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2Physics

2Physics Quote:
"About 200 femtoseconds after you started reading this line, the first step in actually seeing it took place. In the very first step of vision, the retinal chromophores in the rhodopsin proteins in your eyes were photo-excited and then driven through a conical intersection to form a trans isomer [1]. The conical intersection is the crucial part of the machinery that allows such ultrafast energy flow. Conical intersections (CIs) are the crossing points between two or more potential energy surfaces."
-- Adi Natan, Matthew R Ware, Vaibhav S. Prabhudesai, Uri Lev, Barry D. Bruner, Oded Heber, Philip H Bucksbaum
(Read Full Article: "Demonstration of Light Induced Conical Intersections in Diatomic Molecules" )

Sunday, August 28, 2016

The Real-Space Collapse of a Two Dimensional Polariton Gas

Photos of some of the authors -- From left to right: (top row) Lorenzo Dominici, Dario Ballarini, Milena De Giorgi; (bottom row) Blanca Silva Fernández, Fabrice Laussy, Daniele Sanvitto.

Authors:
Lorenzo Dominici1, Mikhail Petrov2, Michal Matuszewski3, Dario Ballarini1, Milena De Giorgi1, David Colas4, Emiliano Cancellieri5,6, Blanca Silva Fernández1,4, Alberto Bramati6, Giuseppe Gigli1,7, Alexei Kavokin2,8,9, Fabrice Laussy4,10, Daniele Sanvitto1.

Affiliation:
1CNR NANOTEC—Istituto di Nanotecnologia, Lecce, Italy,
2Spin Optics Laboratory, Saint Petersburg State University, Russia,
3Institute of Physics, Polish Academy of Sciences, Warsaw, Poland,
4Física Teorica de la Materia Condensada, Universidad Autónoma de Madrid, Spain,
5Department of Physics and Astronomy, University of Sheffield, UK,
6Laboratoire Kastler Brossel, UPMC-Paris 6, ÉNS et CNRS, France,
7Università del Salento, Dipartimento di Matematica e Fisica “Ennio de Giorgi”,  Lecce, Italy,
8CNR-SPIN, Tor Vergata, Rome, Italy,
9Physics and Astronomy, University of Southampton, UK,
10Russian Quantum Center, Moscow Region, Skolkovo, Russia.

Can photons in vacuum interact?
The answer is not, since the vacuum is a linear medium where electromagnetic excitations and waves simply sum up, crossing themselves with no interaction. There exist a plenty of nonlinear media where the propagation features depend on the concentration of the waves or particles themselves. For example travelling photons in a nonlinear optical medium modify their structures during the propagation, attracting or repelling each other depending on the focusing or defocusing properties of the medium, and giving rise to self-sustained preserving profiles such as space and time solitons [1,2] or rapidly rising fronts such as shock waves [3,4].

One of the highest nonlinear effects can be shown by photonic microcavity (MC) embedding quantum wells (QWs), which are very thin (few tens of atomic distances) planar layers supporting electronic dipolar oscillations (excitons). What happens when a drop of photons, like a laser pulse, is trapped in a MC between two high reflectivity mirrors, and let to interact during this time with the electromagnetic oscillations of the QWs? If the two modes, photons and excitons, are tuned in energy each with the other, they cannot exist independently anymore and the result is the creation of a mixed, hybrid fluid of light and matter, which are known as the polaritons [5].

More specifically, we study the two-dimensional fluids of microcavity exciton polaritons, which can be enumerated among quantum or bosonic gases, and their hydrodynamics effects. Things become pretty nice since these polaritons behave partially as photons, in their light effective masses and fast speeds, and partially as excitons, with strong nonlinear interactions which can be exploited, for example, in all-optical transistors and logic gates [6]. Moreover, some photons continuously leak-out of the microcavity, bringing with them the information on the internal polariton fluid which can be on the one hand more straightforwardly studied with respect, for example, to atomic Bose-Einstein condensates, on the other hand making them out-of-equilibrium bosonic fluids.
Figure 1 (click on the image to view with higher resolution): Snapshots of the polariton fluid density and phase at significant instants. The amplitude and phase maps (the dashed circles depict the initial pump spot FWHM) have been taken at time frames of 0 ps, 2.8 ps and 10.4 ps, which correspond, respectively, to the pulse arrival, the ignition of the dynamical peak and its maximum centre density. The Figure has been extracted from Ref. [7].

In a recent study [7], we point out a very intriguing and unexpected effect, the dynamical concentration of the initial photonic pulse, upon its conversion into a polariton drop of high density. The accumulation of the field in a robust bright peak at the centre, as represented in Figure 1, is indeed surprising because it is at odds with the repulsive interactions of polaritons, which are expected to lead only to the expansion of the polariton cloud. The global phenomenology is spectacular because it is accompanied with the initial Rabi oscillations of the fluid [8,9] on a sub-picosecond scale, the formation of stable ring dark solitons [10,11], and the irradiation of planar ring waves on the external regions. Given the circular symmetry of the system, all these features can be represented in the time-space charts of Figure 2, where a central cross cut of the polariton cloud is represented during time.
Figure 2 (click on the image to view with higher resolution): Time-space charts of the polariton redistribution during time, for both the amplitude (a) and phase (b). The y-axis represents a central cross-cut of the circular-symmetry of the system and the x-axis represents time with a sample stepof 50 fs. Initially the polariton fluid oscillates with a Rabi period of about 800 fs (vertical stripes in the map), while the central density rapidly decays to zero before starting to rise as a bright peak. The two solid lines in both charts mark the phase disturbance delimiting the expanding region with large radial phase-gradient. The Figure has been extracted from Ref. [7].

From an application-oriented perspective we can devise features such as the enhancement ratio of the centre density with respect to the initial one (up to ten times in some experiments), the localization or shrinking factor of the original size (up to ten times as well), and the response speed (few picosecond rise time) and stability time (few tens of picosecond, well beyond the initial pulse length). These features can be tuned continuously with the intensity of the source laser pulse. Figure 3 reports the time dependence of the total population and of the relative centre density in one exemplificative case. The experiments have been reported in Nature Communications [7] and deserve, at least in a divulgative context, its own definition, which effect we like to refer to as the 'polariton backjet'. Indeed, its features are such to intuitively resemble the backjet of a water drop upon a liquid surface, while we devised the physics at the core as a collective polaron effect. This consists in the heating of the semiconductor lattice, resulting in the dynamical redshift of the exciton resonance. It is an interesting case of retarded nonlinearity inversion, leading to the self-sustained localization of the polariton condensate.
Figure 3. Total population and centre density versus time. Blue line are the experimental data of the area-integrated emission intensity, and the black line is a fit based on a model of coupled and damped oscillators. The red curve to be plotted on the right axis is the centre density versus time relative to that at the time of pulse arrival. The real enhancement factor obtained here in the centre density is 1.5, reached in a rise time of t = 10 ps. The Figure has been extracted from Ref. [7] Supplementary information.

The results have been obtained on a very high-quality QW-MC sample (quality factor of 14000) and upon implementing a state-of-the-art real-time digital holography setup. This latter is based on the coherence characteristics of the resonant polariton fluid and the possibility of retrieving its amplitude and phase distribution during ultrafast times upon the interference of the device emission with the laser pulse itself. Indeed this allowed also to prepare other interesting experiments dedicated to peculiar phenomena, such as the Rabi oscillations and their coherent [8] or polarization control [9] and the integer and half-integer quantum vortices [12] which can be excited on the polariton fluid. For most of these cases we could retrieve the complex wavefunction (which is given by an amplitude and phase) of the polariton fluid, with time steps of 0.1 or 0.5 ps and space steps as small as 0.16 micrometers. Fundamentally it is like making a movie on the micrometer scale with a 1.000.000.000.000 slow-motion ratio, as in the following video:



The fabrication and use of high quality microcavity polariton devices coupled to the most advanced characterization technique is opening a deep insight on fundamental properties of the coupling between light and matter and into exotic phenomena linked to condensation, topological states and many-body coherent and nonlinear fluids. Applications can be expected on the front of new polariton lasers, sub-resolution pixels, optical storage and clocks, data elaboration and multiplexing, sensitive gyroscopes, polarization and angular momentum shaping for optical tweezers and advanced structured femtochemistry.

References:
[1] S. Barland, M. Giudici, G. Tissoni, J. R. Tredicce, M. Brambilla, L. Lugiato, F. Prati, S. Barbay, R. Kuszelewicz, T. Ackemann, W. J. Firth, G.-L. Oppo, "Solitons in semiconductor microcavities", Nature Photonics, 6, 204–204 (2012). Abstract.
[2] Stephane Barland, Jorge R. Tredicce, Massimo Brambilla, Luigi A. Lugiato, Salvador Balle, Massimo Giudici, Tommaso Maggipinto, Lorenzo Spinelli, Giovanna Tissoni, Thomas Knödl, Michael Miller, Roland Jäger, "Cavity solitons as pixels in semiconductor microcavities", Nature, 419, 699–702 (2002)  Abstract.
[3] Wenjie Wan, Shu Jia, Jason W. Fleischer, "Dispersive superfluid-like shock waves in nonlinear optics", Nature Physics, 3, 46–51 (2006). Abstract.
[4] N. Ghofraniha, S. Gentilini, V. Folli, E. DelRe, C. Conti, "Shock waves in disordered media", Physical Review Letters, 109, 243902 (2012). Abstract.
[5] Daniele Sanvitto, Stéphane Kéna-Cohen, "The road towards polaritonic devices", Nature Materials (2016). Abstract.
[6] D. Ballarini, M. De Giorgi, E. Cancellieri, R. Houdré, E. Giacobino, R. Cingolani, A. Bramati, G. Gigli, D. Sanvitto, "All-optical polariton transistor", Nature Communications, 4, 1778 (2013). Abstract.
[7] L. Dominici, M. Petrov, M. Matuszewski, D. Ballarini, M. De Giorgi, D. Colas, E. Cancellieri, B. Silva Fernández, A. Bramati, G. Gigli, A. Kavokin, F. Laussy,  D. Sanvitto, "Real-space collapse of a polariton condensate", Nature Communications, 6, 8993 (2015). Abstract.
[8] L. Dominici, D. Colas, S. Donati, J. P. Restrepo Cuartas, M. De Giorgi, D. Ballarini, G. Guirales, J. C. López Carreño, A. Bramati, G. Gigli, E. del Valle, F. P. Laussy, D. Sanvitto, "Ultrafast Control and Rabi Oscillations of Polaritons", Physical Review Letters, 113, 226401 (2014). Abstract.
[9] David Colas, Lorenzo Dominici, Stefano Donati, Anastasiia A Pervishko, Timothy CH Liew, Ivan A Shelykh, Dario Ballarini, Milena de Giorgi, Alberto Bramati, Giuseppe Gigli, Elena del Valle, Fabrice P Laussy, Alexey V Kavokin, Daniele Sanvitto "Polarization shaping of Poincaré beams by polariton oscillations", Light: Science & Applications, 4, e350 (2015). Abstract.
[10] Yuri S. Kivshar, Xiaoping Yang, "Ring dark solitons", Physical Review E, 50, R40–R43 (1994). Abstract.
[11] A S Rodrigues, P G Kevrekidis, R Carretero-González, J Cuevas-Maraver, D J Frantzeskakis, F Palmero, "From nodeless clouds and vortices to gray ring solitons and symmetry-broken states in two-dimensional polariton condensates", Journal of Physics: Condensed Matter, 26, 155801 (2014). Abstract.
[12] Lorenzo Dominici, Galbadrakh Dagvadorj, Jonathan M. Fellows, Dario Ballarini, Milena De Giorgi, Francesca M. Marchetti, Bruno Piccirillo, Lorenzo Marrucci, Alberto Bramati, Giuseppe Gigli, Marzena H. Szymańska, Daniele Sanvitto, "Vortex and half-vortex dynamics in a nonlinear spinor quantum fluid", Science Advances, 1, e1500807 (2015). Abstract.

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Sunday, August 21, 2016

Recent Supernova Debris on the Moon

Thomas Faestermann (left) and Gunther Korschinek.

Authors: Thomas Faestermann, Gunther Korschinek

Affiliation: Technische Universität München, 85748 Garching, Germany.

Stars with a mass of more than about 8 times the solar mass usually end in a supernova explosion (SN). 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. The interstellar space is not empty but contains dust and atomic particles, of course in minuscule densities.

A SN is cleaning up the surrounding space such that empty bubbles (around 0.06 atoms per cm3) are formed surrounded by denser space (around 10 atoms per cm3). The sun is embedded in a so called local bubble [1], indicating that one or even more SNe should have happened near the solar system in the past. Considering these ideas we have started already in the past to search for SN traces on our Earth. The best suited isotope for such a signature is 60Fe. It has a half-life of 2.6 Myr [2] and it is not produced naturally on Earth, however it is also formed in small amounts by cosmic rays in interplanetary dust particles.

To detect and measure such extremely tiny amounts of 60Fe an ultrasensitive method is needed. Accelerator mass spectrometry (AMS) is the only choice in this case. We have developed this method for many years using the Munich tandem accelerator, and achieve, besides a facility in Australia, the highest sensitivity worldwide [3]. The principle is the following: negative ions are formed in an ion source, acceleration with a voltage of a few kV and then pass a combination of electric and magnetic fields as in a conventional mass spectrometer. Subsequently they are accelerated in the tandem accelerator to a high velocity on the order of 7% of the speed of light. In the tandem the negative ions traverse a thin carbon foil where they lose a certain number of electrons to become multiply charged positive ions.

This process is so effective that absolutely no interfering molecules can survive. Thus a typical limitation in conventional mass spectrometry, molecular background, vanishes. In addition, because of the high energy of the ions, nuclear physics techniques are applied to reduce drastically possible interferences of stable isobars. In our case it is 60Ni in our iron samples which is suppressed that much that an isotopic ratio 60Fe/Fe of a few times 10-17 can still be measured.

Our first studies in the past were focused on deep sea ferromanganese crusts. These depositions are very slowly growing, around 2 to 3 mm/Myr, on the bottom of the oceans, and accumulate elements present in the ocean water. As they collect also 10Be, a radioactive isotope with a half-life of 1.387 Myr, formed by cosmic rays on Nitrogen and Oxygen in our atmosphere, samples taken from different depths in the crust can be dated via the decreasing concentration of 10Be in deeper layers. The results of the most conclusive studies [4,5] are shown in fig.1.
Figure 1: (click on figure to view with higher resolution) The 60Fe/Fe concentrations as measured in different depths of the ferromanganese crust 237KD (red points). The peak of an enhanced 60Fe/Fe concentration at an age of around 2-3 Myr is due to the flux of SN-formed 60Fe which has entered the solar system at that time. The blue triangles are from a separate measurement series where we have carefully leached out iron from crust samples and then analyzed. The vertical bars indicate 68% uncertainties, the horizontal ones the age range covered by the sample.

From the measured concentrations we had deduced the 60Fe flux at that time and also the distance of one or more SNe. The critical point was however, the transport of the 60Fe from the upper atmosphere through all atmospheric processes towards the biosphere in the ocean until the final deposition in the ferromanganese crust. To circumvent this difficulty we considered [6] to search for 60Fe in lunar samples collected by US Astronauts between 1969 and 1972 and brought to earth. Together with colleagues from the Rutgers University, New Jersey (USA), we applied successfully for selected sample material from the astronomical laboratory of the Johnson space center (NASA).

An enhanced 60Fe concentration in lunar material would be a clear proof of our previous measurements and the conclusions drawn. It must have been deposited everywhere in our solar system, on all the planets and their moons. In addition, the total amount of 60Fe would provide solid data for the fluence and also the distance of the SNe because the 60Fe has been collected directly on the surface of the Moon.

The drawback is however that the moon does not deliver the chronological information like the crust samples. The lunar surface (regolith) is constantly stirred and mixed by the impact of micrometeorites (a process called gardening) and also sporadic impacts by full-sized meteorites, thus losing any precise time information. A further drawback is that 60Fe is also formed by the much higher cosmic ray flux via nuclear reactions on Ni which is present in lunar regolith, albeit only in tiny concentrations. To quantify this contribution we compared the lunar data with data from iron meteorites, which have been exposed for many millions of years to cosmic rays, and which we investigated as well. We know that cosmogenic 60Fe is formed by nuclear reactions only on the heaviest stable nickel isotope 64Ni. We know also that another long-lived radioisotope 53Mn (T1/2 = 3.7 Myr) is formed by cosmic rays on stable iron. In the case of additional SN produced 60Fe the concentration ratios of 60Fe/Ni to 53Mn/Fe should be higher in the lunar samples than in the meteoritic data.

Fig. 2 shows the comparison of 11 lunar samples (red points) with meteoritic samples (green points). Instead of concentrations we plot by convention their activity (disintegrations per minute) relative to the amount of the target element Ni and Fe. The meteoritic data follow, as expected, a proportionality (the range between the green lines), indicating that 60Fe like 53Mn is produced by cosmic rays; the scatter of the activities is mainly due to differences in the meteoroid geometry. Most of the lunar samples have 60Fe activities well above the expected relationship of the meteorite samples because of the SN contribution. Only three of the lunar samples have activities comparable to cosmic ray origin; they are from greater depth or have a complicated history; e.g. sample 3 is eroded material from the surface of a rock thus has no SN contribution.
Figure 2: (click on figure to view with higher resolution) The measured activities of 60Fe versus 53Mn in meteoritic and lunar samples. Units are disintegrations per minute per kg Fe and Ni, for 53Mn and 60Fe, respectively. Samples 1 through 11 (red) are lunar samples; the other values (green) are for iron meteorites. The area between the green straight lines indicates the 68% error band for cosmic ray produced 53Mn and 60Fe activities in meteorites.

Any 60Fe signal is expected to be distributed downward due to gardening of the lunar surface [7]. In Fig. 3 we show the SN produced 60Fe concentration (cosmic ray contribution subtracted) as a function of the depth (areal density) of the samples. The deposition of the 60Fe on the lunar surface must have happened on a time scale of Myr, since already considerable gardening has happened and, on the other hand, cannot have happened more than some 3 half-lives, i.e. 8 Myr, ago to be still detectable. Thus it is very likely that it coincides with the 60Fe surplus in the ferromanganese crust, which was collected between 1.7 and 2.6 Myr ago. In a time period of around 2.2 Myr, gardening is expected down to a few g/cm2. It is reasonable, therefore, to integrate the measured 60Fe concentration over this range, in order to estimate the local fluence of 60Fe. Nevertheless we found also elevated concentrations of 60Fe down to a depth of 20 g/cm2 (Fig. 3), indicating possible excavations by meteorites and/or down-slope movements.
Figure 3: (click on figure to view with higher resolution) Depth dependence of the SN produced 60Fe concentration and estimation of the local fluence of  60Fe on the Moon’s surface. The dashed curves represent two different integration scenarios. They symbolize a lower and an upper limit. The error bars indicate a 68% confidence level.

Thus, an inclusion of these deep samples yields an upper limit of 60Fe for the integration to obtain a local interstellar fluence of 60Fe. As the lower limit (smallest depth) we adopted that of sample 4. From the data we can estimate a range for 60Fe/kg soil. Including corrections for the decay, and assuming a uniform spread over the lunar surface we end up with a fluence between 0.8 x 108 atoms/cm2 and 4 x 108 atoms/cm2 which was deposited during the past about 4 Myr. If we assume that this fluence came from a single SN and that the (typical) theoretical 60Fe mass of 2x10-5 solar masses has been ejected and formed dust to penetrate the solar system, then the SN would have happened 300 to 600 light years away.

In conclusion, our results show for the first time that the SN-formed 60Fe has been also collected by the Moon, thus confirming the SN origin of previous measurements of 60Fe on Earth. It delivers also more solid data for the fluence of 60Fe which allow better theoretical estimation of other long-lived radioisotopes released by the SNe around 2 Myr ago. Theoretical considerations interpret our findings as SN activity in an association of young stars. They even seem to find good candidates like the Sco-Cen association [8] where the exploding stars could have been 2 Myr ago at a distance of around 300 light years or the Tuc-Hor association at about 150 light years [9].

In addition, further evidence for the SN activity has been added recently. An enhancement of 60Fe has been found in ocean sediments at an Australian laboratory [10] and by our group [11]. This gives us a much better timing information than the crust and shows that the SN activity lasted for about 1 Myr and started about 2.7 Myr ago. Even in cosmic rays 15 nuclei of 60Fe have been detected with the spectrometer CRIS aboard NASA’s satellite ACE (Advanced Composition Explorer) [12]. The authors conclude that at least two SNs must have occurred within 3000 light years from the sun during the last few Myr. Analysis of the spectra of high-energy cosmic rays leads to similar conclusions [13].

References:
[1] T. W. Berghöfer, D. Breitschwerdt, "The origin of the young stellar population in the solar neighborhood - A link to the formation of the Local Bubble?”, Astronomy & Astrophysics, 390, 299 (2002). Abstract.
[2] K. Knie, T. Faestermann, G. Korschinek, G. Rugel, W. Rühm, C. Wallner, "High-sensitivity AMS for heavy nuclides at the Munich Tandem accelerator”, Nuclear Instruments and Methods in Physics Research B, 172, 717 (2000). Abstract.
[3] G. Rugel, T. Faestermann, K. Knie, G. Korschinek, M. Poutivtsev, D. Schumann, N. Kivel, I. Günther-Leopold, R. Weinreich, M. Wohlmuther, “New Measurement of the 60Fe Half-Life”, Physical Review Letters, 103, 072502 (2009). Abstract.
[4] K. Knie, G. Korschinek, T. Faestermann, E. A. Dorfi, G. Rugel, A. Wallner, "60Fe Anomaly in a Deep-Sea Manganese Crust and Implications for a Nearby Supernova Source”, Physical Review Letters, 93, 171103 (2004). Abstract.
[5] C. Fitoussi, G. M. Raisbeck, K. Knie, G. Korschinek, T. Faestermann, S. Goriely, D. Lunney, M. Poutivtsev, G. Rugel, C. Waelbroeck, A. Wallner, “Search for Supernova-Produced 60Fe in a Marine Sediment”, Physical Review Letters, 101, 121101 (2008). Abstract.
[6] L. Fimiani, D. L. Cook, T. Faestermann, J. M. Gómez-Guzmán, K. Hain, G. Herzog, K. Knie, G. Korschinek, P. Ludwig, J. Park, R. C. Reedy, G. Rugel, “Interstellar 60Fe on the Surface of the Moon", Physical Review Letters, 116, 151104 (2016). Abstract.
[7] D.E.Gault, F. Hoerz, D.E. Brownlee, J.B. Hartung, "Mixing of the lunar regolith”, Proc. 5th Lunar Science Conference, Vol. 3, 2365 (1974). Abstract.
[8] D. Breitschwerdt, J. Feige, M. M. Schulreich, M. A. de. Avillez, C. Dettbarn, B. Fuchs,  “The locations of recent supernovae near the Sun from modelling 60Fe transport”, Nature, 532, 73 (2016). Abstract.
[9] Brian J. Fry, Brian D. Fields, John R. Ellis, “Radioactive Iron Rain: Transporting 60Fe in Supernova Dust to the Ocean Floor”,  Astrophysical Journal, 827, 48 (2016). Abstract.       
[10] A. Wallner, J. Feige, N. Kinoshita, M. Paul, L. K. Fifield, R. Golser, M. Honda, U. Linnemann, H. Matsuzaki, S. Merchel, G. Rugel, S. G. Tims, P. Steier, T. Yamagata, S. R. Winkler “Recent near-Earth supernovae probed by global deposition of interstellar radioactive 60Fe”. Nature, 532, 69 (2016). Abstract.
[11] Peter Ludwig, Shawn Bishop, Ramon Egli, Valentyna Chernenko, Boyana Deneva, Thomas Faestermann, Nicolai Famulok, Leticia Fimiani, José Manuel Gómez-Guzmán, Karin Hain, Gunther Korschinek, Marianne Hanzlik, Silke Merchel, Georg Rugel, “Time-resolved 2-million-year-old supernova activity discovered in Earth’s microfossil record”, PNAS, 113, 9123 (2016). Abstract.
[12] W. R. Binns, M. H. Israel, E. R. Christian, A. C. Cummings, G. A. de Nolfo, K. A. Lave, R. A. Leske, R. A. Mewaldt, E. C. Stone, T. T. von Rosenvinge, M. E. Wiedenbeck, "Observation of the 60Fe nucleosynthesis-clock isotope in galactic cosmic rays", Science, 352, 677 (2016). Abstract.
[13] M. Kachelrieß, A. Neronov, D. V. Semikoz “Signatures of a Two Million Year Old Supernova in the Spectra of Cosmic Ray Protons, Antiprotons, and Positrons”, Physical Review Letters, 115, 181103 (2016). Abstract.

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Sunday, August 14, 2016

Quantum Tunneling of Water in Ultra-Confinement

From Left to Right: (top row) Alexander I. Kolesnikov, George F. Reiter, Narayani Choudhury, Timothy R. Prisk, Eugene Mamontov; (bottom row) Andrey Podlesnyak, George Ehlers,  David J. Wesolowski, Lawrence M. Anovitz.

Authors: Alexander I. Kolesnikov1, George F. Reiter2, Narayani Choudhury3, Timothy R. Prisk4, Eugene Mamontov1, Andrey Podlesnyak5, George Ehlers5, Andrew G. Seel6, David J. Wesolowski4, Lawrence M. Anovitz4

Affiliation:
1Chemical and Engineering Materials Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA,
2Physics Department, University of Houston, Texas, USA,
3Math and Science Division, Lake Washington Institute of Technology, Kirkland, Washington, USA; School of Science, Technology, Engineering and Math, University of Washington, Bothell, Washington, USA,
4Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA,
5Quantum Condensed Matter Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA,
6ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, United Kingdom.

The quantum-mechanical behavior of light atoms plays an important role in shaping the physical and chemical properties of hydrogen-bonded liquids, such as water [1,2]. Tunneling is a classic quantum effect in which a particle moves through a potential barrier despite classically lacking sufficient energy to transverse it. The tunneling of hydrogen atoms in condensed matter systems has been observed for translational motions through metals, anomalous proton diffusion in water phases, and in the rotation of methyl and ammonia groups, and Gorshunov et al. inferred on the basis of terahertz spectroscopy measurements that water molecules inside the mineral beryl may undergo rotational tunneling [3, 4].

The crystal structure of beryl, shown in Figure 1, contains hexagonally shaped nanochannels just wide enough to contain single water molecules. In a recently published paper [5], we presented evidence from inelastic neutron scattering experiments and ab initio computational modeling that these water molecules do, in fact, undergo rotational tunneling at low temperatures. In their quantum-mechanical ground state, the hydrogen atoms are delocalized among the six symmetrically-equivalent positions about the channels so that the water molecule on average assumes a double-top like shape.
Figure 1: The crystal structure of beryl

The first set of inelastic neutron scattering experiments was performed using the CNCS and SEQUOIA spectrometers located at Oak Ridge National Laboratory's Spallation Neutron Source. A number of transitions are observed in the energy spectrum that can only be attributed to quantum-mechanical tunneling. Alternative origins for these transitions, such as vibrational modes or crystal field effects of magnetic impurities, are inconsistent with the temperature and wavevector dependence of the energy spectrum. However, they are consistent with an effective one-dimensional orientational potential obtained from Density Functional Theory and Path Integral Molecular Dynamics calculations.

To confirm these results we performed neutron Compton scattering of experiments on beryl single-crystals using the VESUVIO spectrometer at the Rutherford Appleton Laboratory. In this technique, a high-energy incident neutron delivers an impulsive blow to a single atom in the sample, transferring a sufficiently large amount of kinetic energy to the target atom that it recoils freely from the impact. The momentum distribution n(p) of the hydrogen atoms may then be inferred from the observed dynamic structure factor S(Q, E) in this high-energy limit, providing a direct probe of the momentum-space wavefunction of the water hydrogens in beryl.
Figure 2: the measured momentum distribution n(p) in neutron Compton scattering experiments.

The tunneling behavior of the water protons is revealed in our neutron Compton scattering experiments by the measured momentum distribution n(p), illustrated as a color contour plot in Figure 2. The variation of n(p) with angle is due to vibrations of the O—H covalent bond. If it is true that water molecules undergo rotational tunneling between the six available orientations, then n(p) will include oscillations or interference fringes as a function of angle. On the other hand, if the water molecules are incoherently and randomly arranged among the possible positions, then no such interference fringes will be observed. As marked by the yellow line in Figure 2, the interference fringes were clearly observed in our experiment! The water molecule is, therefore, in a coherent superposition of states over the six available orientational positions.

Taken together, these results show that water molecules confined in the channels in the beryl structure undergo rotational tunneling, one of the hallmark features of quantum mechanics.

References:
[1] Michele Ceriotti, Wei Fang, Peter G. Kusalik, Ross H. McKenzie, Angelos Michaelides, Miguel A. Morales, Thomas E. Markland, "Nuclear Quantum Effects in Water and Aqueous Systems: Experiment, Theory, and Current Challenges", Chemical Reviews, 116, 7529 (2016). Abstract.
[2] Xin-Zheng Li, Brent Walker, Angelos Michaelides, "Quantum nature of the hydrogen bond", Proceedings of the national Academy of Sciences of the United States of America, 108, 6369 (2011). Abstract.
[3] Boris P. Gorshunov, Elena S. Zhukova, Victor I. Torgashev, Vladimir V. Lebedev, Gil’man S. Shakurov, Reinhard K. Kremer, Efim V. Pestrjakov, Victor G. Thomas, Dimitry A. Fursenko, Martin Dressel, "Quantum Behavior of Water Molecules Confined to Nanocavities in Gemstones", The Journal of Physical Chemistry Letters, 4, 2015 (2013). Abstract.
[4] Boris P. Gorshunov, Elena S. Zhukova, Victor I. Torgashev, Elizaveta A. Motovilova, Vladimir V. Lebedev, Anatoly S. Prokhorov, Gil’man S. Shakurov, Reinhard K. Kremer, Vladimir V. Uskov, Efim V. Pestrjakov, Victor G. Thomas, Dimitri A. Fursenko, Christelle Kadlec, Filip Kadlec, Martin Dressel, "THz–IR spectroscopy of single H2O molecules confined in nanocage of beryl crystal lattice", Phase Transitions, 87, 966 (2014). Abstract.
[5] Alexander I. Kolesnikov, George F. Reiter, Narayani Choudhury, Timothy R. Prisk, Eugene Mamontov, Andrey Podlesnyak, George Ehlers, Andrew G. Seel, David J. Wesolowski, Lawrence M. Anovitz, "Quantum Tunneling of Water in Beryl: A New State of the Water Molecule", Physical Review Letters, 116, 167802 (2016). Abstract.

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Sunday, July 31, 2016

There Are Many Ways to Spin a Photon

Left to Right: Paul Eastham, Kyle Ballantine, John Donegan 

 Authors: Kyle E. Ballantine, John F. Donegan, Paul R. Eastham

 Affiliation: School of Physics and CRANN, Trinity College Dublin, Ireland

Can a boson, like a photon, have half-integer angular momentum? In three dimensions, no. The familiar quantum numbers l and ml, for orbital angular momentum; s and ms, for spin angular momentum; and j and mj for the resulting total angular momentum, are all integers. However, a beam of light singles out a particular direction in space. The electric field, which must be perpendicular to this direction, is essentially a two-dimensional vector, specified over the plane perpendicular to the beam. Particles moving in two dimensions can have strange properties, including quantum numbers which are fractions of those expected in the general three-dimensional setting [1]. Given the restricted geometry of a beam of light, and the analogy with quantum mechanics in two-dimensions, it is intriguing to ask whether we could see similar effects there.

In our recent paper [2] we find that this is indeed the case: we show there is a physically reasonable form of angular momentum in a beam of light, which has an unexpected half-integer spectrum.

The study of light’s angular momentum [3] is an old one, going back to Poynting’s realization that circularly polarized light carries angular momentum because the electric field vector rotates. This spin angular momentum is one contribution to the total angular momentum carried by a light wave; the other is the orbital angular momentum, which arises from the spatial variation of the wave amplitude. We were led to the idea of the half-quantized angular momentum by the structure of beams generated by conical refraction, which is shown in Figure 1.

Figure 1: Cross section of conically refracted beam. The beam is a hollow cylinder, as can be seen from the intensity plotted in the gray scale. The direction of linear polarization at each point around the beam is shown by the red arrows; it takes a half-turn for one full turn around the beam. Figure adapted from [2].

This exotic form of refraction was discovered in our own institution, Trinity College Dublin, almost 200 years ago, by William Rowan Hamilton and Humphrey Lloyd. They showed that on passing through a “biaxial” crystal a ray of light became a hollow cylinder [4]. At each point around the cylinder the light is linearly polarised, meaning the electric field oscillates in a particular direction. However, if we take one full turn around the beam, the direction of linear polarisation takes only a half-turn. Conical refraction has introduced a topological defect into the beam [5]: a knot in the wave amplitude, which cannot be untied by smooth deformations of polarisation or phase. Similar transformations can be achieved using inhomogeneous polarizers called q-plates.

Any beam of light a beam can be decomposed into beams which have an exact value of some angular momentum. These are eigenstates of that angular momentum, defined by the property that when they are rotated they change only by a phase. For spin angular momentum, the relevant rotation is that of the electric field vectors, while for orbital angular momentum, it is a rotation of the amplitude. These rotations are both symmetries of Maxwell’s equations in the paraxial limit, so that they can be performed independently, or in any combination.

Thus the choice of basis for optical angular momentum, and the definition of the angular momentum operators, is not unique. If we consider beams which are rotationally symmetric under an equal rotation of the image and the polarisation, we get the conventional total angular momentum: the sum of orbital and spin quantum numbers, which is always an integer multiple of Planck’s constant, ħ. We showed that an equally valid choice is those beams which are symmetric when we rotate the image by one angle, and simultaneously rotate the polarisation by a half-integer multiple of that angle. The conically refracted beam is exactly of this form. The corresponding total angular momentum is a sum of the orbital contribution and one-half of the spin contribution, so that these beams have a total angular momentum which is shifted by ħ/2.
Figure 2: (A) Average angular momentum per photon as measured by interferometer. As the input beam is varied the average angular momentum goes from 1/2 to -1/2 in units of Planck's constant. (B) The quantum noise in the measured angular momentum. The minimum value corresponds exactly 1/2 of Planck’s constant being carried by each photon. (This Figure is reproduced from Ref.[2] ).

To measure this effect we built an interferometer, similar to the design used by Leach et al. [6]. The angular momentum eigenstates which make up any beam are, by definition, invariant under rotations up to a phase. When we rotate the beam, this phase means each component will interfere either constructively or destructively with the unrotated beam, so we can infer the amplitude of that component from the resulting intensity. In our experiment we rotated the amplitude and the polarisation by different amounts, which allowed us to measure the different types of angular momentum described above. The experimental results are shown in Fig 2(A). We use a quarter-wave plate (QWP) to vary the polarisation of our laser, and generate conically refracted beams with opposite handedness. As we move gradually between these beams the average of the relevant angular momentum varies between 1/2 and -1/2, in units of ħ.

Since photons with varying integer angular momentum could combine to give a fractional average, we wanted to show each photon carries exactly this amount. Rather than measuring single photons individually, we adopted a technique previously used to measure the charge of quasiparticles in the fractional quantum Hall effect [7]. This relies on the fact that in a current of particles there will be some inherent quantum noise, due to the discrete arrival of those particles, which is proportional to the size of the quantum of that current. We measured the quantum noise in the output angular momentum current of the interferometer described above. Fig 2(B) shows this noise, normalised in such a way that the minimum is the angular momentum carried by each photon, plus any excess classical noise still present. When the input beam is in either conical refraction state, this value dips well below one and approaches one half, demonstrating the half-integer angular momentum of each photon.

The possibility of exotic “fractional” quantum numbers [1] in two-dimensional quantum mechanics is known to occur in practice in electronic systems, and specifically in the quantum Hall effect. Our work is the first to show such behaviour for photons, and suggests that other aspects of this physics might be possible with light. Quantum optics gives the ability to transmit quantum information over large distances and process it at very high speeds. We have identified a new form of a familiar property, optical angular momentum, that may prove useful in such developments, and gives a new twist in our understanding of light.

References:
[1] Frank Wilczek, "Magnetic Flux, Angular Momentum, and Statistics", Physical Review Letters, 48, 1144 (1982). Abstract.
[2] Kyle E. Ballantine, John F. Donegan, Paul R. Eastham, "There are many ways to spin a photon: Half-quantization of a total optical angular momentum", Science Advances, 2, e1501748. Abstract.
[3] L. Allen, Stephen M. Barnett, Miles J. Padgett, "Optical Angular Momentum" (Institute of Physics Publishing, 2003).
[4] M. V. Berry, M. R. Jeffrey, "Conical diffraction: Hamilton's diabolical point at the heart of crystal optics", Progress in Optics, 50, 13 (2007). Abstract.
[5] J. F. Nye, "Lines of circular polarization in electromagnetic wave fields", Proceedings of the Royal Society A, 389, 279 (1983). Abstract.
[6] Jonathan Leach, Johannes Courtial, Kenneth Skeldon, Stephen M. Barnett, Sonja Franke-Arnold, Miles J. Padgett. "Interferometric Methods to Measure Orbital and Spin, or the Total Angular Momentum of a Single Photon", Physical Review Letters, 92, 013601 (2004). Abstract.
[7] C. L. Kane, Matthew P. A. Fisher, "Nonequilibrium noise and fractional charge in the quantum Hall effect", Physical Review Letters, 72, 724 (1994). Abstract.

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Sunday, July 24, 2016

Relativistic Laser-Driven Table-top Intense Terahertz Transition Radiation Sources

From Left to Right: Guo-Qian Liao, Yu-Tong Li, Xiao-Hui Yuan

Authors: Guo-Qian Liao1, Yu-Tong Li1,4, Hao Liu1, Yi-Hang Zhang1, Xiao-Hui Yuan2,4, Xu-Lei Ge2, Su Yang2, Wen-Qing Wei2, Wei-Min Wang1,4, Zheng-Ming Sheng2,3,4, Jie Zhang2,4

Affiliation:
1Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, China
2Key Laboratory for Laser Plasmas (MoE) and Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
3SUPA, Department of Physics, University of Strathclyde, Glasgow, United Kingdom,
4Collaborative Innovation Center of IFSA (CICIFSA), Shanghai Jiao Tong University, Shanghai, China.

Intense terahertz (THz) radiation sources, the frequency of which lies between far-infrared waves and microwaves in the electromagnetic spectrum, are significantly important for THz sciences and applications in many interdisciplinary fields [1]. Currently THz radiation with energies of >100 μJ/pulse is usually obtained with huge-sized accelerators [2]. Laser-plasma interactions provide a unique opportunity to achieve tabletop high-field THz radiation sources. With the relativistic electron beams accelerated by laser wakefields in gas targets, Leemans et al. have obtained ∼0.3 μJ THz pulses through transition radiation [3].

Strong THz radiation from laser-solid interactions has attracted much interest [4,5]. Compared with gas targets, fast electron beams from solid foil targets have much higher charge, up to nC or even near μC. Usually the bunch length of the electron beam accelerated by a femtosecond laser pulse is of the order of ~10 μm, which is smaller than the wavelength of THz radiation. Therefore, the forward fast electrons will induce coherent transition radiation (CTR) in the THz regime when crossing the rear surface-vacuum boundary (see Figure 1). This has so far not yet been verified experimentally.
Figure 1: Illustration of the THz generation due to the CTR of fast electron beams at the rear surface of a foil target irradiated by intense laser pulses.

In our recent work [6], we have experimentally demonstrated intense coherent THz transition radiation by laser-driven, relativistic electron beams crossing the rear surface of a thin solid foil. The experiment was carried out on the femtosecond laser system at the Laboratory for Laser Plasma, Shanghai Jiao Tong University. From the rear side of a 5 μm thick metal foil irradiated by a 2 J/ 30 fs laser pulse, we obtain an intense THz pulse with an energy of ~400 μJ, which is comparable to the energy level of the conventional accelerator based THz sources [2]. The measured THz radiation covers a bandwidth up to 30 THz [see Figure 2(a)], and has an asymmetric “double-wing-like” angular distribution [see Figure 2(b)]. Both CTR-based theoretical calculations and two-dimensional particle-in-cell simulations can well reproduce the experimental measurements.
Figure 2: [click on the image to view with higher resolution(a) Experimentally measured (blue circle dashed) and simulated (black solid) frequency spectra of the THz radiation from the metal foil. (b) Angular distributions of the THz radiation measured (blue circle), simulated (black dashed), and calculated with CTR model (red solid), all of which are normalized by the THz intensity at 75°.

The CTR model predicts that the THz radiation intensity is closely dependent on the target parameters, for example, the size and dielectric property of the target. To verify this, several types of targets are adopted to understand the THz generation. For the mass-limited metal targets, the observed dependence of THz intensity on the target sizes [see Figure 3(a)] can be explained by the CTR model modified by diffraction effect [7]. For the metal-PE double layered targets, we find that there exists an optimal PE thickness when increasing the thickness of the PE layer from 15 μm to 500 μm [see Figure 3(b)]. This can be explained by the CTR model considering the formation-zone effects [8]. Compared with the THz radiation from the PE targets, we find the THz intensity from the targets with a 5 μm thick metal coating at the target rear is dramatically enhanced by over 10 times [see Figure 3(c)]. This is a solid evidence for transition radiation.
Figure 3: [click on the image to view with higher resolution] (a) Experimentally measured THz intensity (blue circles) and theoretically calculated diffraction modification factor D (curves) as a function of target sizes. (b) Measured THz intensity at 75° (black square) and -75° (blue circle) from the metal-PE targets as a function of the thickness of the PE layer. (c) Comparison of the THz signals measured from the 40 μm thick PE targets with or without a 5 μm metal coating at the rear.

The laser-plasma-based THz transition radiation presented here could be a promising tabletop high-energy THz source. Moreover, it may provide a potential diagnostic to infer the spatiotemporal distribution of the high-flux fast electron beams generated in laser-solid interactions.

References:
[1] M. Tonouchi, “Cutting-edge terahertz technology”, Nature Photonics, 1, 97 (2007). Abstract.
[2] Ziran Wu, Alan S. Fisher, John Goodfellow, Matthias Fuchs, Dan Daranciang, Mark Hogan, Henrik Loos, Aaron Lindenberg, “Intense terahertz pulses from SLAC electron beams using coherent transition radiation”, Review of Scientific Instruments, 84, 022701 (2013). Abstract.
[3] W. P. Leemans, C. G. R. Geddes, J. Faure, Cs. Tóth, J. van Tilborg, C. B. Schroeder, E. Esarey, G. Fubiani, D. Auerbach, B. Marcelis, M. A. Carnahan, R. A. Kaindl, J. Byrd, M. C. Martin, “Observation of terahertz emission from a laser-plasma accelerated electron bunch crossing a plasma-vacuum boundary”, Physical Review Letters, 91, 074802 (2003). Abstract.
[4] G. Q. Liao, Y. T. Li, C. Li, L. N. Su, Y. Zheng, M. Liu, W. M. Wang, Z. D. Hu, W. C. Yan, J. Dunn, J. Nilsen, J. Hunter, Y. Liu, X. Wang, L. M. Chen, J. L. Ma, X. Lu, Z. Jin, R. Kodama, Z. M. Sheng, J. Zhang, “Bursts of terahertz radiation from large-scale plasmas irradiated by relativistic picosecond laser pulses”, Physical Review Letters, 114, 255001 (2015). Abstract.
[5] A. Gopal, S. Herzer, A. Schmidt, P. Singh, A. Reinhard, W. Ziegler, D. Brömmel, A. Karmakar, P. Gibbon, U. Dillner, T. May, H-G. Meyer, G. G. Paulus, “Observation of Gigawatt-class THz pulses from a compact laser-driven particle accelerator”, Physical Review Letters, 111, 074802 (2013). Abstract.
[6] Guo-Qian Liao, Yu-Tong Li, Yi-Hang Zhang, Hao Liu, Xu-Lei Ge, Su Yang, Wen-Qing Wei, Xiao-Hui Yuan, Yan-Qing Deng, Bao-Jun Zhu, Zhe Zhang, Wei-Min Wang, Zheng-Ming Sheng, Li-Ming Chen, Xin Lu, Jing-Long Ma, Xuan Wang, Jie Zhang, “Demonstration of coherent terahertz transition radiation from relativistic laser-solid interactions”, Physical Review Letters, 116, 205003 (2016). Abstract.
[7] C. B. Schroeder, E. Esarey, J. van Tilborg, W. P. Leemans, “Theory of coherent transition radiation generated at a plasma-vacuum interface”, Physical Review E, 69, 016501 (2004). Abstract.
[8] Luke C. L. Yuan, C. L. Wang, H. Uto, “Formation-zone effect in transition radiation due to ultrarelativistic particles”, Physical Review Letters, 25, 1513 (1970). Abstract.

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Sunday, July 17, 2016

Demonstrating Quantum Advantage with the Simplest Quantum System -- Qubit

From left to right: Xiao Yuan, Ke Liu, Xiongfeng Ma, Luyan Sun.

Authors: Xiao Yuan, Ke Liu, Luyan Sun, Xiongfeng Ma

Affiliation:
Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, China.

Along the search for quantum algorithms, the sophisticated quantum speed-up generally arises with delicately designed quantum circuits by manipulating quantum states that contain intricate multipartite correlations. While the essence of quantum correlation originates from coherent superposition of different states, it is natural to expect the essence of quantum advantage to also originate from coherence. This raises a fundamental question: Can quantum advantage be obtained even with the simplest quantum state system, qubit, i.e., superposition of a two level system. The question was answered affirmatively in our recent work published in Physical Review Letters on June 29th [1].

In our everyday life, a classical coin is called p-coin if it outputs a head and a tail with probability p and 1-p respectively. Given an unknown p-coin, a simple yet interesting problem is to construct an f (o)-coin, where f (p) is a given function of p and f(p)∈[0,1]. For example, when f (p)=1/2, a rather simple but heuristic strategy is given by Von Neumann [2]. Flip the p-coin (p ≠ 0) twice. If the outcomes are the same, start over; otherwise, output the second coin value as the 1/2-coin output. In general, such construction processing is called a Bernoulli factory. Solved by Keane and O’Brien [3], it says that not all functions can be constructed classically. Generally speaking, a necessary condition for f(p) being constructible is that f(p) ≠ 0 or 1 when p ∈ (0,1). A simple example is f (p) = 4p (1-p), where we have f (1/2)=1.
Figure 1: Classical and quantum coin.

As shown in Fig.1, a p-coin corresponds to a machine that outputs identically mixed qubit states, ρ= p|0⟩⟨0| + (1-p)|1⟩⟨1|, where p∈[0,1]. In general, such unknown p can also be encoded in a quantum way, |p⟩ = √p |0⟩ + √(1-p) |1⟩, which is called by a quoin. As classical coins can always be constructed via a quoin, a natural question is whether the set of quantum constructible functions (via a quantum Bernoulli factory) is strictly larger than the classical set.

Remarkably, Dale et al. [4] have theoretically proved the necessary and sufficient conditions for quantum Bernoulli factory. Especially for the function f(p) = 4 p (1-p), they proposed a method to construct it by simultaneously measuring two p-quoins. Essentially, entanglement is not necessary for constructing quantum Bernoulli factory. Therefore, we focus on the function f(p) = 4p (1-p) and show the quantum advantage in both theory and experiment with the simplest quantum system.

In practice, we cannot realize exact f(p)-coin due to imperfections, which may cause the realized function classically constructible. However, the number of classical coins N required to construct f(p) generally scales poorly to the inverse of the deviation. Thus, we need to implement high-fidelity state preparation and measurement to reduce the deviation as small as possible in order to faithfully demonstrate the quantum advantage. Superconducting quantum systems have made tremendous progress in the last decade, including a realization of long coherence times, showing great stability with fast and precise qubit manipulations, and demonstrating high-fidelity quantum non-demolition (QND) qubit measurement. Thus, it serves as a perfect candidate for our test.
Figure 2: Experimental setup. (a) Optical image of a transmon qubit located in a trench, which dispersively couples to two 3D Al cavities. (b) Optical image of the single-junction transmon qubit. (c) Scanning electron microscope image of the Josephson junction. (d) Schematic of the device with the main parameters.

The experiment setup is shown in Fig. 2. The necessary high fidelity (~99.6%) and QND qubit detection can be realized with the help of a near-quantum-limited Josephson parametric amplifier [4,5]. A randomized benchmark calibration shows that the single-qubit gate fidelity is about 99.8%, allowing for a highly precise qubit manipulation. Therefore, with the high fidelity state preparation, manipulation and measurement, we are able to achieve fexp (1/2)=0.965. For a special model of the experiment data, we show that more than 105 classical coins are needed for simulating this model, while the average number of quoins for our protocol is about 20.

Our experimental verification sheds light on a fundamental question about what the essential resource for quantum information processing is, which may stimulate the search for more protocols that show quantum advantages without multipartite correlations. Considering the conversion from coherence to multipartite correlation, investigating the power of coherence may also be helpful in understanding the power of multipartite correlation and universal quantum computation.

References:
[1] Xiao Yuan, Ke Liu, Yuan Xu, Weiting Wang, Yuwei Ma, Fang Zhang, Zhaopeng Yan, R. Vijay, Luyan Sun, Xiongfeng Ma, "Experimental Quantum Randomness Processing Using Superconducting Qubits", Physical Review Letters, 117, 010502 (2016). Abstract.
[2] J. Von Neumann, "Various Techniques used in connection with random digits", Journal of Research of the National Bureau of Standards -- Applied Mathematics Series, 12, 36 (1951). PDF File.
[3] M. S. Keane, George L. O’Brien, "A Bernoulli factory", ACM Transactions on Modeling and Computer Simulation, 4, 213 (1994). Abstract.
[4] Howard Dale, David Jennings, Terry Rudolph, Nature Communications, 6, 8203 (2015). Abstract.
[5] M. Hatridge, R. Vijay, D.H. Slichter, John Clarke, I. Siddiqi, "Dispersive magnetometry with a quantum limited SQUID parametric amplifier", Physical Review B, 83, 134501 (2011). Abstract.

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Sunday, July 10, 2016

Nonlinear Medium for Efficient Steady-State Directional White-Light Generation

From Left to Right: (top row) Nils W. Rosemann, Jens P. Eußner, Andreas Beyer, Stephan W. Koch; (bottom row) Kerstin Volz, Stefanie Dehnen, Sangam Chatterjee 
(credit for Sangam's picture: Tim van de Bovenkamp)

Authors: Nils W. Rosemann1,2, Jens P. Eußner2,3, Andreas Beyer1,2, Stephan W. Koch1,2, Kerstin Volz1,2, Stefanie Dehnen2,3, Sangam Chatterjee1,2,4

Affiliations:
1Fachbereich Physik, Philipps-Universität Marburg, Marburg, Germany.
2Wissenschaftliches Zentrum für Materialwissenschaften, Philipps-Universität Marburg, Marburg, Germany.
3Fachbereich Chemie, Philipps-Universität Marburg, Marburg, Germany.
4Institute of Experimental Physics I, Justus-Liebig-University, Giessen, Germany.

Tailored light sources have greatly advanced over the past decades. In particular, the development of light-emitting diodes[1] (LED) was the last milestone in the field of illumination. This includes the virtually omnipresent white LEDs where ultraviolet emitting gallium nitride (GaN) LEDs [2] excite light converting phosphors to cover the visible spectrum. They are reasonably priced and are starting to replace incandescent or compact fluorescent sources for lighting and display applications [3,4].

For many scientific uses, the development of the laser was a comparable milestone [5]. Lasers are light sources with well-defined and well-manageable properties, making them an ideal tool for scientific research. Nevertheless, at some points the inherent (quasi-)monochromaticity of lasers is a drawback. Using a convenient converting phosphor can produce a broad spectrum but also results in a loss of the desired laser properties, in particular the high degree of directionality. To generate true white light while retaining this directionality, one can resort to nonlinear effects like soliton formation [6]. Unfortunately, nonlinear effects usually require large field-strength, thus large-scale, expensive pulsed or high-power lasers. On the route towards a more favorable solution, we recently presented an amorphous cluster compound that converts the infrared (IR) light of a reasonably priced laser diode into a broad visible spectrum while retaining the desired laser properties [7].

The compound contains clusters with a tin-sulfur based core and four organic ligands per formula unit. The core is composed of an adamantane-like scaffold, [Sn4S6]. It has a tetrahedral shape and is thus lacking inversion symmetry. This is accompanied by a random orientation of the four ligands R = 4-(CH2=CH)-C6H4 (Fig. 1a). The ligands consolidate the structure of the core [8,9] and prevent crystallization of the compound, hence prevent any long-range order. As a result, the compound is obtained as an amorphous white powder (Fig. 1b).
Figure 1: (a) Molecular structure of the adamantane-like cluster molecule, with tin and sulfur atoms drawn as blue and yellow spheres, respectively; carbon (grey) and hydrogen (white) atoms are given as wires. (b) Photograph of the as prepared powder.

Upon irradiation with infrared laser light, the compound emits a warm white-light (Fig. 2a). Its spectrum is virtually independent of the excitation wavelength in the range from 725 to 1050 nm. Variation of the laser intensity, however, results in a slight shift of the spectral weight towards higher energies for higher intensities (Fig. 2b). This common impression of a dimming tungsten-halogen light bulb could lead to the assumption that the novel light-emission is also thermal. However, the input-output characteristic of the white-light process scales highly nonlinear. Additionally, the emitted intensity depending on the color temperature of the observed spectra differs vastly from the Stefan-Boltzmann law. These two points exclude a thermal process to be the source of the observed white light. Furthermore, spontaneous emission can be ruled out: exciting the compound above the absorption edge, i.e., with photon energies above 3.0 eV, changes the emitted spectrum drastically.
Figure 2: (a) Photograph of the cluster compound embedded in a polymer and sandwiched between two glass slips. The compound is excited in the bright center spot, using 800nm laser. (b) White-light spectra for different pump intensities, from low (grey) to high intensity (black). For reference, the emission of a black-body emitter at 2856K is shown.

The largest advantage application-wise is found in its directionality, i.e., the angular emission characteristics. When the sample is excited in a transmission like geometry, the spatial distribution of the white-light is found to be very close to that of the driving laser. In combination with the very low threshold of the nonlinear process, this enables the use of this light source for many applications where a broad spectrum and low-etendue are required, e.g., in microscopes or optical coherence tomography systems.

To explain the white-light emitting process, we developed a semi-classical model. This model ascribes the white-light emission to the driven movement of an electron in the clusters ground state potential. During this process, the electron gets accelerated by the IR-laser and subsequent deceleration of the electron leads to the emission of radiation just like Bremsstrahlung. Implementing this process numerically leads to an excellent agreement of theory and experiment. While such anharmonic oscillator models are commonly applied for nonlinear optical phenomena, here, the shape of the simulated ground state potential is completely based on experimentally verified parameters and results from first-principle calculations. This model does not yield the observed directionality that only could be ascribed to a phased-array effect caused by the driving continuous wave-laser.

Finally, we find that the compound can be used to coat semiconductor substrates like gallium arsenide or silicon. This enables the possibility of functionalization of well established III/V semiconductor laser diodes.

References:
[1] H. J. Round, “A note on carborundum”,  Electrical World, 49.6, 309 (1907). Abstract.
[2] Shuji Nakamura, Takashi Mukai, Masayuki Senoh, “Candela-class high-brightness InGaN/AlGaN double-heterostructure blue-light-emitting diodes”, Applied Physics Letters, 64, 1687 (1994). Abstract.
[3] Fred Schubert, Jong Kyu Kim, “Light-emitting diodes hit the centenary milestone”, Compound Semiconductor, pages 20-22 (October, 2007). Article.
[4] Siddha Pimputkar, James S. Speck, Steven P. DenBaars, Shuji Nakamura, “Prospects for LED lighting”, Nature Photonics, 3, 180–182 (2009). Abstract.
[5] T. H. Maiman, “Stimulated optical radiation in ruby”, Nature, 187, 493–494 (1960). Abstract.
[6] Robert R. Alfano, "The Supercontinuum Laser Source" (Springer, 2013).
[7] Nils W. Rosemann, Jens P. Eußner, Andreas Beyer, Stephan W. Koch, Kerstin Volz, Stefanie Dehnen, Sangam Chatterjee, “A highly efficient directional molecular white-light emitter driven by a continuous-wave laser diode”, Science, 352, 1301–1304, (2016). Abstract.
[8] Hermann Berwe, Alois Haas, “Thiastannacyclohexane (R2SnS)3 und -adamantane (RSn)4S6 Synthesen, Eigenschaften und Strukturen”, Chemische Berichte, 120, 1175–1182 (1987). Abstract.
[9] Jens P. Eußnera, Stefanie Dehnen, “Bronze, silver and gold: functionalized group 11 organotin sulfide clusters”, Chemical Communications, 50, 11385–8 (2014). Abstract.

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Sunday, June 26, 2016

Direct Detection of the 229Th Nuclear Clock Transition

From left to right: Peter G. Thirolf, Lars v.d. Wense, Benedict Seiferle.

Authors: Lars von der Wense1, Benedict Seiferle1, Mustapha Laatiaoui2,3, Jürgen B. Neumayr1, Hans-Jörg Maier1, Hans-Friedrich Wirth1, Christoph Mokry3,4, Jörg Runke2,4, Klaus Eberhardt3,4, Christoph E. Düllmann2,3,4, Norbert G. Trautmann4, Peter G. Thirolf1

Affiliations:
1Ludwig-Maximilians-Universität München, 85748 Garching, Germany.
2GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt, Germany.
3Helmholtz Institut Mainz, 55099 Mainz, Germany.
4Johannes Gutenberg Universität, 55099 Mainz, Germany.

The measurement of time has always been an important tool in science and society [1]. Today’s most precise time measurements are performed with optical atomic clocks, which achieve a precision of about 10-18, corresponding to 1 second uncertainty in more than 15 billion years, a time span which is longer than the age of the universe [2]. By comparing two of such clocks, which are shifted in height by just a few centimetres, also the time dilation due to general relativistic effects becomes measurable [3].

Despite such stunning precision, these clocks could be outperformed by a different type of clock, the so called “nuclear clock” [4]. The nuclear clock makes use of a nuclear transition instead of an atomic shell transition as so far applied. The expected factor of improvement in precision of such a new type of clock has been estimated to be up to 100, in this way pushing the ability of time measurement to the next level [5]. The reason for the expected improvement is the size of the nucleus, which is orders of magnitude smaller than the size of the atom, thus leading to significantly improved resilience against external influences.

Many potential applications for a nuclear clock are currently under discussion. These include practical applications such as improved satellite-based navigational systems, data transfer, gravity detectors [6] as well as fundamental physical applications like gravitational wave detection [7] and testing for potential changes in fundamental constants [8].

Using existing technology, there is only one nuclear state known, which could serve for a nuclear clock. This is the first excited nuclear isomeric state of 229Th. Among all known (more than 175,000) nuclear excitations, this isomeric state exhibits a unique standing due to its extremely low excitation energy of only a few electronvolts [9]. The energy is that low, that it would allow for a direct laser excitation of the nuclear transition, which is the prerequisite for the development of a nuclear clock.

The existence of this isomeric state was shown in 1976, based on indirect measurements [10]. However, despite significant efforts, the direct detection of the isomeric decay could not be achieved within the past 40 years [11]. In the recently presented work [12], our group was able to solve this long-standing problem, leading to the first direct detection of the 229Th nuclear clock transition. This direct detection is important, as it paves the way for the determination of all decay parameters relevant for optical excitation of the isomeric state. It is thus a breakthrough step towards the development of a nuclear clock.
Figure 1: (click on the image to view with higher resolution) Experimental setup used for the production of a purified 229Th ion beam and the direct detection of the isomeric state. For details we refer the reader to the text and to Ref. [12].

The detection was achieved by producing a low energy, pure 229Th ion beam, with a fractional content of 229Th in the isomeric state. The isomer was produced by making use of a 2% decay branch of the alpha-decay of 233U into the isomeric state. The setup used for ion beam production is shown in Fig. 1 and will be described in the following section. The ions were collected with low kinetic energy onto the surface of a micro-channel-plate (MCP) detector, triggering the isomer’s decay and leading to its detection at the same time. The obtained signal is shown in Fig. 2. A high signal-to-background ratio could be achieved owing to the concept of spatial separation of the 233U source and the point of isomer detection. Many comparative investigations were performed in order to unambiguously show that the detected signal originates from the 229Th isomeric decay [12].

Figure 2: 229Th isomeric decay signal as observed during 2000 second integration time on the MCP detector allowing for spatially resolved signal read out.

For the production of a low-energy 229Th ion beam, a 233U source was used, which was placed inside of a buffer-gas stopping cell, filled with 40 mbar of ultra-pure helium. 229Th isotopes, as produced in the alpha-decay of 233U, are leaving this source due to their kinetic recoil energy of 84 kiloelectronvolts. These recoil isotopes were stopped in the helium buffer-gas, thereby staying charged due to the large ionization potential of helium. The low-energy 229Th ions, produced in this way, were guided through the helium background towards the exit of the stopping cell by electric fields, provided by a radio-frequency funnel system. The exit of the stopping cell consists of a Laval-nozzle system, leading to the formation of a supersonic gas jet. This gas jet injects the ions into a radio-frequency quadrupole (RFQ) ion-guide, leading to the formation of an ion beam. This ion beam is further purified with the help of a quadrupole mass-separator (QMS). In this way, a low-energy, pure 229Th ion beam was produced, possessing a fractional isomeric content of about 2%.

The next envisaged steps towards the development of a nuclear clock will be performed within the framework of the EU-funded Horizon 2020 collaboration named “NuClock” (www.nuclock.eu). Experiments will be carried out that aim for a precise determination of the isomer’s energy and half-life as being the basis for the first direct laser excitation of a nuclear transition.

References:
[1] David Landes, "Revolution in Time: Clocks and the Making of the Modern World" (Harvard University Press, Cambridge, 2000).
[2] T.L. Nicholson, S.L. Campbell, R.B. Hutson, G.E. Marti, B.J. Bloom, R.L. McNally, W. Zhang, M.D. Barrett, M.S. Safronova, G.F. Strouse, W.L. Tew, J. Ye, "Systematic evaluation of an atomic clock at 2 X 10-18 total uncertainty", Nature Communications, 6, 6896 (2015). Abstract.
[3] Andrew D. Ludlow, Martin M. Boyd, Jun Ye, E. Peik, P. O. Schmidt, "Optical atomic clocks", Review Modern Physics, 87, 637-701 (2015). Abstract.
[4] E. Peik, Chr. Tamm, "Nuclear laser spectroscopy of the 3.5 eV transition in 229Th", Europhysics Letters, 61, 181-186 (2003). Abstract.
[5] C. J. Campbell, A. G. Radnaev, A. Kuzmich, V. A. Dzuba, V. V. Flambaum, A. Derevianko, "Single-Ion nuclear clock for metrology at the 19th decimal place", Physical Review Letters, 108, 120802 (2012). Abstract.
[6] Marianna Safronova, "Nuclear physics: Elusive transition spotted in thorium", Nature, 533, 44-45 (2016). Abstract.
[7] Shimon Kolkowitz, Igor Pikovski, Nicholas Langellier, Mikhail D. Lukin, Ronald L. Walsworth, Jun Ye, "Gravitational wave detection with optical lattice atomic clocks", arXiv:1606.01859 [physics.atom-ph] (2016).
[8] V.V. Flambaum, "Enhanced effect of temporal variation of the fine structure constant and the strong interaction in 229Th", Physical Review Letters, 97, 092502 (2006). Abstract.
[9] B.R. Beck, J.A. Becker, P. Beiersdorfer, G.V. Brown, K.J. Moody, J.B. Wilhelmy, F.S. Porter, C.A. Kilbourne, R.L. Kelley, "Energy splitting of the ground-state doublet in the nucleus 229Th", Physical Review Letters, 98, 142501 (2007). Abstract.
[10] L.A. Kroger, C.W. Reich, "Features of the low energy level scheme of 229Th as observed in the alpha decay of 233U", Nuclear Physics A, 259, 29-60 (1976). Abstract.
[11] Ekkehard Peik, Maxim Okhapkin, "Nuclear clocks based on resonant excitation of gamma-transitions", Comptes Rendus Physique, 16, 516-523 (2015). Abstract.
[12] Lars von der Wense, Benedict Seiferle, Mustapha Laatiaoui, Jürgen B. Neumayr, Hans-Jörg Maier, Hans-Friedrich Wirth, Christoph Mokry, Jörg Runke, Klaus Eberhardt, Christoph E. Düllmann, Norbert G. Trautmann, Peter G. Thirolf, "Direct detection of the 229Th nuclear clock transition", Nature, 533, 47 (2016). Abstract.

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