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2Physics Quote:
"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."
-- Nils W. Rosemann, Jens P. Eußner, Andreas Beyer, Stephan W. Koch, Kerstin Volz, Stefanie Dehnen, Sangam Chatterjee
(Read Full Article: "Nonlinear Medium for Efficient Steady-State Directional White-Light Generation"

Sunday, October 30, 2016

Experimental Simulation of the Exchange of Majorana Zero Modes

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

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

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

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

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

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

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

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

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

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

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

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

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

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Sunday, October 16, 2016

Carbon Nanotubes as Exceptional Electrically Driven On-Chip Light Sources

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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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.

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.

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 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.

[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].

[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.


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

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.

[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.

[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

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.

[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.
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