into equally spaced stripes of a and b? On the top is an image of the original polymer melt configuration for randomly seeded interaction parameters. On the bottom shows the structures that result from using our algorithm to elicit self-assembly. Note the substrate has been colored based on the affinity for each type.

Speaking broadly, materials by design is a radical shift in how we transform bulk matter into useful technology. Historically materials have been either discovered by accident or appropriated from nature to perform technological functions. What we're after is the capacity to systematically identify which materials produce a target response. The benefit of this paradigm is that increasingly complex materials could be cooked up automatically to meet specific technological demands. Our algorithm is a small part of this growing field, but the hope is that it will inspire others to consider their expertise on materials within the new context of design.

Our experience in the past has been that it can be difficult to get started on building design engines for a new material. If the problem isn't posed the right way or the optimizer isn't appropriately tailored, it may require a substantial investment of time to construct an optimization scheme that actually works. What we tried to show in this paper is that our formalism works broadly over a range of very different physical problems without any need for additional modifications. It works out of the box, so to speak, for designing any material that can be simulated using a statistical physics approach. Our hope is that this robustness will translate into a reduction in the time researchers need to spend building design algorithms, and free them up to focus on the task of making exotic materials.

Some of our recent work along these lines can be found here:
[1] Marc Z. Miskin, Gurdaman Khaira, Juan J. de Pablo, Heinrich M. Jaeger, "Turning statistical physics models into materials design engines", Proceedings of the National Academy of Sciences, 113, 34-39 (2016). Full Text.
[2] Marc Z. Miskin, Heinrich M. Jaeger, "Adapting granular materials through artificial evolution", Nature Materials, 12, 326-331 (2013). Abstract.
[3] Marc Z. Miskin, Heinrich M. Jaeger, "Evolving design rules for the inverse granular packing problem", Soft Matter, 10, 3708-3715 (2014). Abstract.
[4] Jian Qin, Gurdaman S. Khaira, Yongrui Su, Grant P. Garner, Marc Miskin, Heinrich M. Jaeger, Juan J. de Pablo, "Evolutionary pattern design for copolymer directed self-assembly", Soft Matter, 9, 11467–11472 (2013). Abstract.

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Sunday, March 06, 2016

A New Approach to Quantum Entanglement for Identical Particles

Rosario Lo Franco (right) and Giuseppe Compagno (left)

Authors: Rosario Lo Franco1 and Giuseppe Compagno2

1Dipartimento di Energia, Ingegneria dell'Informazione e Modelli Matematici, Università di Palermo, Italy,
2Dipartimento di Fisica e Chimica, Università di Palermo, Italy.

Entanglement for distinguishable particles is well established from a conceptual point of view with standard tools capable to identify and quantify it [1, 2]. This is instead not the case for identical particles, bosons (e.g., photons, atoms) and fermions (e.g., electrons), where particle identity may give place to fictitious contributions to entanglement which has been the origin of a long-standing debate [2-4]. For all practical purposes, when two identical particles are spatially separated, as in experiments with photons in different optical modes or with strongly repelling trapped ions, no ambiguity is possible for which particle has a given property so they can be effectively treated as distinguishable objects [3]: in this case, no physical contribution to entanglement arises due to indistinguishability.

Figure 1: Asymmetric double-well configuration. One particle has a localized (orange) wave function A in the left well L, while one particle has a (blue) wave function B which overlaps with A, being nonzero in both the left well L and the right well R. This is a typical instance where one particle can tunnel from a site to the other one and indistinguishability counts.

This aspect comes from a natural requirement known as cluster decomposition principle stating that distant experiments are not influenced by each other [6]. Otherwise, quantum indistinguishability comes into play when the constituting particles are close enough to spatially overlap. This happens for all the applications of quantum information processing based, for instance, on quantum dot technology with electrons [7,8] or on Bose-Einstein condensates [9,10], where the particles have the possibility to tunnel from a location to the other (Fig. 1). Hence, correctly treating identical particle entanglement, besides its fundamental interest, is a central requirement in quantum information theory. Despite this, the analysis of identical particle entanglement has been suffering both conceptual and technical pitfalls [2-4].

The ordinary approach to deal with identical particles in quantum mechanics textbooks consists in assigning them unobservable labels which give rise to a new fictitious system of distinguishable particles [5]. In order that this new system behaves as the original (bosonic or fermionic) one, only symmetrized or anti-symmetrized states with respect to labels are allowed. The byproduct is that, according to the usual notion of non-separability employed in quantum information theory to define entanglement, such states entangled. Ordinary entanglement measures, such as the von Neumann entropy of the reduced state obtained by partial trace, fail then to be directly applied to these states. In particular, they witness entanglement even for independent separated particles which are clearly uncorrelated and also show contradictory results for bosons and fermions [3].

As a consequence, methods utilizing notions at variance with the ordinary ones adopted for distinguishable particles have been formulated to overcome this issue [3,4]. In any case, these alternative methods remain technically awkward and unsuited to quantify entanglement under general conditions of scalability and wave function overlap. The use of new notions to discuss quantum entanglement for identical particles looks surprising, not less than the introduction of unobservable labels which is in contrast with the quantum mechanical requirement that the state of any physical system is uni-vocally described by a complete set of commuting observables. So far, there has not been general agreement even whether the entanglement between two identical particles in the same site may exist [3, 11, 12]. The characterization of quantum entanglement for identical particles has thus remained problematic, jeopardizing the general understanding and exploitation of composite systems.

In our recent work [13], we provide a straightforward description of entanglement in systems of identical particles, based on simple physical concepts, which unambiguously answers the general question: when and at which degree the identity of quantum particles plays a physical role in determining the entanglement among the particles? This is achieved by introducing a novel approach for identical particles without resorting to fictitious labels, differently from the usual textbook practice. The core of this approach is that the state of several identical particles must be considered a whole entity while the transition probability amplitude between two of such states is expressible in terms of single-particle amplitudes by applying the basic quantum-mechanical superposition principle with no which-way information to alternative paths. Our approach enables the determination of entanglement for both bosons and fermions by the same notions usually adopted in entanglement theory for distinguishable particles, such as the von Neumann entropy of the reduced state. The latter is obtained through the partial trace defined by local single-particle measurements.

Figure 2: Panel A. Entanglement as a function of system parameters for a fixed degree of spatial overlap for bosons (blue dotted line) and fermions (orange dashed line), compared to the corresponding entanglement of nonidentical particles (red solid line). Panel B. Density plot of bosonic entanglement as a function of both relative phase in the system state and degree of spatial overlap.

We have analyzed a system of two identical qubits (two-level systems) with orthogonal internal states (opposite pseudospins). The qubits are supposed to have wave functions (spatial modes) which can overlap at an arbitrary extent. A simple system which realizes this condition is that of the asymmetric double-well configuration illustrated in Fig. 1. When the two particles partially overlap in a spatial region where local single-particle measurements can be done, entanglement depends on their overlap and an ordering emerges for different particle types, fermions or bosons (Fig. 2). Moreover, identical particles are found to be at least as entangled as non-identical ones placed in the same quantum state.

This result suggests that identical particles may be more efficient than distinguishable ones for entanglement-based quantum information tasks. The main findings of this analysis can be summarized as: (i) an absolute degree of entanglement for identical particles, independent of local measurements, can be assigned only when the particles are spatially separated or in the same site; (ii) the act of bringing identical particles into overlapping spatial modes creates an “entangling gate” whose effectiveness depends on the amount of overlap. Our results finally show that a natural creation of maximally entangled states is possible just by moving two identical particles with opposing pseudospin states into the same site, supplying theoretical support to recent observations in an experiment with ultracold atoms transported in an optical tweezer [14]. This gives a definitive positive answer whether identical particles in the same site can be entangled.

Our approach contributes, from a fundamental point of view, to clarify the relation between quantum entanglement and identity of particles. It remarkably allows the quantitative study of entanglement under completely general conditions of overlap and scalability, motivating studies on correlations other than entanglement [15] in the context of identical particle systems. Moreover, our study paves the way to interpret experiments which use quantum correlations in relevant scenarios where identical particles can overlap.

[1] Luigi Amico, Rosario Fazio, Andreas Osterloh, Vlatko Vedral, “Entanglement in many-body systems”, Review of Modern Physics, 80, 517 (2008). Abstract.
[2] Ryszard Horodecki, Paweł Horodecki, Michał Horodecki, Karol Horodecki, “Quantum entanglement”, Review of Modern Physics, 81, 865 (2009). Abstract.
[3] 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). Full Text.
[4] F. Benatti, R. Floreanini, K. Titimbo, “Entanglement of identical particles”, Open Systems & Information Dynamics, 21, 1440003 (2014). Abstract.
[5] Claude Cohen-Tannoudji, Bernard Diu, Franck Laloë, “Quantum mechanics. Vol. 2” (Willey-VCH, Paris, France, 2005).
[6] Asher Peres, “Quantum Theory: Concepts and Methods” (Kluwer Academic,1995).
[7] Michael H. Kolodrubetz, Jason R. Petta, “Coherent holes in a semiconductor quantum dot”, Science 325, 42 (2009). Abstract.
[8] Z.B. Tan, D. Cox, T. Nieminen, P. Lähteenmäki, D. Golubev, G.B. Lesovik, P.J. Hakonen, “Cooper pair splitting by means of graphene quantum dots”, Physical Review Letters, 114, 096602 (2015). Abstract.
[9] Immanuel Bloch, Jean Dalibard, Wilhelm Zwerger, “Many-body physics with ultracold gases”, Review of Modern Physics, 80, 885 (2008). Abstract.
[10] Marco Anderlini, Patricia J. Lee, Benjamin L. Brown, Jennifer Sebby-Strabley, William D. Phillips, J.V. Porto, “Controlled ex-change interaction between pairs of neutral atoms in an optical lattice”, Nature, 448, 452 (2007). Abstract.
[11] GianCarlo Ghirardi, Luca Marinatto, Tullio Weber, “Entanglement and properties of composite quantum sys-tems: a conceptual and mathematical analysis”, Journal of Statistical Physics, 108, 49 (2002). Abstract.
[12] N. Killoran, M. Cramer, M. B. Plenio, “Extracting entanglement from identical particles”, Physical Review Letters, 112, 150501 (2014). Abstract.
[13] Rosario Lo Franco, Giuseppe Compagno, “Quantum entanglement of identical particles by standard information-theoretic notions”, Scientific Reports, 6, 20603 (2016). Full Text.
[14] A.M. Kaufman, B.J. Lester, M. Foss-Feig, M.L. Wall, A.M. Rey,  C.A. Regal, “Entangling two transportable neutral atoms via local spin exchange”, Nature 527, 208 (2015). Abstract.
[15] Kavan Modi, Aharon Brodutch, Hugo Cable, Tomasz Paterek, Vlatko Vedral, “The classical-quantum boundary for corre-lations: Discord and related measures”, Review of Modern Physics, 84, 1655 (2012). Abstract.


Sunday, February 28, 2016

Polarized Light Modulates Light-Dependent Magnetic Compass Orientation in Birds

From Left to Right: Rachel Muheim, Sissel Sjöberg, Atticus Pinzon-Rodriguez

Authors: Rachel Muheim, Sissel Sjöberg, Atticus Pinzon-Rodriguez

Affiliation: Department of Biology, Lund University, Sweden.

Magnetic compass orientation of birds depends on polarization of light

A wide range of animals, including birds, use directional information from the Earth’s magnetic field for orientation and navigation [1]. The magnetic compass of birds is light dependent and suggested to be mediated by light-induced, biochemical reactions taking place in specialized photoreceptors [2,3]. The photopigment molecules form magnetically sensitive radical-pair intermediates upon light excitation. The ratio of the spin states of the radical pairs (i.e., singlet vs. triplet state) is affected by Earth-strength magnetic fields, which thereby alters the response of the photopigments to light. In birds, such magneto-sensitive photoreceptors have been proposed to be arranged in an ordered array in the eye. Depending on their alignment to the magnetic field, they would show an increased or decreased sensitivity to light [2,3]. The animals would thereby perceive the magnetic field as a magnetic modulation pattern centered on the magnetic field lines, either superimposed on the visual field or mediated by a separate channel [4]. Cryptochromes have been proposed as putative candidate receptor molecules and found to be expressed in the retinas of birds exhibiting magnetic orientation behavior [2,5–7].

Hitherto, the majority of biophysical models on magnetic field effects on radical pairs have assumed that the light activating the magnetoreceptor molecules is non-directional and unpolarized, and that light absorption is isotropic. Yet, natural skylight enters the avian retina unidirectionally, through the cornea and the lens, and is often partially polarized. Also, the putative magnetoreceptor molecules, the cryptochromes, absorb light anisotropically, i.e., they preferentially absorb light of a specific direction and polarization. This implies that the light-dependent magnetic compass is intrinsically polarization sensitive [8,9].

Zebra Finch Bird

We developed a behavioural training assay to test putative interactions between the avian magnetic compass and polarized light. Thereby, we trained zebra finches to magnetic and/or overhead polarized light cues in a 4-arm “plus” maze to find a food reward with the help of their magnetic compass [10]. We found that overhead polarized light affected the birds’ ability to use their magnetic compass. The birds were only able to reliably find the food reward when the polarized light was aligned parallel to the magnetic field, but not when it was aligned perpendicular to the magnetic field [10]. We found this effect when using both 100% and 50% polarized light.
4-arm “plus” maze.

Our findings demonstrate that the magnetic compass of birds, and likely other animals, is polarization sensitive, which is a fundamentally new property of the light-dependent magnetic compass. Thus, the primary magnetoreceptor is photo- and polarization selective, as recently suggested by biophysical models [9]. The magnetic compass thus seems to be based on light-induced rotational order, thereby relaxing the requirement for an intrinsic rotational order of the receptor molecules (as long as rotational motion is restricted). The putative cryptochrome magnetoreceptors may therefore be distributed in any, also non-randomly oriented, cells in the avian retina [9]. Similar effects are expected to occur also in other organisms orienting with a light-dependent magnetic compass based on radical-pair reactions. Our findings thereby add a new dimension to the understanding of how not only birds, but animals in general, perceive the Earth’s magnetic field.

It remains to be shown to what degree birds in nature are affected by different alignments of polarized light and the Earth’s magnetic field. It could be a mechanism to enhance the magnetic field around sunrise and sunset, when polarized light is aligned roughly parallel to the magnetic field and when many migratory songbirds are believed to determine their departure direction and calibrate the different compasses with each other for the upcoming night’s flight. During midday, when polarized light and the magnetic field are aligned roughly perpendicular to each other, the magnetic field would be less prominent, thus would be less likely to interfere with visual tasks like foraging and predator detection [10].

[1] Roswitha Wiltschko, Wolfgang Wiltschko, "Magnetic Orientation in Animals" (Springer, 1995).
[2] Thorsten Ritz, Salih Adem, Klaus Schulten, "A model for photoreceptor-based magnetoreception in birds", Biophysics Journal, 78, 707–718 (2000). Article.
[3] Christopher T. Rodgers, P. J. Hore, "Chemical magnetoreception in birds: The radical pair mechanism", Proceedings of the National Academy of Sciences, 106, 353–360 (2009). Abstract.
[4] Ilia A. Solov'yov, Henrik Mouritsen, Klaus Schulten, "Acuity of a cryptochrome and vision-based magnetoreception system in birds", Biophysics Journal, 99, 40–49 (2010). Article.
[5] Miriam Liedvoge, Henrik Mouritsen, "Cryptochromes—a potential magnetoreceptor: what do we know and what do we want to know?" Journal of Royal Society Interface, 7, S147 –S162 (2010). Abstract.
[6] Christine Nießner, Susanne Denzau, Julia Christina Gross, Leo Peichl, Hans-Joachim Bischof, Gerta Fleissner, Wolfgang Wiltschko, Roswitha Wiltschko, "Avian ultraviolet/violet cones identified as probable magnetoreceptors", PLOS ONE, 6, 0020091 (2011). Abstract.
[7] Kiminori Maeda, Alexander J. Robinson, Kevin B. Henbest, Hannah J. Hogben, Till Biskup, Margaret Ahmad, Erik Schleicher, Stefan Weber, Christiane R. Timmel, P.J. Hore, "Magnetically sensitive light-induced reactions in cryptochrome are consistent with its proposed role as a magnetoreceptor", Proceedings of the National Academy of Sciences, 109, 4774–4779 (2012). Abstract.
[8] Rachel Muheim,  "Behavioural and physiological mechanisms of polarized light sensitivity in birds", Philosophical Transactions of the Royal Society B : Biological Sciences, 366, 763 –771 (2011). Abstract.
[9] Jason C.S. Lau, Christopher T. Rodgers, P.J. Hore, "Compass magnetoreception in birds arising from photo-induced radical pairs in rotationally disordered cryptochromes", Journal of Royal Society Interface, 9, 3329–3337 (2012). Abstract.
[10] Rachel Muheima, Sissel Sjöberga, Atticus Pinzon-Rodrigueza, "Polarized light modulates light-dependent magnetic compass orientation in birds", Proceedings of the National Academy of Sciences, 113, 1654-1659 (2016). Abstract.

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Sunday, February 21, 2016

Single-Photon Sources Combine High Purity, Indistinguishability and Efficiency All Together

From left to right: Chao-Yang Lu, Jian-Wei Pan, Sven Höfling and Christian Schneider.

Authors: Chao-Yang Lu1, Christian Schneider2, Sven Höfling1,2,3,  Jian-Wei Pan1

1CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, China.
2Technische Physik, Physikalisches Institat and Wilhelm Conrad Rontgen-Center for Complex Material Systems, Universitat Wurzburg, Germany.
3SUPA, School of Physics and Astronomy, University of St. Andrews, UK.

One-sentence summary: A single-photon source has been demonstrated which, for the first time, combines the features of high efficiency and near-perfect levels of purity and indistinguishabilty, opening the way to scalable multi-photon experiments on a semiconductor chip.

Spontaneous parametric down conversion has served as an excellent workhorse for fundamental test of quantum mechanics, quantum teleportation and optical quantum computing [1]. In this nonlinear optics process, the emission of photon pairs is probabilistic (with a probability of p) and inevitably accompanied by higher-order emission events (on the order of p2), which strongly limit the scalability for optical quantum information processing. So far, up to eight-photon entanglement—created from four independent photon pairs—have been demonstrated [2].

Past 2Physics article by Chao-Yang Lu and/or Jian-Wei Pan :
March 22, 2015: "Quantum Teleportation of Multiple Properties of A Single Quantum Particle" by Chao-Yang Lu and Jian-Wei Pan
January 04, 2015: "Achieving 200 km of Measurement-device-independent Quantum Key Distribution with High Secure Key Rate" by Yan-Lin Tang, Hua-Lei Yin, Si-Jing Chen, Yang Liu, Wei-Jun Zhang, Xiao Jiang, Lu Zhang, Jian Wang, Li-Xing You, Jian-Yu Guan, Dong-Xu Yang, Zhen Wang, Hao Liang, Zhen Zhang, Nan Zhou, Xiongfeng Ma, Teng-Yun Chen, Qiang Zhang, Jian-Wei Pan
June 30, 2013: "Quantum Computer Runs The Most Practically Useful Quantum Algorithm" by Chao-Yang Lu and Jian-Wei Pan.

In an attempt to overcome this obstacle, increasing attention has turned to single quantum emitters, such as self-assembled semiconductor quantum dots (QD), trapped atoms or ions, single defects in diamond or monolayer, and single molecules. In the past two decades, although many previous proof-of-principle experiments have established photon antibunching — an unambiguous evidence for single-photon emission, a scalable extension to multiple photonic quantum bits remain elusive.

To be useful for multi-photon applications such as Boson sampling, a perfect single quantum emitters should fulfill the following wish list: (1) High quantum efficiency: The decay of excited states should predominantly result in an emitted photon. (2) Deterministic generation: Upon a pulsed excitation, the source should deterministically emit one photon in a push-button fashion. (3) High purity: The emission should have a vanishing multi-photon probability. (4) High indistinguishability: Individual photons emitted at different trials should be quantum mechanically identical to each other. (5) High collection efficiency: The radiated photons should be extracted with a high efficiency to a single spatial mode.

Past 2Physics article by Sven Höfling :
May 17, 2015: "A Current Out Of Fluctuations" by Pierre Pfeffer, Fabian Hartmann, Sven Höfling, Martin Kamp, Lukas Worschech.

Among the discovered single quantum emitters so far, QDs have the highest quantum efficiency in solid state and narrowest linewidth at cryogenic temperature, and thus are promising as deterministic single-photon emitters. However, despite the extensive efforts, simultaneously fulfilling all the five criteria in the wish list proved challenging. Most previous experiments either relied on non-resonant excitation of a QD-microcavity that degraded the photon purity and indistinguishability [3,4], or used resonant excitation of a QD in a planar cavity that limited the extraction efficiency [5].
Figure 1: (a) Scanning electron microscopy image of a typical QD micropillar. (b) Numerical simulation of the photon emission from the QD-micropillar. (c) The photons collected into the first lens per pulse versus single-photon purity versus pump power.

Recently, the USTC-Wurzburg joint team exploited s-shell pulsed resonant excitation of a Purcell-enhanced QD-micropillar to deterministically generate resonance fluorescence single photons [6] which for the first time combines all the features in the wish list. The experiments were performed on an InAs/GaAs QD embedded inside a 2.5 micron diameter micropillar cavity (see Fig.1a) with a quality factor of 6124 and a Purcell factor of 6.3. Great efforts are made to find a single perfect QD at a sweet point where at 7.8 K the QD is to spatially coupled and spectrally resonant to the micropillar. At pi pulse, we detect 3.7 million single photon counts per second. The overall system efficiency is 4.6%. After correcting for detection efficiency and optical loss, we estimate that 66% of the generated single photons are collected into the first objective lens. Figure 1c summarizes the combined performance of the efficiency and single-photon purity as a function of pump power. It should be noted that the high generation and extraction efficiency are obtained with little compromise of the single-photon purity (g2(0) ≤ 0.009).

The overall system efficiency 4.6% — the highest reported in QDs — can be improved using techniques such as orthogonal excitation and detection of RF, near-unity-efficiency superconducting nanowire single-photon detection, and antireflection coatings of the optical elements. At this stage already, the performance of the single-photon source is already about ten time brighter than the triggered single-photon source used in eight-photon entanglement, but requires a pump power that is 7 orders of magnitude lower.
Figure 2: Quantum interference between two single photons separated by ~13 ns where the photon polarization set at cross (a) and parallel (b). A zoom-in near the zero time delay is shown in (c).

Another crucial demand is that the photons should possess a high degree of indistinguishability. We note that the pulsed resonant excitation is more critically needed for QDs with large Purcell factors where the reduced radiative lifetime approaches the time jitter. The single photons' indistinguishability is tested using two-photon Hong-Ou-Mandel interference. Figure 2a and 2b show histograms of normalized two-photon counts for orthogonal and parallel polarization at an emission time separation of ~13 ns, respectively. An almost vanishing zero-delay peak is observed for two photons with identical polarization (see Fig. 2c for a zoom-in). We obtain a degrees of indistinguishability to be 0.978.

Such a single-photon source can be readily used to perform multi-photon experiments on a solid-state platform. Immediate applications include implementation of Boson sampling [7] — an intermediate quantum computation where it is estimated that with 20-30 single photons one can demonstrate complex tasks that is difficult for classical computers. In addition to the photonic applications, the high-efficiency fluorescence extraction would also allow a fast high-fidelity single-shot readout of single electron spins, and efficiently entangling distant QD spins.

[1] Jian-Wei Pan, Zeng-Bing Chen, Chao-Yang Lu, Harald Weinfurter, Anton Zeilinger, Marek Żukowski, "Multi-photon entanglement and interferometry", Review of Modern Physics, 84, 777–838 (2012). Abstract.
[2] Xing-Can Yao, Tian-Xiong Wang, Ping Xu, He Lu, Ge-Sheng Pan, Xiao-Hui Bao, Cheng-Zhi Peng, Chao-Yang Lu, Yu-Ao Chen, Jian-Wei Pan, "Observation of eight-photon entanglement", Nature Photonics, 6, 225–228 (2012). Abstract.
[3] Charles Santori, David Fattal, Jelena Vučković, Glenn S. Solomon, Yoshihisa Yamamoto, "Indistinguishable photons from a single-photon device", Nature, 419, 594–597 (2002). Abstract.
[4] Stefan Strauf, Nick G. Stoltz, Matthew T. Rakher, Larry A. Coldren, Pierre M. Petroff, Dirk Bouwmeester, "High-frequency single-photon source with polarization control", Nature Photonics, 1, 704 (2007). Abstract.
[5] Yu-Ming He, Yu He, Yu-Jia Wei, Dian Wu, Mete Atatüre, Christian Schneider, Sven Höfling, Martin Kamp, Chao-Yang Lu, Jian-Wei Pan, "On-demand semiconductor single-photon source with near-unity indistinguishability", Nature Nanotechnology, 8, 213–217 (2013). Abstract.
[6] Xing Ding, Yu He, Z.-C. Duan, Niels Gregersen, M.-C. Chen, S. Unsleber, S. Maier, Christian Schneider, Martin Kamp, Sven Höfling, Chao-Yang Lu, Jian-Wei Pan, "On-Demand Single Photons with High Extraction Efficiency and Near-Unity Indistinguishability from a Resonantly Driven Quantum Dot in a Micropillar", Physical Review Letters, 116, 020401 (2016). Abstract.
[7] Scott Aaronson, Alex Arkhipov, The computational complexity of linear optics, Proceedings of the 43rd annual ACM symposium on Theory of computing, 2011, San Jose (ACM, New York, 2011), p. 333. Full Article.

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Sunday, February 14, 2016

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])

[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.

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