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2Physics

2Physics Quote:
"Random access memory (RAM) is used extensively in a wide variety of instruments. It is based on the bistable operation of electronic transistors and memorizes bit information. Recently, its optical counterpart, optical RAM (o-RAM), has become highly desirable in high-speed network processing, especially for routers, because it is more efficient to manage network information all-optically without power-consuming electric-to-optical (EO) or OE conversions. Various o-RAM devices have been proposed and fabricated, but so far they have been too big, too power-consuming, or too difficult to integrate."
-- Eiichi Kuramochi, Kengo Nozaki, Akihiko Shinya, Masaya Notomi
(Read Full Article: "Over 100-bit Integrated All-Optical Memory on a Photonic Crystal Chip is Demonstrated" )

Sunday, September 28, 2014

When Magnetism Meets Optics

S. Mangin (Left) and E. E. Fullerton

Authors: 

C.H. Lambert, M. Salah, N. Bergeard, G. Malinowski, M. Hehn, S. Mangin,
Equipe Nanomagnetisme et Electronique de Spin de l’Institut Jean Lamour UMR CNRS 7198, Université de Lorraine, France

Y. Fainman, E. E. Fullerton,
Center For Magnetic Recording Research, University of California San Diego (UCSD), USA 

M. Cinchetti, M. Aeschlimann, 
Department of Physics and Research Center OPTIMAS, University of Kaiserlautern- Allemagne, Germany 

B. Varaprasad, Y. Takahashi, K. Hono, 
National Institute for Materials Science, Japan

With the fast development of mass storage units all around the world (clouds, data centers…) the pressure to increase the density, speed and energy efficiency of conventional hard disk drives is becoming stronger and stronger. The discovery of “All-optical control of ferromagnetic thin films and nanostructures” might open up new technological horizons in magnetic recording. This work is the results of a collaboration between scientists and engineers from University of California San Diego, Universite de Lorraine, Kaiserlauter Universitat and National Institute for Materials Science in Tsukuba, Japan published in Science on September 14th 2014 [1].

 The authors found that they could control the final state of the magnetization of a broad range of magnetic materials using laser pulses of circularly polarized light instead of an applied magnetic fields. In particular these researchers find out that the magnetization of some magnetic material similar to those used in the recording industry can be manipulated directly with a laser beam. The ability to optically control magnetic materials the density and access time of data on hard drives could be increased dramatically.

Image: Writing with a laser on a magnetic thin film.

The first observation of “all optical switching” of magnetic materials was performed in 2007 by the group from T. Rasing in Nijmegen on a very particular ferrimagnetic alloy GdFeCo [2]. Since this discovery there has been extensive studies of optical switching of this material class including detailed studies of the magnetic response to optical excitations of both the rare-earth (Gd) and transition metal (Fe and Co) elements. Based on these studies a detailed understanding has emerged of the ultra-fast physics of rare-earth-transition-metal alloys [3,4]. However, the extent of the practical impact of this research is limited by the materials that are not compatible with many modern technologies. By extending these exciting studies to new classes of materials such as ferromagnets, the “all-optical” magnetization switching has made a significant step to demonstrate its potential for technological impact.

These results further show that theoretical understanding of all-optical switching needs to be re-examined. Most recent theories predicted that the all-optical reversal should only occur in ferrimagnetic materials, where the overall magnetization is the result of the competition between two magnetic sub-lattices that are antiferromagnetically coupled. Our results show that all-optical switching is not exclusive to ferrimagnetic materials and therefore antiferromagnetic exchange coupling between two magnetic sublattices is not required. The results do suggest that heating near the Curie point is important for the all-optical switching in ferromagnetic materials. Near the Curie point then a small symmetry-breaking from circularly polarized light (e.g. the inverse Faraday effect or transfer of angular momentum from the light to the magnetic system) can deterministically determine the magnetization direction. However details of this process still need to be determined.


Video: Writing with a laser on a magnetic thin film : Micrometer size "Etch A Sketch".

References:
[1] C-H. Lambert, S. Mangin, B. S. D. Ch. S. Varaprasad, Y. K. Takahashi, M. Hehn, M. Cinchetti, G. Malinowski, K. Hono, Y. Fainman, M. Aeschlimann, E. E. Fullerton, "All-optical control of ferromagnetic thin films and nanostructures".  Science, 345, 1337-1340 (2014). Abstract.
[2] C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, Th. Rasing, "All-optical magnetic recording with circularly polarized light". Physical Review Letters, 99, 047601 (2007). Abstract.
[3] Andrei Kirilyuk, Alexey V Kimel, Theo Rasing, "Laser-induced magnetization dynamics and reversal in ferrimagnetic alloys". Reports on Progress in Physics, 76, 026501 
(2013). Abstract.
[4] S. Mangin, M. Gottwald, C-H. Lambert, D. Steil, V. Uhlíř, L. Pang, M. Hehn, S. Alebrand, M. Cinchetti, G. Malinowski, Y. Fainman, M. Aeschlimann, E.E. Fullerton, "Engineered materials for all-optical helicity-dependent magnetic switching".  Nature Materials, 13, 286–292 (2014). Abstract.

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Sunday, September 21, 2014

Bio-inspired Plasmonic Structures Built on Virus Capsids and DNA Origami Tiles

Debin Wang (left) and James J. De Yoreo

Authors: Debin Wang1,2, James J. De Yoreo1,2

Affiliation:
1Materials Sciences Division and the Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California, USA.
2Fundamental and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington, USA.

The use of biomolecular scaffolds to direct the organization of inorganic or organic nanomaterials addresses the grand challenge of assembling multiple functional units with precise control over their spatial arrangement at the molecular level [1-3]. Biomolecules, such as peptides, proteins, and nucleic acids have all been used as building blocks for bottom-up assembly of intricate structures thanks to their inherent chemical and biological addressability, structural precision, and efficiency of synthesis [4].

In photosynthetic bacteria, light-harvesting units are organized with molecular-level precision around the photochemical units [5-6]. In this way, they generate antenna complexes that ensure efficient photon absorption and energy transfer. In a similar way, biomimetic assembly of plasmonic nanostructures can provide molecular-level spatial precision, creating potential improvements in efficiency of light-harvesting platforms, light-emitting devices, and optical sensors [7-8].

Recently, we reported the bottom-up assembly of hierarchical plasmonic nanostructures using DNA origami tiles and MS2 virus capsids [9]. These bio-inspired structures serve as programmable scaffolds that provide molecular level control over the distribution of fluorescent dye molecules and nanometer-scale control over their distance from a gold nanoparticle antenna (Fig. 1). While previous studies on DNA origami assembly of plasmonic nanostructures focused on the distance-dependent response of single fluorescent dye molecules [10-11], these hybrid structures allowed us to investigate the plasmonic response of an entire ensemble of fluorescent molecules.
Figure 1. Bio-inspired assembly of plasmonic nanostructures using DNA origami and MS2 virus capsids. TEM imaging and profile analysis confirmed tight control over the distance between fluorophore labelled virus capsids and gold nanoparticle antennae. Correlated Raman-AFM imaging provided direct single-particle measurements of fluorescence intensities. Adapted with permission from ACS Nano 2014, 8, 7896-7904. Copyright 2014 American Chemical Society.

We studied the collective plasmon-coupled response of fluorophore-labeled capsids to the presence of an AuNP as a function of their separation distance. We demonstrated tight control over this distance by exploiting the programmable nature of DNA origami templates and the ability to site-specifically modify MS2 virus capsids (Fig.1). Using finite-difference time-domain (FDTD) numerical simulations in conjunction with atomic force microscopy (AFM) and correlated scanning confocal fluorescence microscopy, we then showed that the utilizing a 3D ensemble of dye molecules can effectively suppress the fluorescence quenching in the single molecule quenching regime, presumably due to the size effect of the capsid scaffold (Fig. 1). FDTD simulations also showed that increasing the size of the AuNPs to be commensurate with that of the capsids optimizes the fluorescence enhancement (Fig.2).
Figure 2. Finite-difference-time-domain (FDTD) numerical simulations predict the plasmon-coupled response of the bio-inspired nanostructures. Adapted with permission from ACS Nano 2014, 8, 7896-7904. Copyright 2014 American Chemical Society.

Looking forward, we plan to use this bio-inspired light harvesting platform to explore the effect of variations in nanoparticle size, choice of fluorophore, arrangement of fluorophores, and even the capsid shape on device performance. More generally, our assembly strategy establishes the possibility of using biological scaffolds to build hierarchical plasmonic nanostructures to address the need for energy harvesting in solar energy applications.

References:
[1] Trevor Douglas, Mark Young, "Viruses: Making Friends with Old Foes". Science, 312, 873-875 (2006). Abstract.
[2] James J. Storhoff, Chad A. Mirkin, "Programmed Materials Synthesis with DNA". Chemical Reviews, 99, 1849-1862 (1999). Abstract.
[3] Andre V. Pinheiro, Dongran Han, William M. Shih, Hao Yan, "Challenges and Opportunities for Structural DNA Nanotechnology". Nature Nanotechnology, 6, 763-772 (2011). Abstract.
[4] Shuguang Zhang, "Fabrication of Novel Biomaterials through Molecular Self-Assembly". Nature Biotechnology, 21, 1171-1178 (2003). Abstract.
[5] Svetlana Bahatyrova, Raoul N. Frese, C. Alistair Siebert, John D. Olsen, Kees O. van der Werf, Rienk van Grondelle, Robert A. Niederman, Per A. Bullough, Cees Otto, C. Neil Hunter, "The Native Architecture of a Photosynthetic Membrane". Nature, 430, 1058-1062 (2004). Abstract.
[6] Pascal Anger, Palash Bharadwaj, Lukas Novotny, "Enhancement and Quenching of Single-Molecule Fluorescence". Physical Review Letters, 96, 113002 (2006). Abstract.
[7] Stephan Link, Mostafa A. El-Sayed, "Size and Temperature Dependence of the Plasmon Absorption of Colloidal Gold Nanoparticles". Journal of Physical Chemistry B, 103, 4212-4217 (1999). Abstract.
[8] Joanna Malicka, Ignacy Gryczynski, Zygmunt Gryczynski, Joseph R Lakowicz, "Effects of Fluorophore-to-Silver Distance on The Emission of Cyanine-Dye-Labeled Oligonucleotides". Analytical Biochemistry, 315, 57-66 (2003). Abstract.
[9] Debin Wang, Stacy L. Capehart, Suchetan Pal, Minghui Liu, Lei Zhang, P. James Schuck, Yan Liu, Hao Yan, Matthew B. Francis, James J. De Yoreo, "Hierarchical Assembly of Plasmonic Nanostructures Using Virus Capsid Scaffolds on DNA Origami Templates". ACS Nano, 8, 7896-7904 (2014). Abstract.
[10] G. P. Acuna, F. M. Möller, P. Holzmeister, S. Beater, B. Lalkens, P. Tinnefeld, "Fluorescence Enhancement at Docking Sites of DNA-Directed Self-Assembled Nanoantennas". Science, 338, 506-510 (2012). Abstract.
[11] Guillermo P. Acuna, Martina Bucher, Ingo H. Stein, Christian Steinhauer, Anton Kuzyk, Phil Holzmeister, Robert Schreiber, Alexander Moroz, Fernando D. Stefani, Tim Liedl, Friedrich C. Simmel, Philip Tinnefeld, "Distance Dependence of Single-Fluorophore Quenching by Gold Nanoparticles Studied on DNA Origami". ACS Nano, 6, 3189-3195 (2012). Abstract.

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Sunday, September 14, 2014

Imaging the Dynamics of Free-Electron Landau States

Transmission electron microscope that was used in the experiment. Foreground: Michael Stöger-Pollach (left) and Peter Schattschneider.
From Left to Right: Th. Schachinger, S. Löffler, A. Steiger-Thirsfeld, K. Y. Bliokh, Franco Nori

Authors: P. Schattschneider1,2,3, Th. Schachinger1, M. Stöger-Pollach2, S. Löffler2, A. Steiger-Thirsfeld2, K. Y. Bliokh4,5, Franco Nori5,6

Affiliation:
1Institute of Solid State Physics, Vienna University of Technology, Austria
2University Service Centre for Electron Microscopy, Vienna University of Technology, Austria
3LMSSMat (CNRS UMR 8579) Ecole Centrale Paris, France
4iTHES Research Group, RIKEN, Wako-shi, Saitama, Japan
5Center for Emergent Matter Science, RIKEN, Wako-shi, Saitama, Japan
6Department of Physics, University of Michigan, Ann Arbor, USA.

Inspired by theoretical calculations [1,2] from RIKEN (Japan), the group at Vienna University of Technology devised a way to generate free-electron Landau states [3], a form of quantized states that electrons adopt when moving through a magnetic field. Landau levels and states of electrons in a magnetic field are fundamental quantum entities underlying the quantum Hall and related effects in condensed matter physics [4]. Landau states can be envisaged as electron vortices occurring naturally in the presence of magnetic fields. The magnetic field plays the same role for electrons as the earth's rotation plays for the creation of cyclones, but here on a nanometer scale, where quantum effects become important [5].

Past 2Physics articles by Konstantin Y. Bliokh:
January 17, 2009: "Optical Magnus Effect: Topological Monopole Deflects Spinning Light".

Classical electrons in a uniform magnetic field propagate freely along the field and form confined circular orbits in the plane perpendicular to the field. The angular velocity of such orbiting is constant and is known as the cyclotron frequency. But quantum mechanics calls for a counter-intuitive behaviour [2]. The researchers were able to induce intrinsic rotation in single moving electrons. It was observed [3] that Landau modes with different azimuthal quantum numbers belong to three classes, which are characterized by rotations with zero, Larmor and cyclotron frequencies, respectively. This is in sharp contrast to the uniform cyclotron rotation of classical electrons, and in perfect agreement with recent theoretical predictions [2].

States with different quantum numbers are produced using nanometre-sized electron vortex beams, with a radius chosen to match the waist of the Landau states, in a quasi-uniform magnetic field. Scanning the beams along the propagation direction [3], the researchers reconstructed the rotational dynamics of the Landau wave functions with angular frequency of the order of 100 GHz.

Figure 1: A holographic fork mask generates a row of vortex beams with different azimuthal indices m. These beams are focused by a magnetic lens and are studied in the region of maximal quasi-uniform magnetic field (red arrow on the left). The focal plane is shifted a few Rayleigh ranges below the observation plane z=0 to reduce the Gouy-phase rotation. A knife-edge stop is placed at zk, where it blocks half of each of the beams. Varying the position zk of the knife edge allows the observation of the spatial rotational dynamics of the cut beams propagating to the observation plane [3].

The focusing lenses of a transmission electron microscope were used [3] to reconfigure the vortices so that they almost perfectly resembled Landau states. In an electron vortex beam, the wave current swirls around a common center similar to air in a tornado [6]. Measuring the rotation can be compared to determining how many times a thin wire is wound around a rod. When looking at the wire directly, it is extremely difficult to count the number of windings. But when stretching it along the direction of the rod, the wire takes the form of a well-spaced spiral, for which it is easy to count the revolutions. This is precisely what happens with Landau states: they were 'elongated' to vortex beams. That way, their rotation could be measured [3] with very high accuracy.

This is a very exciting finding that will contribute to a better understanding of the fundamental quantum features of electrons in magnetic fields [3]. In addition to showing that the rotational dynamics of the electrons are more complex and intriguing than was once believed, the new findings could have practical implications for technology. Taking Landau states into free space, away from the solids where they normally play a key role [4,7], can inspire new ideas in materials science.

This will certainly lead to novel insights and a better understanding of the delicate interaction between magnetic fields and matter, which might one day give rise to new and better technologies such as sensors, memory devices, or nanomanipulation.

References:
[1] Konstantin Yu. Bliokh, Yury P. Bliokh, Sergey Savel’ev, Franco Nori, "Semiclassical dynamics of electron wave packet states with phase vortices". Physical Review Letters, 99, 190404 (2007). Abstract.
[2] Konstantin Y. Bliokh, Peter Schattschneider, Jo Verbeeck, Franco Nori, "Electron vortex beams in a magnetic field: a new twist on Landau levels and Aharonov-Bohm states". Physical Review X, 2, 041011 (2012). Abstract.
[3] P. Schattschneider, Th. Schachinger, M. Stöger-Pollach, S. Löffler, A. Steiger-Thirsfeld, K. Y. Bliokh, Franco Nori, "Imaging the dynamics of free-electron Landau states". Nature Communications, 5, 4586 (2014). Full Article.
[4] Daijiro Yoshioka, "The Quantum Hall Effect" (Springer, 2002).
[5] J. Verbeeck, H. Tian, P. Schattschneider, "Production and Application of Electron Vortex Beams". Nature, 467, 301 (2010). Abstract.
[6] Giulio Guzzinati, Peter Schattschneider, Konstantin Y. Bliokh, Franco Nori, Jo Verbeeck, "Observation of the Larmor and Gouy rotations with electron vortex beams". Physical Review Letters, 110, 093601 (2013). Abstract.
[7] David L. Miller, Kevin D. Kubista, Gregory M. Rutter, Ming Ruan, Walt A. de Heer, Markus Kindermann, Phillip N. First, Joseph A. Stroscio, "Real-space mapping of magnetically quantized graphene states". Nature Physics, 6, 811–817 (2010). Abstract.

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Sunday, September 07, 2014

Single Photon Transistor Mediated by Rydberg Interaction

From Left to Right: Hannes Gorniaczyk, Christoph Tresp, Johannes Schmidt, Ivan Mirgorodskiy, Sebastian Hofferberth

Authors: Christoph Tresp, Ivan Mirgorodskiy, Hannes Gorniaczyk, Sebastian Hofferberth 

Affiliation:
Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universität Stuttgart, Germany.

Link to Rydberg Quantum Optics, Emmy Noether Group >>

Introduction:

In analogy to their electronic counterparts, all-optical switches and transistors are required as basic building blocks for both classical and quantum optical information processing [1,2]. Reaching the fundamental limit of such devices, where a single gate photon modifies the transmission or phase accumulation of multiple source photons, requires strong effective interaction between individual photons. Engineering sufficiently strong optical nonlinearities to facilitate photon-photon interaction is one of the key goals of modern optics. Immense progress towards this goal has been made in a variety of systems in recent years. Most prominent so far are cavity QED experiments where a high finesse resonator enhances the interaction between light and atoms [3,4] or artificial atoms [5,6].

In this work, we demonstrate a free-space all-optical transistor operating on the single photon level using a novel approach to realize effective photon-photon interaction [7], which is based on mapping the strong interaction of Rydberg atoms [8] onto slowly travelling photons using electromagnetically induced transparency [9]. This technique has already been used to demonstrate highly efficient single-photon generation [10], attractive interaction between single photons [11], entanglement generation between light and atomic excitations [12], and most recently single-photon all-optical switching [13].

However, demonstration of amplification, that is, controlling many photons with a single one, has so far only been achieved in a cavity QED setup [14]. Gain > 1 is one of the key properties of the electric transistor that lies at the heart of its countless applications. In our experiment, we demonstrate an all-optical transistor with optical gain G > 10 [15]. Similar results have been obtained by the group of G. Rempe, their results have been published in parallel to ours [16].

Experiment:

The level scheme and geometry of our transistor are illustrated in Fig. 1 (a, b). Photons in the weak gate pulse are stored as Rydberg excitations in an atomic ensemble by coupling the ground state |g> to the Rydberg state |rg> via the strong gate control field. After this storage process, a second weak pulse, the source pulse, is sent through the medium at reduced velocity due to EIT provided by the source control laser coupling to the Rydberg state |rs>.
FIG. 1: (a) Level scheme, (b) simplified schematic, and (c) pulse sequence of our all-optical transistor. (d) The absorption spectrum for the source field (dots) over the full intermediate state absorption valley shows the EIT window on resonance; the gate field spectrum (circles) is taken around the two-photon resonance at Δ = 40 MHz. The solid lines are fits to the EIT spectra.

In the absence of the gate pulse, source photons travel through the transparent medium (Fig. 1d). If a gate photon has been stored, the strong interaction between the two Rydberg states destroys the EIT condition for the source photons in the medium, resulting in absorption. To observe this conditional switching, we record the number of transmitted source photons in a time interval tint after the gate excitation pulse, cf. Fig. 1 (c). For the experimental realization of this scheme, we prepare 2.5 X 104 87Rb atoms at a temperature of T = 40 µK in an optical dipole trap. All four lasers required for the transistor scheme are focused into this medium along a single direction (Fig. 1b). The weak gate and source pulses are recorded on single photon counters.

Results:

We first investigate the relative attenuation of a weak source pulse as a function of mean incident gate photons. In Fig. 2 (a) we plot the switch contrast in the source beam transmission as a function of the mean incoming gate photon number. For an average gate photon number of Ng,in = 1.04(3), we observe a switch contrast Ccoh = 0.39(4). The switch contrast is mainly determined by the Poissonian statistics of our coherent gate photons, which sets a fundamental upper bound. In other words, a perfect switch with coherent gate photons has a switch contrast Ccoh = 1 - exp(-Ng,in) (dashed line in Fig. 2 (a)). How close our switch approaches this fundamental limit depends on the gate photon storage efficiency and the source attenuation caused by a single gate excitation. In Fig. 2 (b) we plot the switch contrast versus the mean number of stored gate photons, which is smaller than the mean incident gate photon number due to not perfect gate photon storage. Finally, by again taking the Poissonian statistics of the input light into account, we extrapolate the switch contrast caused by a single stored excitation to be Cexc = 0.9.
FIG. 2: Switch contrast (red) as function of (a) mean number of incident gate photons and (b) mean number of stored photons. The dashed line indicates the fundamental limit set by the photon statistics of the coherent gate input. Black data points represent the calculated switch contrast expected for (a) one-, two- and three-photon Fock input states or (b) deterministic single and two stored gate excitations.

Next, we investigate how many source photons can be switched by our system. To quantify the gate-induced change in source transmission, we consider the optical gain
G = Ns,outno gate - Ns,outwith gate. In Fig. 3 (a), we plot the measured optical gain for an average input of gate photons Ng,in = 0.75(3). For this gate input, we observe a maximum optical gain G(Ng,in = 0.75) = 10(1). Further increase of the optical gain at fixed gate input is limited by the self-blockade of the source beam, which results in nonlinear source transmission even in the absence of gate photons [7, 17]. The red (blue) data points in Fig. 3 (b) show the source photon transfer function when Ng,in = 0 (Ng,in = 0.75(3)). For the given integration time the source transmission saturates at 46 photons, which limits the maximum gain we can observe. On the other hand, the self-nonlinearity of the source light does not affect the transistor performance, we observe a constant switch contrast of C = 0.22(3), consistent with the mean gate input, even for incoming source photons up to ~250. Based on this robustness, we can again extrapolate the transistor performance for a true single photon gate input (Fig. 3 green line) and a single stored excitation (grey line). For a single excitation, we calculate the maximally achievable optical gain of our current system as Gst = 28(2).
FIG. 3: (a) Optical gain of our transistor, measured for coherent gate input Ng,in = 0.75(3) (blue data), and extrapolated to single photon Fock state input (green line), and single stored excitation (black line). (b) Source photon transfer function without (red) and with coherent gate input Ng,in = 0.75(3) (blue). We observe a constant switch contrast between the two data sets over the whole source input range. The green (black) solid line are again the estimated behavior of the system for a single-photon Fock input state (a single stored excitation). Shaded regions are error estimates.

Discussion and outlook:

In summary, we have demonstrated a free-space single photon transistor based on two-color Rydberg interaction. Further improvements of our system could enable a high optical gain, high efficiency optical transistor, so far only realized in a cavity QED setup [14]. One approach to overcome the self-nonlinearity of the source photons has already been demonstrated by the Rempe group, who employ a two-color Förster resonance in their transistor scheme [16].

A key step towards turning our transistor into device which can perform quantum operations on single or few photons is the retrieval of gate photon(s) after the switch process, which could enable multi-photon entanglement protocols and creation of non-classical light-states with large photon numbers. Finally, our system is a highly sensitive probe for studying Rydberg interaction on the few-particle level [18]. In particular, the combination of two independently controlled Rydberg-EIT schemes enables novel fields of study, such as the interplay between slow light propagation and Rydberg exchange interaction [19], or realization of a two-photon phase gate based on Rydberg-polariton collision [20].

References:
[1] H. John Caulfield and Shlomi Dolev, "Why future supercomputing requires optics". Nature Photonics, 4, 261 (2010). Abstract.
[2] Jeremy L. O'Brien, Akira Furusawa, Jelena Vuckovic, "Photonic quantum technologies". Nature Photonics, 3, 687 (2009). Abstract.
[3] K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup, H. J. Kimble, "Photon blockade in an optical cavity with one trapped atom". Nature, 436, 87 (2005). Abstract.
[4] Tatjana Wilk, Simon C. Webster, Axel Kuhn, Gerhard Rempe, "Single-Atom Single-Photon Quantum Interface". Science, 317, 488 (2007). Abstract.
[5] P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, Lidong Zhang, E. Hu, A. Imamoglu, "A Quantum Dot Single-Photon Turnstile Device". Science, 290, 2282 (2000). Abstract.
[6] Dirk Englund, Andrei Faraon, Ilya Fushman, Nick Stoltz, Pierre Petroff, Jelena Vuckovic, "Controlling cavity reflectivity with a single quantum dot". Nature, 450, 857 (2007). Abstract.
[7] J. D. Pritchard, D. Maxwell, A. Gauguet, K. J. Weatherill, M. P. A. Jones, C. S. Adams, "Cooperative Atom-Light Interaction in a Blockaded Rydberg Ensemble". Physical Review Letters, 105, 193603 (2010). Abstract.
[8] M. Saffman, T. G. Walker, K. Mølmer, "Quantum information with Rydberg atoms". Review of Modern Physics, 82, 2313 (2010). Abstract.
[9] Michael Fleischhauer, Atac Imamoglu, Jonathan P. Marangos, "Electromagnetically induced transparency: Optics in coherent media". Review of Modern Physics, 77, 633 (2005). Abstract.
[10] Y. O. Dudin and A. Kuzmich, "Strongly Interacting Rydberg Excitations of a Cold Atomic Gas". Science 336, 887 (2012). Abstract.
[11] Ofer Firstenberg, Thibault Peyronel, Qi-Yu Liang, Alexey V. Gorshkov, Mikhail D. Lukin, Vladan Vuletić, "Attractive photons in a quantum nonlinear medium". Nature, 502, 71 (2013). Abstract.
[12] L. Li, Y. O. Dudin, and A. Kuzmich, "Entanglement between light and an optical atomic excitation". Nature, 498, 466 (2013). Abstract.
[13] Simon Baur, Daniel Tiarks, Gerhard Rempe, Stephan Dürr, "Single-Photon Switch Based on Rydberg Blockade". Physical Review Letters, 112, 073901 (2014). Abstract.
[14] Wenlan Chen, Kristin M. Beck, Robert Bücker, Michael Gullans, Mikhail D. Lukin, Haruka Tanji-Suzuki, Vladan Vuletić, "All-Optical Switch and Transistor Gated by One Stored Photon". Science 341, 768 (2013). Abstract.
[15] H. Gorniaczyk, C. Tresp, J. Schmidt, H. Fedder, S. Hofferberth, "Single-Photon Transistor Mediated by Interstate Rydberg Interactions". Physical Review Letters, 113, 053601 (2014). Abstract.
[16] Daniel Tiarks, Simon Baur, Katharina Schneider, Stephan Dürr, Gerhard Rempe, "Single-Photon Transistor Using a Förster Resonance". Physical Review Letters, 113, 053602 (2014). Abstract.
[17] Thibault Peyronel, Ofer Firstenberg, Qi-Yu Liang, Sebastian Hofferberth, Alexey V. Gorshkov, Thomas Pohl, Mikhail D. Lukin, Vladan Vuletić, "Quantum nonlinear optics with single photons enabled by strongly interacting atoms". Nature, 488, 57 (2012). Abstract.
[18] L. Béguin, A. Vernier, R. Chicireanu, T. Lahaye, A. Browaeys, "Direct Measurement of the van der Waals Interaction between Two Rydberg Atoms". Physical Review Letters, 110, 263201 (2013). Abstract.
[19] Weibin Li, Daniel Viscor, Sebastian Hofferberth, Igor Lesanovsky, "Electromagnetically Induced Transparency in an Entangled Medium". Physical Review Letters, 112, 243601 (2014). Abstract.
[20] Alexey V. Gorshkov, Johannes Otterbach, Michael Fleischhauer, Thomas Pohl, Mikhail D. Lukin, "Photon-Photon Interactions via Rydberg Blockade". Physical Review Letters, 107, 133602 (2011). Abstract.

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Sunday, August 31, 2014

A True Randomness Generator Exploiting a Very Long and Turbulent Path

From Left to Right: Paolo Villoresi,  Davide Marangon, Giuseppe Vallone

Authors:
Davide G. Marangon, Giuseppe Vallone,  Paolo Villoresi

Affiliation:
Department of Information Engineering, University of Padova, Italy.

Random numbers are the main ingredients of cryptographic protocols for both Classical and Quantum Information. However, it is well known that to rely on random numbers produced with deterministic algorithms can be very risky and it is of fundamental priority to discover physical processes to generate "pure" random numbers. Usually True Random Number Generators (TRNG) are implemented by exploiting classical or quantum microscopical processes. However it can be shown that random numbers can be extracted from macroscopic physical systems.


In the 60s, the famous "Butterfly Effect" captured the idea that when one deals with the terrestrial atmosphere, very tiny perturbations such as the air moved by the tail strokes of a butterfly can lead to very huge consequences as a hurricane in some other place in the world. Terrestrial atmosphere indeed may be seen as a physical system ruled by a chaotic dynamic. Moreover, while statistical models are available for average trends, the prediction of the instantaneous motion of the air mass in a spot is out of reach.

From the textbooks we know that the propagation of light through an inhomogeneous medium is strongly influenced by the refractive index distribution. We experimentally investigated this phenomenon with the purpose of realizing if such propagation along a free-space path may induce a useful randomness. An intuition of such effect manifested during the campaigns for the experiments we carried out at the Canarias on the quantum Communications along extremely long links [1, 2]. The atmospheric turbulence in the path is very strong, preventing for example the direct application of interferometry [3]. However, the effect of turbulence is crucial there for the application of a method that exploits brief moments of high transmissivity for good communication [2]. We tried to turn it here instead into a useful resource for randomness.
FIG. 1. The experiment was set up between the islands of La Palma and Tenerife where a laser beam (with λ = 810 nm) was exchanged between the two islands. After propagating across a 143 km Free Space Optical link, the wavefront of the beam features a randomly composed speckle pattern as consequence of the distortions induced by the atmosphere.

The experiment we describe here was set between the two islands of La Palma and Tenerife: on the rooftop of the Jacobus Kaptein Telescope (JKT) building at an altitude of 2360 m; our transmitting telescope for the Quantum Communication was aimed to send a continuous laser beam towards the ESA Optical Ground Station (OGS) 143 km far away, at Izana, near the mount Teide, see Figure 1. The telescope -- that was designed and realized in Padova -- is a refractor based on a 230 mm aspheric singlet. In the path, the turbulent atmosphere is comparable to a dynamic volumetric scatterer and the electromagnetic field is subjected to phase delays and amplitude fluctuations, induced by the inhomogeneities of the refractive index of the air [4–6]. The receiver then observes a beam profile which does not feature the typical intensity Gaussian distribution, rather a collection of clear and dark spots of irregular shape, the so-called speckle pattern. The speckle pattern evolves according the unpredictable dynamic of the turbulence as consequence of the random walks the electromagnetic field suffers while propagating. Therefore at the receiving plane a continuously and randomly evolving distribution of speckles was acquired with a CMOS camera and for every frame one has a variable number of spots randomly taking different spatial configurations [7].

Randomness is then extracted by using the geometrical complexity of the frames evaluating the centers of mass, the so-called centroids, of those speckle areas with the same intensity. For the implementation of the method the relevant pixels in CCD are labelled sequentially with an index s, s ∈ {1, . . . , N}, the nf  speckle centroids of the frame f are elaborated, an ordered sequence Sf = {s, s, . . . , snf } with s1 < s2 < · · · < snf  is formed, by considering then the pixels where a centroid falls in. The pixel grid can be regarded as the classical collection of urns where the turbulence randomly throws balls (the centroids) in, see Figure 2. Because of the random nature of the process, the centroids visit every part of the grid with the same probability. A given frame f  “freezes” one Sf  out of the
possible and equally likely sequences of nf centroids. Among all of combinations, a given Sf can be univocally identified with its lexicographic index I (Sf )
with 0 ≤ I (Sf ) ≤ Tf  - 1. Basically, (2) enumerates all the possible arrangements which succeed a given centroids configuration. As an uniform RNG is supposed to yield numbers identically and independently distributed (i.i.d.) in a range [X,Y ], as this method generates a random integer in the range [0, Tf - 1]. In order then to optimize the conversion from integer to random bits without introducing any bias, an efficient algorithmic procedure was applied to the bits [8].
FIG. 2. (click on the figure to view higher resolution) The figure represents a scheme of the mechanism employed to extract randomness from the frames of the captured video. Every frame features a different spatial disposition of centroids (the yellow crosses). To every centroid configuration, a univocal lexicographic index is associated. The lexicographic index then is converted in random bits.

In this proof of principle, a generation rate of 400 kbit/s was achieved but it can be easily enhanced by using cameras with higher resolutions. Another point, worth to be stressed, is that this method does not rely on sensitive and hardly detectable processes which require extremely tuned hardware: indeed unavoidable hardware non-idealities can induce bits dependencies and bias. In addition, from the theoretical point of view, the strength of the method lies in the fact the dynamic of turbulent atmosphere on such a long link represents a physical process which is practically impossible to be predicted, both analytically (at the present time only statical models are given) and numerically (it would require an unbounded computational power).

In addition to a sound knowledge of the physical process employed, it is necessary to apply statistical tests in order to exclude the presence of defects caused by a faulty hardware. This has been done by applying the most stringent test batteries for randomness such as the Alphabit and Rabbit batteries belonging to the TESTU01, the NIST SP-800-22 suite and the AIS31 suite. All the tests were successfully passed.

The presented procedure then could be an efficient method to generate random numbers to be employed in long range QC setups. More in detail, bits generated in this way could be used in connection with other protocols involving Quantum Random Number Generator: for example in the first well known experiment of randomness expansion by means of non-locality [9] the initial seed was obtained by mixing numbers obtained with several generators including atmospheric radio electromagnetic noise. Finally, the extraction algorithm can be easily adapted to other paradigms involving spatial random complex patterns.

References:
[1] Ivan Capraro, Andrea Tomaello, Alberto Dall’Arche, Francesca Gerlin, Ruper Ursin, Giuseppe Vallone, Paolo Villoresi, "Impact of turbulence in long range quantum and classical communication". Physical Review Letters, 109, 200502, (2012). Abstract.
[2] Giuseppe Vallone, Davide Marangon, Matteo Canale, Ilaria Savorgnan, Davide Bacco, Mauro Barbieri, Simon Calimani, Cesare Barbieri, Nicola Laurenti, Paolo Villoresi, "Turbulence as a Resource for Quantum Key Distribution in Long Distance Free-Space Links". arXiv:1404.1272 [quant-ph] (2014).
[3] Cristian Bonato, Alexander V. Sergienko, Bahaa E. A. Saleh, Stefano Bonora, Paolo Villoresi, "Even-Order Aberration Cancellation in Quantum Interferometry". Physical Review Letters, 101, 233603 (2008). Abstract.
[4] Larry C. Andrews and Ronald L. Phillips, "Laser beam propagation through random media", volume 152 (SPIE press, 2005). 
[5] R. L. Fante, "Electromagnetic beam propagation in turbulent media". Proceedings of the IEEE, 63, 1669,(1975). Abstract.
[6] R. L. Fante, "Electromagnetic beam propagation in turbulent media - An update". Proceedings of the IEEE, 68, 1424 (1980). Abstract.
[7] Davide G. Marangon, Giuseppe Vallone, Paolo Villoresi, "Random bits, true and unbiased, from atmospheric turbulence". Scientific Reports, 4 : 5490 (2014). Full Article.
[8] Peter Elias. "The efficient construction of an unbiased random sequence". Annals of Mathematical Statistics, 43, 865 (1972). Full Article.
[9] S. Pironio, A. Acín, S. Massar, A. Boyer de la Giroday, D.N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T.A. Manning,  C. Monroe. "Random numbers certified by Bell’s theorem". Nature, 464, 1021 (2010). Abstract.

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