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2Physics

2Physics Quote:
"Stars with a mass of more than about 8 times the solar mass usually end in a supernova explosion. Before and during this explosion new elements, stable and radioactive, are formed by nuclear reactions and a large fraction of their mass is ejected with high velocities into the surrounding space. Most of the new elements are in the mass range until Fe, because there the nuclear binding energies are the largest. If such an explosion happens close to the sun it can be expected that part of the debris might enter the solar system and therefore should leave a signature on the planets and their moons." -- Thomas Faestermann, Gunther Korschinek (Read Full Article: "Recent Supernova Debris on the Moon" )

Sunday, January 22, 2017

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

Kathrin Altwegg 

Author: Kathrin Altwegg and the ROSINA Team 

Affiliation: Physikalisches Institut, University of Bern, Switzerland.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Sunday, January 15, 2017

On The Quest of Superconductivity at Room Temperature

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

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

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

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

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

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

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

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

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

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

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

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Sunday, January 08, 2017

Indications of an Influence of Solar Neutrinos on Beta Decays

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

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

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

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

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

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

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

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

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

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

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

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

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

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Sunday, December 18, 2016

A Compact Gravimeter Based On An Atom Chip

From Left to Right: Martina Gebbe, Sven Abend, Matthias Gersemann, Holger Ahlers, Hauke Müntinga; (top right) Claus Lämmerzahl, (bottom right] Ernst M. Rasel.

Authors: Sven Abend1, Martina Gebbe2, Matthias Gersemann1, Holger Ahlers1, Hauke Müntinga2, Enno Giese3,4, Naceur Gaaloul1, Christian Schubert1, Claus Lämmerzahl2, Wolfgang Ertmer1, Wolfgang P. Schleich3,5, Ernst M. Rasel1

Affiliation:
1Institut für Quantenoptik, Leibniz Universität Hannover, Germany,
2ZARM, Universität Bremen, Germany,
3Institut für Quantenphysik and Center for Integrated Quantum Science and Technology (IQST), Universität Ulm, Germany,
4Department of Physics and Max Planck Centre for Extreme and Quantum Photonics, University of Ottawa, Canada,
5Texas A&M University Institute for Advanced Study (TIAS), Institute for Quantum Science and Engineering (IQSE) and Department of Physics and Astronomy, Texas A&M University, College Station, Texas, USA,

Introduction to cold-atom gravimetry
The precise knowledge of gravity is important in the fields of geodesy, geophysics and metrology. Detecting small variations in the local gravitational force, for example, can provide information about the presence of mineral resources. Tectonic movements or volcanic activities can also be deduced by this method. Satellites allow the observation of the gravitational field of the whole planet yielding important parameters for climate studies such as sea-surface heights [1] or ice masses [2]. Moreover, gravity is a force that cannot be shielded and, thus, influences the measurement of other standard units.

Absolute classical gravimeters are based on tracing the free fall of macroscopic corner-cubes with laser interferometers, while the lab frame serves as inertial reference. Quantum inertial sensors operate similarly using freely falling atoms as test masses. They are based on the wave-particle duality stating that particles also have a wave nature and can therefore show diffraction and interference.

Prior to performing atom interferometry atoms have to be trapped and cooled close to absolute zero by a combination of magnetic fields and laser light. Room temperature atoms with velocities of hundreds of meters per second would almost immediately collide with the walls of the experimental chamber and leave no time to perform experiments. After release from the trap laser pulses direct the falling atoms along two different paths and let them recombine. The acceleration of free fall can then be read out from the interference pattern of the atomic wave functions.

Nowadays, commercially available quantum gravimeters feature an accuracy better than one part in 10⁸ of gravity [3,4] and are competitive to classical sensors. Their sensitivity could be improved by cooling the atoms further down until they reach an ultracold state of matter, called a Bose-Einstein condensate (BEC) where only a single quantum state is occupied. The size of a BEC is about 100 times smaller than typical millimeter-sized laser cooled clouds commonly used in atomic gravimeters. Such an ultracold cloud allows a more precise control of the atomic position and reduces the error due to spatially nonuniform laser pulse intensities.

In our paper [5] we have demonstrated an atom-chip fountain gravimeter, using a BEC source with an intrinsic sensitivity of one part in 107 of gravity, where all operations can be performed in a volume of less than a one centimeter cube.

Mach-Zehnder atom interferometer in free fall

In an atom interferometer beam splitting is based on the diffraction by an optical lattice generated by two counter-propagating laser beams. In our case, Bragg diffraction is employed, which can be described by the absorption and stimulated emission of a photon. During this process the atom receives an additional momentum kick. The duration and amplitude of the Bragg laser pulse determine the amount of atoms diffracted to another momentum state.

The Mach-Zehnder interferometer starts with a beam splitter pulse that gives a velocity kick with 50% probability resulting in an equal superposition of two atomic momentum states (see Figure 1(b)). After a free evolution time of T, the momentum states are inversed by a mirror pulse. At a time 2T a final pulse recombines the wave packets and an interferometer signal consisting of two output ports separated by a velocity difference is created. The atom number in each of these ports is detected via imaging with a CCD camera. An acceleration such as gravity leads to a path difference between the two interferometer arms and influences the population of the output ports. In principle, each atom participates independently in the interferometer. Large ensembles, however, are important to obtain detectable and statistically significant signals.

In such a free fall interferometer an important feature is the T square scaling of the phase shift, which directly links to the sensitivity. Hence, a gravitational sensor considerably benefits from an extension of the interferometer time. Unperturbed evolution times in the order of seconds can only be reached in very large devices [6], or on microgravity platforms [7]. In a compact, earth-bound device, however, the atom cloud can only fall a short distance, which limits T to the order of milliseconds.
Figure 1: (click on the image to view with higher resolution) Atom-chip-based gravimeter (a) and spacetime trajectories of an atom cloud in a Mach-Zehnder interferometer without (b) and with relaunch (c). Adapted from Reference [5]..

Measuring gravitation with a compact atom-chip setup
Figure 2: Centimeter-sized atom chip used for BEC generation.

BEC-based inertial sensors have usually been large, laboratory-sized experiments [9]. Our apparatus features a compact setup, provided amongst others by the use of a centimeter-wide atom chip [9,10], which allows a fast, robust and efficient generation of BECs (Figure 2). Inside a small vacuum chamber we repeatedly produce up to 15,000 condensed Rubidium-87 atoms at a temperature of 50nK [8, 11]. Each experimental cycle consisting of BEC generation and performing atom interferometry takes about 15 seconds.

The atom chip is not only used for the whole state preparation of the BEC but also acts as a reference mirror inside the chip gravimeter (see Figure 1(a)). It is oriented horizontally and retroreflects the light pulses coming from an upwards-pointing laser. The interferometer region extends about 1 cm below the atom chip. Since the atoms are freely falling along the optical lattice, its velocity has to be constantly increased in order to match the gravitational acceleration of the atoms. If lattice and atomic acceleration are identical, only one state entering the interferometer is detected at the output. This means, our interference signal, the normalized population assumes a minimum independent of the pulse interval T. Local gravity is than deduced from the optical lattice acceleration which can be measured very precisely.

Figure 3(a) shows interference signals in dependence of the lattice acceleration for pulse intervals of T=1,3 and 5ms in a dropped interferometer. The acceleration of free fall was determined to be g = (9.8134 ± 0.0006) m/s². After repeating the measurements with the maximal interrogation time T=5ms over 8h we achieved a relative precision of one part in 10⁵ of gravity (see Figure 3(b)).
Figure 3: (click on the image to view with higher resolution) Measuring gravitational acceleration in a single fall interferometer. (a) Normalized atom number in one output port of the MZI for T = 1, 3, 5 ms depending on the acceleration of the Bragg lattice. (b) Allan deviation of the acceleration improves with the square root (black line) of the integration time t reaching a precision of 1 part in 10⁵ of gravity after 8 hours. Source: Reference [5].

In order to improve the sensitivity of our interferometer we developed a simple and efficient fountain sequence illustrated in Figure 1(c). At the bottom of the detection zone the atoms are caught and tossed upwards with an optical lattice generated by the same laser light beams that are used for interferometry. This way, we are able to enhance the total free evolution time by a factor of three, without increasing the free-fall baseline of the experiment.

The interferometer starts directly after the relaunch and can be extended to T=25ms. Its intrinsic sensitivity equals one part in 10⁷ which represents a 20-fold increase in comparison to the simple fall setup. Due to the environmental conditions and the absence of any vibrational isolation we were not able to observe fringes any more. However, we did a statistical analysis of the data and determined a high interferometric contrast of 80%.

Conclusion and outlook

In conclusion, we demonstrated the first miniaturized atom-chip fountain gravimeter without and with relaunch. The new fountain scheme leads to extended interferometer times without changing the compact volume of a one centimeter cube. The sensor is currently limited by the large vibrations in our system, which we aim to suppress in the future.

The current sensitivity of 1 part in 10⁷ of gravity is about two orders of magnitude lower compared to state-of-the-art sensors. However, with an advanced apparatus [12], which produces 10⁵ atoms in a BEC per second, and small improvements in the measurement scheme, we believe an intrinsic sensitivity of one part in 10⁹ is feasible. At the same time, further miniaturization can be done by using for example a pyramidal-shaped retroreflector [13] that reduces the size of the laser system. All these improvements open up the route to a backpack-sized device for high-precision absolute gravimetry utilized in remote locations.

References:
[1] B. D. Tapley, D. P. Chambers, S. Bettadpur, J. C. Ries, "Large scale ocean circulation from the GRACE GGM01 Geoid". Geophysical Review Letters, 30(22) (2003). Full Article.
[2] Isabella Velicogna, John Wahr. "Measurements of Time-Variable Gravity Show Mass Loss in Antarctica“. Science, 311, 1754 (2006). Abstract.
[3] Muquans, http://www.muquans.com/.
[4] AOSense, http://www.aosense.com/.
[5] S. Abend, M. Gebbe, M. Gersemann, H. Ahlers, H. Müntinga, E.Giese, N. Gaaloul, C. Schubert, C. Lämmerzahl, W. Ertmer, W. P. Schleich, and E. M. Rasel, “Atom-chip fountain gravimeter”, Physical Review Letters, 117, 203003 (2016). Abstract.
[6] T. Kovachy, P. Asenbaum, C. Overstreet, C. A. Donnelly, S. M. Dickerson, A. Sugarbaker, J. M. Hogan, M. A. Kasevich, "Quantum superposition at the half-metre scale", Nature, 528, 530 (2015). Abstract.
[7] H. Müntinga, H. Ahlers, M. Krutzik, A. Wenzlawski, S. Arnold, D. Becker, K. Bongs, H. Dittus, H. Duncker, N. Gaaloul, C. Gherasim, E. Giese, C. Grzeschik, T. W. Hänsch, O. Hellmig, W. Herr, S. Herrmann, E. Kajari, S. Kleinert, C. Lämmerzahl, W. Lewoczko-Adamczyk, J. Malcolm, N. Meyer, R. Nolte, A. Peters, M. Popp, J. Reichel, A. Roura, J. Rudolph, M. Schiemangk, M. Schneider, S. T. Seidel, K. Sengstock, V. Tamma, T. Valenzuela, A. Vogel, R. Walser, T. Wendrich, P. Windpassinger, W. Zeller, T. van Zoest, W. Ertmer, W. P. Schleich, E. M. Rasel, "Interferometry with Bose–Einstein Condensates in Microgravity", Physical Review Letters, 110, 093602 (2013). Abstract.
[8] J. E. Debs, P. A. Altin, T. H. Barter, D. Döring, G. R. Dennis, G. McDonald, R. P. Anderson, J. D. Close, N. P. Robins, "Cold-atom gravimetry with a Bose–Einstein condensate", Physical Review A 84, 033610 (2011). Abstract.
[9] József Fortágh, Claus Zimmermann, “Magnetic Microtraps for Ultracold Atoms”, Reviews of Modern Physics, 79, 235 (2007). Abstract.
[10] Mark Keil, Omer Amit, Shuyu Zhou, David Groswasser, Yonathan Japha, Ron Folman, “Fifteen Years of Cold Matter on the Atom Chip: Promise, Realizations, and Prospects”, Jornal of Modern Optics, 63, 1840 (2016). Abstract.
[11] T. van Zoest, N. Gaaloul, Y. Singh, H. Ahlers, W. Herr, S. T. Seidel, W. Ertmer, E. Rasel, M. Eckart, E. Kajari, S. Arnold, G. Nandi, W. P. Schleich, R. Walser, A. Vogel, K. Sengstock, K. Bongs, W. Lewoczko-Adamczyk, M. Schiemangk, T. Schuldt, A. Peters, T. Könemann, H. Müntinga, C. Lämmerzahl, H. Dittus, T. Steinmetz, T. W. Hänsch, J. Reichel, "Bose–Einstein condensation in microgravity", Science, 328, 1540 (2010). Abstract.
[12] Jan Rudolph, Waldemar Herr, Christoph Grzeschik, Tammo Sternke, Alexander Grote, Manuel Popp, Dennis Becker, Hauke Müntinga, Holger Ahlers, Achim Peters, Claus Lämmerzahl, Klaus Sengstock, Naceur Gaaloul, Wolfgang Ertmer, Ernst M Rasel, "A high-flux BEC source for mobile atom interferometers", New Journal of Physics, 17, 065001 (2015). Abstract.
[13] Q. Bodart, S. Merlet, N. Malossi, F. Pereira Dos Santos, P. Bouyer, and A. Landragin, "A cold atom pyramidal gravimeter with a single laser beam", Applied Physics Letters, 96, 134101 (2010). Abstract.

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Sunday, December 11, 2016

Ultratransparent Media: Towards the Ultimate Transparency

From left to right: (top row) Jie Luo, Yuting Yang, Zhongqi Yao, Weixin Lu; (bottom row) Bo Hou, Zhi Hong Hang, C. T. Chan, and Yun Lai.

Authors: Jie Luo1, Yuting Yang1, Zhongqi Yao1, Weixin Lu1, Bo Hou1, Zhi Hong Hang1, Che Ting Chan2, Yun Lai1

Affiliation:
1College of Physics, Optoelectronics and Energy & Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, Suzhou 215006, China
2Department of Physics and Institute for Advanced Study, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong.

Transparent media are the foundation of almost all optical instruments, such as optical lens, etc. However, perfect transparency has never been realized in natural transparent solid materials such as glass because of the impedance mismatch with free space or air. As a consequence, there generally exist unwanted reflected waves at the surface of a glass slab, as illustrated in Fig. 1(a). It is well known that non-reflection only occurs at a particular incident angle for a specific polarization, which is known as the Brewster angle effect [1]. Our question is: is it possible to extend the Brewster angle from a particular angle to a wide range of or all angles, so that there is no reflection for any incident angle.

In addition, the virtual image formed by a glass slab placed in air is usually blurred to a certain extent [Fig. 1(a)]. Such a blur indicates the aberration of virtual images, and is caused by the mismatch of equal frequency contours (EFCs) between air (grey lines) and the glass (blue lines).
Figure 1: (a) Virtual image formation through a glass slab, with general reflection and aberration. (b) Aberration-free virtual image formation through an ultratransparent photonic crystal without any reflection due to omnidirectional impedance matching. The black arrows and blue dashed lines in represent the light rays from a point source, and the back tracing lines, respectively. The yellow dashed curves in (b) indicate equal phase surfaces of transmitted rays. The inset graphs show the corresponding EFCs. The figure is adapted from Reference [2].

The purpose of our work [2] is to explore the possibility of realizing the ultimate transparency by artificial optical structures such as photonic crystals (PhCs) [3] and metamaterials [4]. In other words, we pursue the realization of transparent media with the extreme property of omnidirectional impedance matching and the ability of forming aberration-free virtual images, which are hereby denoted as ultratransparent media.

In this work, we propose that omnidirectional impedance matching can be realized by utilizing effective medium with nonlocal parameters, i.e. permittivity and permeability that are dependent on the incident angle. Interestingly, such an effective medium can be realized by using pure dielectric PhCs. Moreover, the EFC of the ultratransparent PhC can be tuned to be a shifted ellipse (red lines) with the same height of the EFC of air (grey lines). By using ray optics, we prove that such an EFC endows the valuable ability of forming aberration-free virtual images, as presented in Fig. 1(b).

Because of the shift of EFC, the PhC is beyond the local medium framework, and effective parameters are nonlocal (i.e. spatially dispersive). Interestingly, such nonlocality leads to additional phase modulation p d, where p is the shift magnitude and d is the slab thickness [Fig. 1(b)].
Figure 2: (a) Illustration of the unit cell of the ultratransparent PhC. (b) The EFC of the PhC. (c) Transmittance through the PhC slab with N (=4, 5, 6, 15) layers of unit cells as functions of the incident angle. The figure is adapted from Reference [2].

An extreme example with almost complete transparency (T>99%) for nearly all incident angles (-89o, +89o) is shown in Fig. 2. The PhC is two-dimensional and its unit cell is shown in Fig. 2(a). For transverse electric polarization, at the working frequency, the EFC is a shifted ellipse (red dashed curve) with the same height as that in free space (grey dashed curve), as shown in Fig. 2(c). The transmittance through such a PhC slab is always near unity (>99%) for nearly all incident angles (<89o), and is almost irrespective of the layer number, N.
Figure 3: (a) Photo of the simplified PhC composed of alumina bars (white) placed inside the microwave field mapper. (b) The EFC of the PhC. (c) Transmittance through the PhC slab in simulations (solid lines) and experiments (triangular dots) and an alumina slab having the same thickness (dashed lines) as the function of incident angles. The figure is adapted from Reference [2].

To prove the theory, we performed proof-of-principle microwave experiments by utilizing a simplified PhC consisting of rectangular alumina bars in a square lattice, as shown in Fig. 3(a). Such a PhC exhibits a shifted elliptical EFC [Fig. 3(b)] and a wide-angle impedance matching effect. The measured transmission data (triangular dots) and simulation results (solid lines) both show high transmittance, which is great enhancement compared to the transmittance through an alumina slab with the same thickness (dashed lines).

Finally, we also note that such ultratransparent media can extend transformation optics (TO) [5, 6] to the general realm of nonlocal media. The traditional TO was founded in the local medium framework and require local media. Here, we demonstrate that ultratransparent media with controllable refractive indexes are also good candidates for TO applications such as invisibility cloaks. Interestingly, due to the nonlocality, the ultratransparent media also enable additional freedom in phase modulation, which is absent in the traditional TO. At optical frequencies, ultratransparent PhCs exhibit the significant advantages of omnidirectional impedance matching, low loss and micro fabrication requirement.

The concept and theory of ultratransparency gives a guideline for realizing the ultimate transparency which is broadband, omnidirectional and polarization-insensitive. Recently, we designed broadband, wide-angle and polarization-insensitive transparent media by using one-dimensional dielectric PhCs [7]. In the future, ultratransparent solid materials may be optimized to exhibit an unprecedented level of transparency and produce no reflection at all in certain ranges of frequencies.

References:
[1] John D. Jackson, "Classical Electrodynamics" (3rd edition, Wiley, New York, 1975).
[2] J. Luo, Y. Yang, Z. Yao, W. Lu, B. Hou, Z. H. Hang, C. T. Chan, and Y. Lai, "Ultratransparent media and transformation optics with shifted spatial dispersions", Physical Review Letters, 117, 223901 (2016). Abstract.
[3] John D. Joannopoulos, Steven G. Johnson, Joshua N. Winn, Robert D. Meade, "Photonic Crystals: Molding the Flow of Light" (2nd edition, Princeton University Press, Princeton, USA, 2008).
[4] Yongmin Liu, Xiang Zhang, "Metamaterials: a new frontier of science and technology", Chemical Society Reviews, 40, 2494-2507 (2011). Abstract.
[5] J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields", Science, 312, 1780-1782 (2006). Abstract.
[6] Ulf Leonhardt, "Optical conformal mapping", Science, 312, 1777-1780 (2006). Abstract.
[7] Zhongqi Yao, Jie Luo, Yun Lai, "Photonic crystals with broadband, wide-angle, and polarization-insensitive transparency", Optics Letters, 41, 5106 (2016). Abstract.

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Sunday, October 30, 2016

Experimental Simulation of the Exchange of Majorana Zero Modes

From left to right: (top row) Jin-Shi Xu, Kai Sun, Yong-Jian Han; (bottom row) Chuan-Feng Li, Jiannis K. Pachos, and Guang-Can Guo.

Authors: Jin-Shi Xu1,2, Kai Sun1,2, Yong-Jian Han1,2, Chuan-Feng Li1,2, Jiannis K. Pachos3, Guang-Can Guo1,2

Affiliation:
1Key Laboratory of Quantum Information, Department of Optics and Optical Engineering, University of Science and Technology of China, China,
2Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, China,
3School of Physics and Astronomy, University of Leeds, UK.

The exchange character of identical particles plays an important role in physics. For bosons, such an exchange leaves their quantum state the same, while a single exchange between two fermions gives a minus sign multiplying their wave function. A single exchange between two Abelian anyons gives rise to a phase factor that can be different than 1 or -1, that corresponds to bosons or fermions, respectively. More exotic exchanging character are possible, namely non-Abelian anyons. These particles have their quantum state change more dramatically, when an exchange between them takes place, to a possibly different state. Such non-Abelian anyons are the Majorana fermions that were first proposed by the physicist Majorana [1].

Majorana zero modes (MZMs) are quasiparticle excitations of topological phases of matter that have the same exchange character of the Majorana fermions, that is, they are non-Abelian anyons. When two MZMs are exchanged, the process cannot be described only by a global phase multiplying their wave function. Instead, their internal states, corresponding to degenerate ground states of the topological system, are transformed by a unitary operator. In addition, states encoded in the ground-state space of systems with MZMs are naturally immune to local errors. The degeneracy of the ground state, driven by the corresponding Hamiltonian, cannot be lifted by any local perturbation. Therefore, the encoded quantum information is topologically protected. These unusual characteristics imply that MZMs may potentially provide novel and powerful methods for quantum information processing [2]. Rapid theoretical developments have greatly reduced the technological requirements and made it possible to experimentally observe MZMs. However, until now, only a few positive signatures of the formation of MZMs have been reported in solid-state systems. The demonstration of the essential characteristic of non-Abelian exchange and the property of topological protection of MZMs is a considerable challenge.

Recently, we use a photonic quantum simulator to experimentally investigate the exchange of MZMs supported in the 1D Kitaev Chain Model (KCM) [3]. The Fock space of the Majorana system is mapped to the space of the quantum simulator by employing two steps. First, we perform the mapping of the Majorana system to a spin-1/2 system via the Jordan-Wigner (JW) transformation. Then we perform the mapping of the spin system to the spatial modes of single photons. In this way, we are able to demonstrate the exchange of two MZMs in a three-site Kitaev chain encoded in the spatial modes of photons. We further demonstrate that quantum information encoded in the degenerate ground state is immune to local phase and flip noise errors.

We consider a three-fermion KCM which is the simplest model that supports isolated two MZMs. Six Majorana fermions are involved and the exchange of two isolated Majoranas can be realized by a set of projective measurement, which can be expressed as imaginary-time evolution (ITE) operators with a sufficiently large evolution time. These processes depend on the corresponding Hamiltonians. Figure 1 shows the exchanging process.
Figure 1: The exchange of Majorana zero modes. The spheres with numbers at their centers represent the Majorana fermions at the corresponding sites. A pair of Majorana fermions bounded by an enclosing ring represents a normal fermion. The wavy lines between different sites represent the interactions between them. The interactions illustrated in a, b, c and d represent different Hamiltonians, respectively. The figure is adapted from Reference [3].

We transformed the KCM to a spin model through the JW transformation. Although these two models have some different physics, they share the same spectra in the ferromagnetic region and their corresponding quantum evolution are equivalent. The geometric phases obtained from the exchanging evolution are invariant under the mapping. As a result, the well-controlled spin system offers a good platform to determine the exchanging matrix and investigate the exchange behavior of MZMs.

In our experiment, the states of three spin-1/2 sites correspond to an eight-dimension Hilbert space, which are encoded in the optical spatial modes of a single photon. To complete the exchange, we implement the ITE by designing appropriate dissipative evolution. The ground state information of the corresponding Hamiltonian is preserved but the information of the other states is dissipated. We use beam-displacers to prepare the initial states and the dissipative evolution is accomplished by passing the photons through a polarization beam splitter. In our case, the optical modes with horizontal polarization are preserved which represent the ground states of the Hamiltonian. The optical modes with vertical polarization are discarded.

Figure 2 shows the experimental results of simulating the exchanging evolution. States encoded in the two-dimension degeneracy space are represented in Bloch spheres. The final states (Figure 2b) after the exchanging evolution are obtained by rotating the initial states (Figure 2a) counterclockwise along the X axis through an angle of π/2. We obtain the exchanging matrix through the quantum process tomography [4]. The real and imaginary parts of the exchanged operator are presented in Figures 2c and d. Compare with the theoretical operation, the fidelity is calculated to be 94.13±0.04%.
Figure 2: Experimental results on simulating the exchanging evolution. a. The six experimental initial states in the Bloch sphere. b. The corresponding experimental final states after the braiding evolution. The final states are shown to be rotated along the X axis by π/2 from the initial states. c. Real (Re) and d. Imaginary (Im) parts of the exchange operator with a fidelity of 94.13±0.04%. The figure is adapted from Reference [3].

Figures 3a and b show the real and imaginary parts of the flip-error protection operator with a fidelity of 97.91±0.03%. Figures 4c and d show the real and imaginary parts of the phase-error protection operator with a fidelity of 96.99±0.04%. The high fidelity reveals the protection from the local flip error and phase error of the information encoded in the ground state space of the Majorana zero modes. The total operation behaves as an identity, thus demonstrating immunity against noise.
Figure 3: Experimental results on simulating local noises immunity. a. Real (Re) and b. Imaginary (Im) parts of the flip-error protection operator, with a fidelity of 97.91±0.03%. c. Real (Re) and d. Imaginary (Im) parts of the phase-error protection operator, with a fidelity of 96.99±0.04%. The high fidelity reveals the protection from the local flip error and phase error of the information encoded in the ground state space of the Majorana zero modes. The figure is adapted from Reference [3].

In our experiment, the optical quantum simulator provides a versatile medium that can efficiently simulate the Kitaev chain model that supports MZMs at its endpoints. It also opens the way for the efficient realization and manipulation of MZMs in complex architectures. The gained know-how can be picked up by other technologies that offer scalability, like ion traps or optical lattices. This work achieves the realization of non-Abelian exchanging and may provide a novel way to investigate topological quantities of quantum systems.

References:
[1] Ettore Majorana, "Symmetrical theory of electrons and positrons", Nuovo Cimento 14, 171 (1937). Abstract.
[2] Chetan Nayak, Steven H. Simon, Ady Stern, Michael Freedman, Sankar Das Sarma, "Non-Abelian anyons and topological quantum computation". Review of Modern Physics, 80, 1083 (2008). Abstract.
[3] Jin-Shi Xu, Kai Sun, Yong-Jian Han, Chuan-Feng Li, Jiannis K. Pachos, Guang-Can Guo, "Simulating the exchange of Majorana zero modes with a photonic system". Nature Communications", 7, 13194 (2016). Abstract.
[4] J. L. O'Brien, G. J. Pryde, A. Gilchrist, D. F. V. James, N. K. Langford, T. C. Ralph, A. G. White, "Quantum process tomography of a Controlled-NOT gate". Physical Review Letters, 93, 080502 (2004). Abstract.

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Sunday, October 16, 2016

Carbon Nanotubes as Exceptional Electrically Driven On-Chip Light Sources

From left to right: (top row) Felix Pyatkov, Svetlana Khasminskaya, Valentin Fütterling; (bottom row) Manfred M. Kappes, Wolfram H. P. Pernice, Ralph Krupke

Authors: Felix Pyatkov1,2, Svetlana Khasminskaya1, Valentin Fütterling1, Randy Fechner1, Karolina Słowik3,4, Simone Ferrari1,5, Oliver Kahl1,5, Vadim Kovalyuk1,6, Patrik Rath1,5, Andreas Vetter1, Benjamin S. Flavel1, Frank Hennrich1, Manfred M. Kappes1,7, Gregory N. Gol’tsman6, Alexander Korneev6, Carsten Rockstuhl1,3, Ralph Krupke1,2, Wolfram H.P. Pernice5

Affiliation:
1Institute of Nanotechnology, Karlsruhe Institute of Technology, Germany
2Department of Materials and Earth Sciences, Technical University of Darmstadt, Germany
3Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology, Germany
4Institute of Physics, Nicolaus Copernicus University, Poland
5Department of Physics, University of Münster, Germany
6Department of Physics, Moscow State Pedagogical University, Russia
7Institute of Physical Chemistry, Karlsruhe Institute of Technology, Germany

Carbon nanotubes (CNTs) belong to the most exciting objects of the nanoworld. Typically, around 1 nm in diameter and several microns long, these cylindrically shaped carbon-based structures exhibit a number of exceptional mechanical, electrical and optical characteristics [1]. In particular, they are promising ultra-small light sources for the next generation of optoelectronic devices, where electrical components are interconnected with photonic circuits.

Few years ago, we demonstrated that electically driven CNTs can serve as waveguide-integrated light sources [2]. Progress in the field of nanotube sorting, dielectrophoretical site-selective deposition and efficient light coupling into underlying substrate has made CNTs suitable for wafer-scale fabrication of active hybrid nanophotonic devices [2,3].

Recently we presented a nanotube-based waveguide integrated light emitters with tailored, exceptionally narrow emission-linewidths and short response times [4]. This allows conversion of electrical signals into well-defined optical signals directly within an optical waveguide, as required for future on-chip optical communication. Schematics and realization of this device is shown in Figure 1. The devices were manufactured by etching a photonic crystal waveguide into a dielectric layer following electron beam lithography. Photonic crystals are nanostructures that are also used by butterflies to give the impression of color on their wings. The same principle has been used in this study to select the color of light emitted by the CNT. The precise dimensions of the structure were numerically simulated to tailor the properties of the final device. Metallic contacts in the vicinity to the waveguide were fabricated to provide electrical access to CNT emitters. Finally, CNTs, sorted by structural and electronic properties, were deposited from a solution across the waveguide using dielectrophoresis, which is an electric-field-assisted deposition technique.
Figure 1: (a) Schematic view of the multilayer device structure consisting of two electrodes (yellow) and a photonic waveguide (purple) that is etched into the Si3N4 layer. Its central part is underetched into the SiO2 layer to a depth of 1.5 µm and photonic crystal holes are formed. The carbon nanotube bridges the electrodes on top of the waveguide. (b,c) False colored scanning electron microscope images of the device. The figure is adapted from Reference [4].

The functionality of the device was verified with optical microscopy and spectroscopy, which allowed detection of light emitted by the CNT and also of the light coupled into the waveguide. An electrically biased CNT generates photons, which efficiently couple into the photonic crystal waveguide, as shown in Figure 2a. The emitted light propagates along the waveguide and is then coupled out again using on-chip grating couplers. Because of the photonic crystal the emission spectrum of the CNT is extremely sharp (Figure 2b) and the emission wavelength can be tailored by our manufacturing process. In addition, the nanotube responds very quickly to electrical signals and hence acts as a transducer for generating optical pulses in the GHz range (Figure 2c). The modulation rates of these CNT-based transducers can in principle be pushed to much higher frequencies up to 100 GHz using more advanced nanostructures.
Figure 2: (click on the image to view with higher resolution) CCD camera image of the electrically biased device. Light emission is observed from the nanotube and from the on-chip grating couplers, both connected with the emitter via the waveguide. (b) Emission spectra simultaneously measured at the grating coupler. (c) A sequence of the driving electrical pulses as well as the recorded waveguided emission pulses (red) in GHz frequency range. The figure is adapted from Reference [4].

Nanophotonic circuits are promising candidates for next-generation computing devices where electronic components are interconnected optically with nanophotonic waveguides. The move to optical information exchange, which is already routinely done in our everyday life using optical fibers, also holds enormous benefit when going to microscopic dimensions – as found on a chip. Essential elements for such opto-electronic devices are nanoscale light emitters which are able to convert fast electrical signals into short optical pulses. Using such ultrafast transducers will allow for reducing power requirements and eventually speed up current data rates. For achieving ultimately compact devices the emitter should be as small as possible and interface efficiently with sub-wavelength optical devices. It would also have to operate at a chosen design wavelength and at high speed.

CNTs integrated into a photonic crystal nanobeam waveguides fulfill these requirements and constitute a promising new class of transducers for on-chip photonic circuits. These novel emitters are particularly interesting because of their simplicity. In contrast to conventional laser sources, CNTs are made entirely from carbon, which is available in abundance and does not require expensive fabrication routines as needed for III-V technologies. Moreover, CNTs can also be readily combined with existing CMOS technology, which makes them attractive for a wide range of applications.

So far we spoke about traditional computers based on binary logic. Going beyond classical computation, quantum computers that exploit the enormous potential of quantum mechanics for complex calculations and cryptography hold promise to revolutionize current information processing approaches. Optical quantum systems that employ single photons to realize quantum bits (qubits) belong to the prominent candidates for such future quantum information processing systems. To build a photonic quantum computer, sources of single photons (e.g. single molecules, quantum dots and semiconducting CNTs [5]), optical quantum gates and single photon detectors are needed. These devices are capable of very fast and reliable emission and detection of distinct photons.

An experimental approach, which allows for showing that a light source emits one photon at a time, consists of measuring intensity correlations in the emitted light. We performed this experiment on a solid silicon-based chip with an electrically driven CNT -- actings as a non-classical light source, waveguides, and two detectors for single photons [6]. The nanophotonic circuit shown in Figure 3 includes these three components: a CNT, a dielectric waveguide for the low-loss light propagation and a pair of superconducting nanowires for the efficient detection of light. A single chip carries dozens of such photonic circuits. The device fabrication process was similar to the realization of photonic crystal waveguides, except that now travelling-wave nanowire detectors were also formed on top of the waveguide.
Figure 3: (click on the image to view with higher resolution) (a,b) Schematics and optical image of device with an electrically driven light emitting nanotube in the middle (E) and single-photon superconducting NbN-detectors at the ends (D) of waveguide. The figure is adapted from Reference [6].

The functionality of the device was verified at cryogenic conditions with a setup which allowed the ultra-fast detection of light that was emitted by the CNT and then coupled into the waveguide. An electrically biased semiconducting CNT generates single photons, which can propagate bidirectionally within the waveguide towards the highly sensitive detectors. The intensity of the emitted light was measured as a function of the electrical bias current through the nanotube (Figure 4a). If only one photon at a time is emitted, the simultaneous detection of two photons with both detectors is highly unlikely. This can be derived from the dip in the second-order correlation function shown in Figure 4b. The low probability of simultaneous many-photon detection underlines the non-classical nature of the light source, which is the first step towards a true single-photon emitter. In essence, we thus realized a fully-integrated quantum photonic circuit with a single photon source and detectors, both of which are electrically driven and scalable.

Figure 4: (a) Measurement of the CNT emission intensity in dependence of bias current. Within the marked region semiconducting CNTs reveal non-classical emitting properties. (b) A measured second order correlation function. The minimum value significantly below unity represents the low possibility for simultaneous emission of two photons. The figure is adapted from Reference [6].

References:
[1] Phaedon Avouris, Marcus Freitag, Vasili Perebeinos, "Carbon-Nanotube Photonics and Optoelectronics", Nature Photonics, 2, 341-350 (2008). Abstract.
[2] Svetlana Khasminskaya, Felix Pyatkov, Benjamin S. Flavel, Wolfram H. P. Pernice, Ralph Krupke ,"Waveguide-Integrated Light-Emitting Carbon Nanotubes", Advanced Materials, 26, 3465-3472 (2014). Abstract.
[3] Randy G. Fechner, Felix Pyatkov, Svetlana Khasminskaya, Benjamin S. Flavel, Ralph Krupke, Wolfram H. P. Pernice, "Directional Couplers with Integrated Carbon Nanotube Incandescent Light Emitters", Optics Express, 24, 966-974 (2016). Abstract.
[4] Felix Pyatkov, Valentin Fütterling, Svetlana Khasminskaya, Benjamin S. Flavel, Frank Hennrich, Manfred M. Kappes, Ralph Krupke, Wolfram H. P. Pernice, "Cavity-Enhanced Light Emission from Electrically Driven Carbon Nanotubes", Nature Photonics, 10, 420-427 (2016). Abstract.
[5] Alexander Högele, Christophe Galland, Martin Winger, Atac Imamoğlu, "Photon Antibunching in the Photoluminescence Spectra of a Single Carbon Nanotube", Physical Review Letters, 100, 217401 (2008). Abstract.
[6] Svetlana Khasminskaya, Felix Pyatkov, Karolina Słowik, Simone Ferrari, Oliver Kahl, Vadim Kovalyuk, Patrik Rath, Andreas Vetter, Frank Hennrich, Manfred M. Kappes, Gregory N. Gol’tsman, Alexander Korneev, Carsten Rockstuhl, Ralph Krupke, Wolfram H.P. Pernice "Fully Integrated Quantum Photonic Circuit with an Electrically Driven Light Source", Nature Photonics (2016). Abstract.

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