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2Physics

2Physics Quote:
"Quantum mechanics tells us that matter can exhibit wave-like or particle-like behavior, depending on the circumstances. Perhaps the most exotic are collective matter waves known as Bose-Einstein condensates consisting of millions of atoms cooled to near absolute zero temperature, where the atoms act in unison and behave as if they had a common purpose. These Bose-Einstein condensates are matter-wave solitons when the interactions between atoms in the condensate are attractive, and when they are confined in a one-dimensional guide."
-- Jason H.V. Nguyen, Paul Dyke, De Luo, Boris A. Malomed, Randall G. Hulet
(Read Full Article "Collisions of Matter-Wave Solitons" )

Sunday, January 25, 2015

Sound Velocity Bound and Neutron Stars

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

Authors: Paulo Bedaque1, Andrew W. Steiner2,3,4 

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

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

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

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

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

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

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

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

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Sunday, January 18, 2015

Novel Electromagnetic Cavities: Bound States in the Continuum

Thomas Lepetit (left) and Boubacar Kanté (right)

Authors: Thomas Lepetit and Boubacar Kanté 

Affiliation: Department of Electrical and Computer Engineering, University of California San Diego, USA. 

In the last 10 years, an intense research effort has been devoted to bringing all-optical signal generation and processing on chip to realize true photonic integrated circuits (PICs). PICs are at their core made of waveguides, which transfer signals to different devices on the circuit, and cavities, which process signals for different functionalities [1]. First, linear devices such as couplers, splitters, and add-drop filters were developed and, more recently, nonlinear devices such as frequency combs, nanolasers, and optical rams have been demonstrated [2-4]. Overall, progress has resulted in devices with increased functionalities that work at lower power and are more compact.

Cavities are an essential building block of PICs because they provide enhanced light-matter interaction. Currently, the most mature technology is based on a silicon on insulator platform and ring resonators. Typically, these dielectric resonators are several microns in diameter [5]. However, due to the difficulty of integration with much smaller electronic components, other technologies such as plasmonics have started to be investigated. One of the main advantages of plasmonic devices, which are made of noble metals such as gold and silver, is that their size is not limited by the wavelength. For example, plasmonic ring resonators of only several hundred nanometers in diameter have been demonstrated [6]. Generally, cavities are characterized by their quality factor Q, which is a measure of their capacity to store signals for a long time. At present, dielectric cavities have reached quality factors of 106, which are only limited by radiation losses coming from sidewall roughness, but typically have a footprint of 80 μm2. In contrast, plasmonic cavities can have a footprint as low as 1.25 μm2 but their quality factors are usually below 102, being limited by thermal losses coming from conduction electrons. Therefore, there is a need for novel cavity designs that can simultaneously achieve high quality factors and low footprints.
Figure 1: Cross-section of the electric field magnitude for the coupled resonators system (Half of it). Resonator 1, whose inner radius is zero, is on top and resonator 2, with a non-zero inner radius, is at the bottom. The symmetry plane on the right of each plot denotes the symmetry plane of interest. Odd modes are mostly confined in resonator 1 and even modes mostly in resonator 2.

Recently, we have demonstrated the possibility of making electromagnetic cavities using a different concept, namely bound states in the continuum (BICs) [7]. BICs were first proposed in 1929 in the context of quantum mechanics by Von Neumann and Wigner [8]. They surprisingly showed that bound states can exist above the continuum threshold, i.e., there are states that do not decay even in the presence of open decay channels. However, due to the theoretical nature of the first proposal, BICs did not become fully appreciated until 1985 when Friedrich and Wintgen showed that they could be interpreted as resulting from the interference of two distinct resonances [9]. In this picture, one resonance traps the other and thus one quality factor decreases while the other one tends to infinity. Since BICs are essentially a wave phenomenon they also appear in electromagnetics where they translate for lossless dielectrics into an infinite quality factor. As a proof of concept, we have designed and measured a BIC in the microwave range using a periodic metasurface [10-11].

BICs are intrinsically sensitive to perturbations as they only exist at a single point in phase space. This is very useful for sensing applications but detrimental for most others. To obtain an extended BIC, we designed a system with two quasi-degenerate BICs. We achieved this by considering a unit cell with two resonators, a disk and a ring (see Figure 1). Odd modes of the disk resonator interfere and lead to one BIC and even modes of the ring resonator interfere and lead to another BIC. We use ceramic resonators of high-permittivity (εr=43±0.75) and they are thus only slightly coupled. Experimentally, to limit the fabrication dispersion inherent to a large array, we made the measurements in a rectangular metallic waveguide (X-band, 8.2-12.4 GHz). It is possible because such a guided setup is equivalent to an infinite array at oblique incidence as shown by image theory.
Figure 2: Modes of two dielectric resonators (εr=43) in a rectangular metallic waveguide (X-band). Both resonators are cylindrical (r=3.5 mm, h1=2.25 mm, h2=3.0 mm) and the second has a non-zero inner radius. a) Resonance frequencies vs. inner radius for even and odd modes. b) Quality factor vs. inner radius for even and odd modes for lossless and lossy resonators.

We explored phase space along a line, by varying the inner radius of the ring resonator, and showed the presence of two avoided resonance crossings (see Figure 2a), which are typical of BICs [12]. As a result, there is an extended region of phase space where the quality factor tends to infinity (see Figure 2b). BICs only serve to cancel radiation losses and in the presence of thermal losses these are the limiting factor. At present, this scheme is therefore practical only for dielectrics but it could be extended to plasmonics by introducing gain materials to achieve loss-compensation.

Beyond the fundamental interest on the limit of quality-factors given a certain volume, there is a sustained interest in reducing the footprint of many cavity-based devices for future PICs. Tailoring the optical potential further, for example by moving away from perfectly periodic structures [13], opens the possibility improving the field confinement and thus shrink devices. Our work is a first step in this promising direction.

References:
[1] L. A. Coldren, S. W. Corzine, and M. Mašanović, “Diode Lasers and Photonic Integrated Circuits”, 2nd edition, Wiley (2012).
[2] Fahmida Ferdous, Houxun Miao, Daniel E. Leaird, Kartik Srinivasan, Jian Wang, Lei Chen, Leo Tom Varghese, Andrew M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs”, Nature Photonics, 5, 770 (2011). Abstract.
[3] M. Khajavikhan, A. Simic, M. Katz, J. H. Lee, B. Slutsky, A. Mizrahi, V. Lomakin, Y. Fainman, “Thresholdless nanoscale coaxial lasers”, Nature 482, 204 (2012). Abstract.
[4] Eiichi Kuramochi, Kengo Nozaki, Akihiko Shinya, Koji Takeda, Tomonari Sato, Shinji Matsuo, Hideaki Taniyama, Hisashi Sumikura, Masaya Notomi, “Large-scale integration of wavelength-addressable all-optical memories on a photonic crystal chip”, Nature Photonics 8, 474 (2014). Abstract.
[5] W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, R. Baets, “Silicon microring resonators”, Laser Photonics Review 6, 47 (2012). Abstract.
[6] Hong-Son Chu, Yuriy Akimov, Ping Bai, Er-Ping Li, “Submicrometer radius and highly confined plasmonic ring resonator filters nased on hybrid metal-oxide-semiconductor waveguide”, Optics Letters, 37, 4564 (2012). Abstract.
[7] Thomas Lepetit, Boubacar Kanté, “Controlling multipolar radiation with symmetries for electromagnetic bound states in the continuum”, Physical Review B Rapid Communications, 90, 241103 (2014). Abstract.
[8] J. von Neumann and E. Wigner, “On unusual discrete eigenvalues”, Zeitschrift für Physik 30, 465 (1929).
[9] H. Friedrich and D. Wintgen, “Interfering resonances and bound states in the continuum”, Physical Review A, 32, 3231 (1985). Abstract.
[10] Boubacar Kanté, Jean-Michel Lourtioz, André de Lustrac, “Infrared metafilms on a dielectric substrate”, Physical Review B, 80, 205120 (2009). Abstract.
[11] Boubacar Kanté, André de Lustrac, Jean Michel Lourtioz, “In-plane coupling and field enhancement in infrared metamaterial surfaces”, Physical Review B, 80, 035108 (2009). Abstract.
[12] Chia Wei Hsu, Bo Zhen, Jeongwon Lee, Song-Liang Chua, Steven G. Johnson, John D. Joannopoulos, Marin Soljačić, “Observation of trapped light within the radiation continuum”, Nature, 499, 188 (2013). Abstract.
[13] Yi Yang, Chao Peng, Yong Liang, Zhengbin Li, Susumu Noda, “Analytical perspective for Bound States in the Continuum in Photonic Crystal Slabs”, Physical Review Letters, 113, 037401 (2014). Abstract.

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Sunday, January 04, 2015

Achieving 200 km of Measurement-device-independent Quantum Key Distribution with High Secure Key Rate

[Left to Right] Hualei Yin, Tengyun Chen, Yanlin Tang.

Authors: Yan-Lin Tang1,2, Hua-Lei Yin1,2, Si-Jing Chen3, Yang Liu1,2, Wei-Jun Zhang3, Xiao Jiang1,2, Lu Zhang3, Jian Wang1,2, Li-Xing You3, Jian-Yu Guan1,2, Dong-Xu Yang1,2, Zhen Wang3, Hao Liang1,2, Zhen Zhang2,4, Nan Zhou1,2, Xiongfeng Ma2,4, Teng-Yun Chen1,2, Qiang Zhang1,2, Jian-Wei Pan1,2

Affiliation:
1National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, Shanghai Branch, University of Science and Technology of China, Hefei, China,
2CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, Shanghai Branch, University of Science and Technology of China, Hefei, China,
3State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai, China,
4Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, China.

 Information security is a long-standing problem in history. Nowadays, with the developing requirement of information transmission, the security becomes a much more sensitive problem. By leveraging the laws of quantum Mechanics, Quantum Key Distribution (QKD) [1] can provide a solution for information-theoretical security. As the most practical application of quantum information technology, it is under rapid development in both theoretical and experimental aspects. Besides the standard BB84 protocol, various protocols are proposed subsequently to adapt to different situations. Meanwhile, the QKD systems are successfully transformed from controlled laboratory environments to real-life implementations, and quite a few commercial QKD systems are available in the market up till now.

Past 2Physics article by Jian-Wei Pan :
June 30, 2013: "Quantum Computer Runs The Most Practically Useful Quantum Algorithm" by Chao-Yang Lu and Jian-Wei Pan.

Despite these tremendous developments, real-world QKD systems still suffer from various attacks [2-4] which explore the loopholes rooted in the deviations of practical implementations from the theoretical models in security proofs. Most of these attacks are targeting at the measurement devices. Among them, the first successful attack is the time-shift attack [3] which explores the loophole of time-dependent efficiency mismatch of two detectors. The most powerful kind of attacks is the detector-blinding attack [4], which fools the detector to work in the unwanted linear mode and forces them to act according to Eve’s will. Although certain countermeasures are provided to close some specific side channels, there might still be some side channels which are hard to estimate and will cause potential threats. So we are looking for an effective solution to close these loopholes once and for all.

Fortunately, Measurement-Device-Independent Quantum Key Distribution (MDIQKD) was invented by H-.K-. Lo in 2012 [5] to remove all side channels from the most vulnerable measurement unit. This protocol is inspired by the time-reversed EPR protocol [6], and it does not rely on any measurement assumption and can thus close all the measurement loopholes once and for all. Since its invention, it has attracted worldwide attention, and has been successfully demonstrated based on various MDIQKD systems, including polarization encoding system [7,8] and time-bin phase-encoding system [9,10]. In view of the performance, these previous MDIQKD demonstrations have limitations as well, such as short distance and a poor key rate (the best is 0.1 bps@50km [10]). This is so because the critical element of MDIQKD protocol is the Bell-state measurement, which requires both perfect interference of two independent laser sources and efficient two-fold coincidence detection. It imposes severe technical challenges on the laser modulation, high-efficiency detection and system stabilization. Therefore, based on the previous results and the intrinsic requirements of MDIQKD, people might still wonder that this ingenious protocol is a fancy but impractical idea.

In this recent work published in Physical Review Letters [11] by our group, we have extended the MDIQKD secure distance to state-of-the-art 200 km, comparable with the limit of regular decoy-state BB84 protocol. The secure key rate is almost three orders of magnitude higher than the previous results of MDIQKD demonstrations. These results are achieved with a fully-automatic highly-stable 75 MHz system and high-efficiency superconducting single photon detectors (SNSPDs), as shown in Fig. 1. We also employ an optimized decoy-state scheme and new post-processing method with a much lower failure probability than previous ones.
Fig.1: (a) Schematic layout of our MDIQKD setup. Alice's (Bob's) signal laser pulses (1550 nm) are modulated into three decoy-state intensities by AM1. An AMZI, AM2~4 and one PM are to encode qubits. Charlie's setup consists of a polarization stabilization system and a BSM system. The polarization stabilization system in each link includes an electric polarization controller (EPC), a polarization beam splitter (PBS) and an InGaAs/InP single-photon avalanche photodiode (SPAPD). The BSM system includes an interference BS and two SNSPDs. (b) Time calibration system. Two synchronization lasers (SynL, 1570 nm) are adopted, with the 500 kHz shared time reference generated from a crystal oscillator circuit (COC) and with the time delayed by a programmable delay chip (PDC). Alice (Bob) receives the SynL pulses with a photoelectric detector (PD) and then regenerates a system clock of 75 MHz. WDM: wavelength division multiplexer, ConSys: control system. (c) Phase stabilization system. Circ: circulator, PC: polarization controller, PS: phase shifter.

This is the first time we increase the repetition rate to 75 MHz, compared with 1MHz of our previous demonstration [10]. The repetition rate improvement owes to the laser source with good waveform, the high-speed electrical control system, and the superconducting single photon detector with a small time jitter of a few 10 ps [12]. In terms of high-speed laser modulation, we remark that the speed improvement for MDIQKD is not as easy as that for regular BB84 protocol, since the indistinguishability of two independent laser sources has some subtle requirements for laser modulation. Firstly, we should adopt direct laser modulation to ensure the phase is intrinsically randomized to avoid the unambiguous-state-discrimination attack [13]. The problem is that in a high-speed situation, the current mutation will induce severe overshoot, ringing and chirp inside the laser pulse. Especially, the chirp adds an extra phase at the tail of our laser pulse. Thus, we cut off the tail part by an amplitude modulator (AM), to optimize the laser interference and ensure the waveform indistinguishability. Secondly, regarding the vacuum state modulation (based on the vacuum+weak decoy state scheme), we should take the influence of the direct laser modulation into consideration, which is not a severe problem for regular BB84 protocol. We find that when we randomly modulate some laser pulses into vacuum state by not sending triggering signal to the laser (namely direct laser modulation), the interference visibility will decrease to a very bad level. This is because of the aperiodic triggering signals to the laser which introduce large temperature fluctuation and wavelength fluctuation. The wavelength fluctuation thus causes imperfect interference. To avoid this effect, instead of direct vacuum modulation, we adopt an alternative method of external vacuum modulation by AM. We utilize three AMs, within which only one is for decoy state encoding, and the other two are mainly used for qubit encoding and are also beneficial to decrease the vacuum intensity. Thus a high extinction ratio of the vacuum state of more than 10000 : 1 is achieved.

This is also the first time superconducting nanowire single-photon detectors (SNSPD), one of the best single photon detectors at near-infrared (NIR) wavelengths, is applied in an MDIQKD system. Since the BSM, the essence of MDIQKD, requires two-fold coincidence detection, the key rate is proportional to the square of detection efficiency. In our experiment, operated below 2.2 K with a Gifford-McMahon cryocooler, two SNSPDs with detection efficiencies of 40% and 46% largely improve the key rate. Besides, the low dark count rate of 10 Hz helps to achieve an enough signal-to-noise ratio even at 200 km distance. Besides the high detection efficiency and low dark count, there is another important property, small timing jitter of a few 10 ps, which is beneficial for QKD performance, especially the system timing jitter and repetition rate. We can expect an improvement of 1 GHz up to 10 GHz MDIQKD system adopting the SNSPD in the near future.

Another important element for achieving 200 km distance is the system stabilization. Since the 200 km situation will make the system stability difficult because of the severe fiber fluctuation, and make it even harder with weak feedback signals due to large fiber attenuation. Besides, since the detection rate is slower in 200 km, we need more time to accumulate enough data required by strict fluctuation analysis. In short, we need our system to work in a worse environment for a longer time. Faced with these problems, we build a fully-automatic feedback system without manual efforts to precisely calibrate and stabilize all the parameters, such as the time, spectrum, polarization and the phase reference. Although the whole feedback system is a challenge in engineering, it is critical to enable continuous running and will be a necessary component in practical MDIQKD system.
Fig.2: Bird's-eye view of the field-environment MDIQKD. Alice is placed in Animation Industry Park in Hefei (AIP), Bob in an office building (OB), and Charlie in the University of Science and Technology of China (USTC). Alice (Bob) is on the west (east) side of Charlie. AIP-USTC link is 25 km (7.9 dB), and OB-USTC link is 5 km (1.3 dB).

To further show the practical value of MDIQKD in an unstable environment, we have moved the system into installed fiber network and implemented a field test as shown in Fig. 2 [14]. Previously, an MDIQKD field test was attempted over an 18.6 km deployed fiber, however, a secure key was not actually generated since random modulated decoy state was not performed. In comparison, our field test strictly adopts the decoy-state scheme to guarantee the source security. With optimized decoy-state parameters and Chernoff bound in strict fluctuation analysis with tight failure probability of 2×10−9, we have achieved secure key rates of 67 bps (@50km in the laboratory for 130.0 hours) and 17 bps (@30km in the field test for 18.2 hours), shown in Fig.3, which are at least two orders of magnitude higher than previous results.
Fig. 3: Secure key rates of experiments in the laboratory and in the field test, as well as the simulation results. The four dots correspond to the experimental results with the fiber transmitting loss of 9.9 dB (50 km), 19.9 dB (100 km), 29.8 dB (150 km) and 39.6 dB (200 km). The solid curve shows the result calculated by simulating the vacuum+weak decoy state scheme with the experimental parameters. The dashed curve represents the optimal result with infinite number of decoy states. The square marks the field test result, which is 17 bps. Also shown are results from the previous demonstration for comparison.

These technological advances in our work constitute a critical ingredient for quantum repeater [15], the core resource for long distance quantum communication. Besides, the MDIQKD protocol has an intrinsic property which is desirable for constructing quantum network [16] with the star-type structure. We can place the expensive detection system in the server node to perform the BSM operation, and all the users can share this system. Furthermore, the techniques of stable BSM we developed have many other applications, such as quantum teleportation [17] and quantum fingerprinting [18].

References:
[1] Charles H. Bennett and Gilles Brassard, "Quantum cryptography: Public key distribution and coin tossing”, in Proceedings of IEEE International Conference on Computers, Systems, and Signal Processing (Bangalore, India, 1984), pp. 175–179. Full Article.
[2] Chi-Hang Fred Fung, Bing Qi, Kiyoshi Tamaki, Hoi-Kwong Lo, “Phase-remapping attack in practical quantum-key-distribution systems”. Physical Review A, 75, 032314 (2007). Abstract.
[3] B. Qi, C.-H. F. Fung, H.-K. Lo, and X. Ma, “Time-shift attack in practical quantum cryptosystems”, Quantum Information & Computation, 7, 073 (2007).
[4] Lars Lydersen, Carlos Wiechers, Christoffer Wittmann, Dominique Elser, Johannes Skaar, Vadim Makarov, “Hacking commercial quantum cryptography systems by tailored bright illumination”, Nature Photonics, 4, 686 (2010). Abstract.
[5] Hoi-Kwong Lo, Marcos Curty, Bing Qi, “Measurement-Device-Independent Quantum Key Distribution”, Physical Review Letters, 108, 130503 (2012). Abstract.
[6] Eli Biham, Bruno Huttner, Tal Mor, “Quantum cryptographic network based on quantum memories”. Physical Review A, 54, 2651 (1996). Abstract.
[7] Zhiyuan Tang, Zhongfa Liao, Feihu Xu, Bing Qi, Li Qian, Hoi-Kwong Lo, “Experimental Demonstration of Polarization Encoding Measurement-Device-Independent Quantum Key Distribution”, Physical Review Letters, 112, 190503 (2014). Abstract.
[8] T. Ferreira da Silva, D. Vitoreti, G. B. Xavier, G. C. do Amaral, G. P. Temporão, J. P. von der Weid, “Proof-of-principle demonstration of measurement-device-independent quantum key distribution using polarization qubits”, Physical Review A, 88, 052303 (2013). Abstract.
[9] A. Rubenok, J. A. Slater, P. Chan, I. Lucio-Martinez, W. Tittel, “Real-World Two-Photon Interference and Proof-of-Principle Quantum Key Distribution Immune to Detector Attacks”, Physical Review Letters, 111, 130501 (2013). Abstract.
[10] Yang Liu, Teng-Yun Chen, Liu-Jun Wang, Hao Liang, Guo-Liang Shentu, Jian Wang, Ke Cui, Hua-Lei Yin, Nai-Le Liu, Li Li, Xiongfeng Ma, Jason S. Pelc, M. M. Fejer, Cheng-Zhi Peng, Qiang Zhang, Jian-Wei Pan, “Experimental Measurement-Device-Independent Quantum Key Distribution”. Physical Review Letters, 111, 130502 (2013). Abstract.
[11] 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, “Measurement-device-independent quantum key distribution over 200 km”. Physical Review Letters, 113, 190501 (2014). Abstract.
[12] Xiaoyan Yang, Hao Li, Weijun Zhang, Lixing You, Lu Zhang, Xiaoyu Liu, Zhen Wang, Wei Peng, Xiaoming Xie, Mianheng Jiang, “Superconducting nanowire single photon detector with on-chip bandpass filter”, Optics Express, 22, 16267 (2014). Abstract.
[13] Yan-Lin Tang, Hua-Lei Yin, Xiongfeng Ma, Chi-Hang Fred Fung, Yang Liu, Hai-Lin Yong, Teng-Yun Chen, Cheng-Zhi Peng, Zeng-Bing Chen, Jian-Wei Pan, “Source attack of decoy-state quantum key distribution using phase information”, Physical Review A, 88, 022308 (2013). Abstract.
[14] 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, “Field Test of Measurement-Device-Independent Quantum Key Distribution”, arXiv:1408.2330 [quant-ph] (2014).
[15] H.-J. Briegel, W. Dür, J. I. Cirac, P. Zoller, “Quantum Repeaters: The Role of Imperfect Local Operations in Quantum Communication”, Physical Review Letters, 81, 5932 (1998). Abstract.
[16] Jane Qiu, “Quantum communications leap out of the lab”, Nature, 508, 441 (2014). Article.
[17] Charles H. Bennett, Gilles Brassard, Claude Crépeau, Richard Jozsa, Asher Peres, William K. Wootters, “Teleporting an unknown quantum state via dual classic and Einstein-Podolsky-Rosen channels”, Physical Review Letters, 70, 1895 (1993). Abstract.
[18] Harry Buhrman, Richard Cleve, John Watrous, Ronald de Wolf, “Quantum Fingerprinting”, Physical Review Letters, 87, 167902 (2001). Abstract.

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Sunday, December 21, 2014

Cosmological Data Prefer An Interacting Vacuum Energy

(From Left to Right) Najla Said, Valentina Salvatelli, Marco Bruni, David Wands.

Authors: Najla Said1, Valentina Salvatelli1,2, Marco Bruni3, David Wands3

Affiliation:
1Physics Department and INFN, Universita di Roma "La Sapienza", Rome, Italy
2Aix-Marseille Universite, Centre de Physique Theorique UMR 7332, France 
3Institute of Cosmology and Gravitation, University of Portsmouth, UK.

Over recent years, a growing number of high precision observations of the primordial Universe and our local cosmic neighbourhood have established a standard cosmological model, called LCDM. In LCDM, the Universe is filled with a constant dark energy, or cosmological constant (Lambda) that is responsible for the present accelerated expansion. Besides dark energy, a similar density of cold dark matter (CDM) supports the growth of large-scale structures (galaxies and clusters of galaxies) in broad agreement with the observations.

A crucial dataset for cosmological research is the Cosmic Microwave Background (CMB). This faint thermal radiation, which fills the whole sky, is a relic of the primordial Universe; it has been fundamental in supporting the homogeneity and isotropy of the Universe and in determining its composition. At the beginning of this year the Planck satellite of the European Space Agency (ESA) released a new set of CMB observations at striking precision, tightly constraining the parameters of the standard model [1].

These primordial Universe observations can be combined with a series of local Universe observations, coming from a number of galaxy surveys (SDSS [2], WiggleZ [3] and others). With these measurements we can map the distribution of structures at different epochs and use these maps to study their evolution up until the present. In particular, spectroscopic galaxy surveys enable us to quantify the clustering of the large-scale structure by measuring the so-called Redshift-Space Distortions (RSD) [4].

Since the late 1990s, the LCDM model has provided a simple framework to consistently describe local and primordial observations, but the latest precise measurements suggest that we may need to review and possibly revise this standard model. The clustering of structures, appears to be weaker than the one inferred from CMB observations assuming the standard LCDM evolution [10]. A common extension to the LCDM model is to allow the dark energy to have a non-constant density that evolves with time, but this, on its own, does not appear to resolve the conflict between different datasets [11].

In our recent work we investigated how the growth of structure is affected by an interaction between dark energy and dark matter [5,6,7]. These two components are usually assumed to evolve independently, and indeed an interaction between the two is not favored if one looks only at CMB measurements, for which the simple LCDM model fits perfectly the observations. We used the formalism of the Interacting Vacuum models, as developed in [5].

Figure 1

Our idea was to study a time-dependent interaction, but without imposing a-priori a specific time dependence. We parametrized the interaction in a simple, linear way, and studied its value at different epochs using a binned function, as sketched in Figure 1. On the x-axis we show the redshift z (a measure of time, where z=0 is today and z>0 is the past), while on the y-axis we show the dimensionless coupling parameter qv. The purple line represents the binned model. The datasets we used for the analysis were the current CMB measurements from Planck and the RSD measurements from a number of surveys (refer to our Letter [8] for details).

The results we found suggested that an interaction at primordial epochs is not favored, but a zero coupling at recent times is excluded at 99% confidence level.

Starting from here we determined a best-fit model in which an interaction in the dark sector began around redshift z=1 (6 billion years ago) finding that, from a Bayesian point of view, this model is favored with respect to LCDM. This best-fit model is represented with the blue line in Figure 1.

We also compared our model to a cosmology with massive neutrinos [9], which is another extension of LCDM that has been proposed to solve the tension between primordial and local observations. In this case too we found that the observational evidence favors an interaction in the dark sector.

Figure 2

In Figure 2 we show the RSD dataset used in our work. On the x-axis we show the redshift z and on the y-axis the fσ8 value, a typical measure of the growth of structure. The grey line, representing the LCDM model, predicts a higher growth than that observed, while our late-time interaction model, the blue line, fits the data much better.

The latest observations thus not only confirm that dark matter decay into dark energy is allowed, but also suggests that this interaction is actually favored with respect to the standard LCDM model.

References:
[1] P. A. R. Ade et al., ``Planck 2013 results. XVI. Cosmological parameters'', Astronomy & Astrophysics, 571, A16 (2014). Abstract.
[2] Lauren Anderson et al., ``The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: Baryon Acoustic Oscillations in the Data Release 10 and 11 galaxy samples''. arXiv:1312.4877 [astro-ph.CO] (2014).
[3] Chris Blake, Sarah Brough, Matthew Colless, Carlos Contreras, Warrick Couch, Scott Croom, Tamara Davis, Michael J. Drinkwater, Karl Forster, David Gilbank, Mike Gladders, Karl Glazebrook, Ben Jelliffe, Russell J. Jurek, I-hui Li, Barry Madore, D. Christopher Martin, Kevin Pimbblet, Gregory B. Poole, Michael Pracy, Rob Sharp, Emily Wisnioski, David Woods, Ted K. Wyder, H. K. C. Yee, "The WiggleZ Dark Energy Survey: the growth rate of cosmic structure since redshift z=0.9", Monthly Notices of the  Royal Astronomical Society, 415, 2876 (2011). Full Article.
[4] Lado Samushia, Beth A. Reid, Martin White, Will J. Percival, Antonio J. Cuesta, Lucas Lombriser, Marc Manera, Robert C. Nichol, Donald P. Schneider, Dmitry Bizyaev, Howard Brewington, Elena Malanushenko, Viktor Malanushenko, Daniel Oravetz, Kaike Pan, Audrey Simmons, Alaina Shelden, Stephanie Snedden, Jeremy L. Tinker, Benjamin A. Weaver, Donald G. York, Gong-Bo Zhao, "The Clustering of Galaxies in the SDSS-III DR9 Baryon Oscillation Spectroscopic Survey: Testing Deviations from Lambda and General Relativity using anisotropic clustering of galaxies'', Monthly Notices of the  Royal Astronomical Society, 429, 1514 (2013). Abstract.
[5] David Wands, Josue De-Santiago, Yuting Wang, "Inhomogeneous vacuum energy", Classical and Quantum Gravity, 29, 145017 (2012). Abstract.
[6] Claudia Quercellini, Marco Bruni, Amedeo Balbi, Davide Pietrobon, "Late universe dynamics with scale-independent linear couplings in the dark sector". Physical Review D, 78, 063527 (2008). Abstract.
[7] Valentina Salvatelli, Andrea Marchini, Laura Lopez-Honorez, Olga Mena, "New constraints on Coupled Dark Energy from the Planck satellite experiment", Physical Review D, 88, 023531 (2013). Abstract.
[8] Valentina Salvatelli, Najla Said, Marco Bruni, Alessandro Melchiorri, David Wands, "Indications of a late-time interaction in the dark sector", Physical Review Letters, 113, 181301 (2014). Abstract.
[9] Richard A. Battye, Adam Moss, "Evidence for massive neutrinos from CMB and lensing observations'', Physical Review Letters, 112, 051303 (2014). Abstract.
[10] E. Macaulay, I. K. Wehus, H. K. Eriksen, "Lower growth rate from recent redshift space distortion measurements than expected from Planck". Physical Review Letters, 111, 161301 (2013). Abstract.
[11] Eduardo J. Ruiz, Dragan Huterer, "Banana Split: Testing the Dark Energy Consistency with Geometry and Growth". arXiv:1410.5832 [astro-ph.CO] (2014).

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posted by Quark @ 8:14 AM      links to this post


Sunday, December 14, 2014

Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor

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

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

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

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

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

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

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

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

Building upon previous proposal to realize Majorana modes in an array of magnetic nanoparticles [9], we proposed to use a chain of magnetic atoms coupled to a superconductor [10]. The key advantage of this platform is that the experimentally properties of this system can easily be studied using standard scanning tunneling microscopy (STM) technique. While ours and other follow-up initial proposals [11-16] consider specific orientation of the magnetic moments, the approach works also for ferromagnetic atomic chains as long as it is coupled to a superconductor with strong spin-orbit coupling (Fig. 1A) [17]. In this case, the large exchange interaction results in a band structure of the chains such that majority spin band is fully occupied while the Fermi level is in the minority spin bands. For example the electronic structure of a linear Iron (Fe) ferromagnetic atomic chain is shown in Fig. 1B. Considering only d-orbitals which are spin-polarized it is easy to show that many of the bandstructure degeneracies are lifted and that for large range of parameters, chemical potential and the exchange energy, such chains are in topologically non-trivial regime characterized by the odd number of crossing at the Fermi level (Fig 1C). When placed on the superconducting substrate with strong-spin orbit coupling the resulting superconductivity on the chain will necessarily be topological in nature resulting in zero energy Majorana bound states located at the chain ends.
Fig. 2: (A) Topograph of the Pb(110) surface after growth of Fe, showing Fe islands and chains indicated by white arrows and atomically clean terraces of Pb (regions with the same color) with size exceeding 1000 Å. (Lower-right inset) Anisotropic atomic structure of the Pb(110) surface (Upper-left insets) images of several atomic Fe chains and the islands from which they grow (scale bars, 50 Å). (B) Topography of the chain colorized by the conductance at H= ±1 T from low (dark blue) to high conductance (dark red). (C) Difference between conductance on and off the chain showing hysteresis behavior. (D and E) Atomic structure of the zigzag chain, as calculated using density functional theory. The Fe chain structure that has the lowest energy in the calculations matches the structural features in the STM measurements, aB is the Bohr radius.

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

We also observed the variation of the spin-polarized STM signal along the chain which is likely due to its electronic and structural properties. Indeed, both topographic features and periodicity of signal variation could be very well explained by our theory collaborators who performed density functional theory modeling. Their calculations suggested that our chains have zig-zag structure which explains both topographic information obtained using STM and matches well with our spin-polarized measurements (Fig. 2D and 2E).
Fig. 3: (A) STM spectra measured on the atomic chain at locations corresponding to those indicated in (B) and (C). For clarity, the spectra are offset by 100 nS. The red spectrum shows the zero-bias peak at one end of the chain. The gray trace measured on the Pb substrate can be fitted using thermally broadened BCS superconducting density of states (dashed gray line, fit parameters Δs = 1.36 meV, T = 1.45 K). (B and C) Zoom-in topography of the upper (B) and lower end (C) of the chain and corresponding locations for spectra marked (1 to 7). Scale bars, 25 Å. (D and E) Spectra measured at marked locations, as in (B) and (C). (F) Spatial and energy-resolved conductance maps of another atomic chain close to its end, which shows similar features in point spectra as in (A). The conductance map at zero bias (middle panel) shows increased conductance close to the end of the chain. Scale bar, 10 Å.

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

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

References: 
[1] Ettore Majorana, "Teoria simmetrica dell’elettrone e del positrone", Il Nuovo Cimento, 171 (1937). Abstract.
[2] A. Yu. Kitaev, "Unpaired Majorana fermions in quantum wires". Physics Uspekhi, 44, 131 (2001). Full Article.
[3] A. Yu. Kitaev, "Fault-tolerant quantum computation by anyons". Annals of Physics. 303, 2 (2003). Abstract.
[4] Jason Alicea, Yuval Oreg, Gil Refael, Felix von Oppen, Matthew P. A. Fisher, "Non-Abelian statistics and topological quantum information processing in 1D wire networks". Nature Physics, 7, 412 (2011). Abstract.
[5] Yuval Oreg, Gil Refael, and Felix von Oppen, "Helical Liquids and Majorana Bound States in Quantum Wires", Physical Review Letters, 105, 177002 (2010). Abstract.
[6] Roman M. Lutchyn, Jay D. Sau, S. Das Sarma, "Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures". Physical Review Letters, 105, 077001 (2010). Abstract.
[7] V. Mourik, K. Zuo, S.M. Frolov, S.R. Plissard, E.P.A.M. Bakkers, L.P. Kouwenhoven, "Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices", Science 336, 1003 (2012). Abstract. 2Physics Article.
[8] Anindya Das, Yuval Ronen, Yonatan Most, Yuval Oreg, Moty Heiblum, Hadas Shtrikman, "Zero-bias peaks and splitting in an Al-InAs nanowire topological superconductor as a signature of Majorana fermions". Nature Physics, 8, 887 (2012). Abstract. 2Physics Article.
[9] T. P. Choy, J. M. Edge, A. R. Akhmerov, C. W. J. Beenakker, "Majorana fermions emerging from magnetic nanoparticles on a superconductor without spin-orbit coupling". Physical Review B, 84, 195442 (2011). Abstract.
[10] S. Nadj-Perge, I. K. Drozdov, B. A. Bernevig, Ali Yazdani, "Proposal for realizing Majorana fermions in chains of magnetic atoms on a superconductor". Physical Review B, 88, 020407 (2013). Abstract.
[11] Falko Pientka, Leonid I. Glazman, Felix von Oppen, "Topological superconducting phase in helical Shiba chains". Physical Review B, 88, 155420 (2013). Abstract.
[12] Jelena Klinovaja, Peter Stano, Ali Yazdani, Daniel Loss, "Topological Superconductivity and Majorana Fermions in RKKY Systems". Physical Review Letters, 111, 186805 (2013). Abstract.
[13] Bernd Braunecker, Pascal Simon, "Interplay between Classical Magnetic Moments and Superconductivity in Quantum One-Dimensional Conductors: Toward a Self-Sustained Topological Majorana Phase". Physical Review Letters, 111, 147202 (2013). Abstract.
[14] M. M. Vazifeh, M. Franz, "Self-Organized Topological State with Majorana Fermions". Physical Review Letters, 111, 206802 (2013). Abstract.
[15] Sho Nakosai, Yukio Tanaka, Naoto Nagaosa, "Two-dimensional superconducting states with magnetic moments on a conventional superconductor". Physical Review B, 88, 180503 (2013). Abstract.
[16] Younghyun Kim, Meng Cheng, Bela Bauer, Roman M. Lutchyn, S. Das Sarma, "Helical order in one-dimensional magnetic atom chains and possible emergence of Majorana bound states". Physical Review B, 90, 060401 (2014). Abstract.
[17] Stevan Nadj-Perge, Ilya K. Drozdov, Jian Li, Hua Chen, Sangjun Jeon, Jungpil Seo, Allan H. MacDonald, B. Andrei Bernevig, Ali Yazdani, "Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor". Science 346, 602-607 (2014). Abstract.
[18] Jian Li, Titus Neupert, B. Andrei Bernevig, Ali Yazdani, "Majorana zero modes on a necklace". arXiv:1404.4058 [cond-mat] (2014).

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posted by Quark @ 9:17 AM      links to this post