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 Pyatkov^1,2, Svetlana Khasminskaya¹, Valentin Fütterling¹, Randy Fechner¹, Karolina Słowik^3,4, Simone Ferrari^1,5, Oliver Kahl^1,5, Vadim Kovalyuk^1,6, Patrik Rath^1,5, Andreas Vetter¹, Benjamin S. Flavel¹, Frank Hennrich¹, Manfred M. Kappes^1,7, Gregory N. Gol’tsman⁶, Alexander Korneev⁶, Carsten Rockstuhl^1,3, Ralph Krupke^1,2, Wolfram H.P. Pernice⁵

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

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

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

Recently we presented a nanotube-based waveguide integrated light emitters with tailored, exceptionally narrow emission-linewidths and short response times [4]. This allows conversion of electrical signals into well-defined optical signals directly within an optical waveguide, as required for future on-chip optical communication. Schematics and realization of this device is shown in Figure 1. The devices were manufactured by etching a photonic crystal waveguide into a dielectric layer following electron beam lithography. Photonic crystals are nanostructures that are also used by butterflies to give the impression of color on their wings. The same principle has been used in this study to select the color of light emitted by the CNT. The precise dimensions of the structure were numerically simulated to tailor the properties of the final device. Metallic contacts in the vicinity to the waveguide were fabricated to provide electrical access to CNT emitters. Finally, CNTs, sorted by structural and electronic properties, were deposited from a solution across the waveguide using dielectrophoresis, which is an electric-field-assisted deposition technique.

Figure 1: (a) Schematic view of the multilayer device structure consisting of two electrodes (yellow) and a photonic waveguide (purple) that is etched into the Si3N4 layer. Its central part is underetched into the SiO2 layer to a depth of 1.5 µm and photonic crystal holes are formed. The carbon nanotube bridges the electrodes on top of the waveguide. (b,c) False colored scanning electron microscope images of the device. The figure is adapted from Reference [4].

The functionality of the device was verified with optical microscopy and spectroscopy, which allowed detection of light emitted by the CNT and also of the light coupled into the waveguide. An electrically biased CNT generates photons, which efficiently couple into the photonic crystal waveguide, as shown in Figure 2a. The emitted light propagates along the waveguide and is then coupled out again using on-chip grating couplers. Because of the photonic crystal the emission spectrum of the CNT is extremely sharp (Figure 2b) and the emission wavelength can be tailored by our manufacturing process. In addition, the nanotube responds very quickly to electrical signals and hence acts as a transducer for generating optical pulses in the GHz range (Figure 2c). The modulation rates of these CNT-based transducers can in principle be pushed to much higher frequencies up to 100 GHz using more advanced nanostructures.

Figure 2: (click on the image to view with higher resolution) CCD camera image of the electrically biased device. Light emission is observed from the nanotube and from the on-chip grating couplers, both connected with the emitter via the waveguide. (b) Emission spectra simultaneously measured at the grating coupler. (c) A sequence of the driving electrical pulses as well as the recorded waveguided emission pulses (red) in GHz frequency range. The figure is adapted from Reference [4].

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

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

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

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

Figure 3: (click on the image to view with higher resolution) (a,b) Schematics and optical image of device with an electrically driven light emitting nanotube in the middle (E) and single-photon superconducting NbN-detectors at the ends (D) of waveguide. The figure is adapted from Reference [6].

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

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

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

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 Cancellieri^5,6, Blanca Silva Fernández^1,4, Alberto Bramati⁶, Giuseppe Gigli^1,7, Alexei Kavokin^2,8,9, Fabrice Laussy^4,10, 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.

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 m_l, for orbital angular momentum; s and m_s, for spin angular momentum; and j and m_j 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.

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 Li^1,4, Hao Liu¹, Yi-Hang Zhang¹, Xiao-Hui Yuan^2,4, Xu-Lei Ge², Su Yang², Wen-Qing Wei², Wei-Min Wang^1,4, Zheng-Ming Sheng^2,3,4, Jie Zhang^2,4

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.

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. Rosemann^1,2, Jens P. Eußner^2,3, Andreas Beyer^1,2, Stephan W. Koch^1,2, Kerstin Volz^1,2, Stefanie Dehnen^2,3, Sangam Chatterjee^1,2,4

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.

Demonstration of Light Induced Conical Intersections in Diatomic Molecules

Left to right: Adi Natan, Matt Ware, Phil Bucksbaum

Authors: Adi Natan¹, Matthew R Ware^1,4, Vaibhav S. Prabhudesai², Uri Lev³, Barry D. Bruner³, Oded Heber³, Philip H Bucksbaum^1,4

Affiliation:
¹Stanford PULSE Institute, SLAC National Accelerator Laboratory, Menlo Park, CA, USA
²Department of Nuclear and Atomic Physics, Tata Institute of Fundamental Research, Mumbai, India
³Faculty of Physics, the Weizmann Institute of Science, Rehovot, Israel
⁴Departments of Physics, Applied Physics, and Photon Science, Stanford University, Stanford, CA, USA

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. These tend to repel when they approach each other, but cannot stay separated everywhere in the multidimensional geometry landscape of a molecule. CIs are ubiquitous in photo-processes in polyatomic molecules and govern key phenomena such as DNA photostability [2], but they are difficult to locate, measure and control, since their positions and features depend on specific molecular system under study. It is therefore of great interest to simulate their effects.

The case for diatomic molecules is different because naturally occurring CIs cannot exist for them: Energy levels are repelled when they approach each other, and there are not enough degrees of freedom for a true crossing. However a strong laser field applied to a diatomic molecule adds one additional degree of freedom, which gives rise to a light-induced artificial CI (LICI) that is predicted to have several features in common with the poly-atomic “wild-type” CI [3-5]. More recent theoretical studies have examined various aspects of this LICI phenomenon [6-9].

The molecular dynamics in the vicinity of a LICI can be explored in the simplest laser-illuminated molecular system, the ground state of the hydrogen molecular ion, H₂⁺ [10]. An infrared laser will induce interactions between the two lowest nuclear potential energy curves, named 1sσ_g and 2pσ_u. The interaction of strong fields with H₂⁺ can be expressed by shifting one of the potential curves by the energy of one photon. The now ”dressed” potential curve crosses at some internuclear separation R where the two states are resonantly coupled by the laser field, the analog of the curve crossings at CIs in polyatomic molecules, as seen in Fig 1(a) . We define the LICI as this crossing point, when the polarization of the laser is perpendicular to the molecular axis. For other angles, there is no crossing, and the dynamics is “adiabatic”, that is, a nuclear wavepacket will travel only on one of the dressed potential curves.

Consider for a moment what it means to have a point of crossing where the field is perpendicular to the molecular axis of a diatomic molecule: This molecule effectively “feels” zero laser field only at this specific angle, so the potential curves assume their field free R-dependence only here. The key to the dynamics induced by the LICI is the special behavior of the molecule as it rotates through this special point, from an angle on one side where it experiences the field, to an angle on the other side where the field is once again felt.

The simplest place to start is H₂⁺ in its ground rotational state, interacting with a strong laser field that couples resonantly the two electronic states. The spherical symmetry of the ground state field-free nuclear probability density, changes rapidly when a strong field is turned on. We can follow how this probability density evolves in the dressed state framework. In the dressed picture, the LICI is a local maximum in the two-dimensional (R,θ) potential energy landscape, while in other angles, the population dissociates adiabatically on the unbound part of the light induced potential curve. This causes the part of the population to accumulate around the LICI and then scatter from it, similar to waves scattering from a cone shape potential barrier. However, unlike scattering of a free particle around a barrier, the scattering described here is of bound nuclear wave packet, which scatters into a multitude of rovibrational states on the ground electronic surface, similar to the non-adiabatic dynamics around a natural CI. The scattering from the LICI leads to dissociation, but imposes a scattering time delay. The coherent addition of all the scattering trajectories creates an interference pattern at various angles and kinetic energy releases (Fig 1 (b), and Fig 1(c)). These quantum interferences are a universal signature for LICIs because they arise from the nature of coherent scattering interference near a point of degeneracy.

Figure 1: [Click on the image to view with higher resolution] (a) The dressed potential energy surfaces of H₂⁺ featuring LICIs. (b) The calculated instantaneous probability of dissociation P(θ,t)_diss from a given vibrational state (for example, v=9) during the interaction with the laser pulse reveals the interference. (c) Experimental (top) and calculated (bottom) angular distributions of H₂⁺ dissociation at kinetic energy releases that correspond to specific initial vibrations states.

We have experimentally demonstrated the effects of LICIs on strong-field photodissociation of H₂⁺ by means of quantum interferences that modify the angular distributions of the dissociating fragments [10]. The interferences depend strongly on the energy difference between the initial state and the LICI. The larger the overlap between the initial state and the LICI, the larger the effective duration of interaction and the more developed the interferences. For example, we can compare the effect among different initial states, starting from an initial state that is nearly resonant, hence has a large overlap with the LICI, such as the vibrational level v = 9 in H₂⁺, to a state that is non-resonant such as v = 7. We observe in both calculation and experiment how these initial states indeed capture the different effective duration of the interaction with the LICI (Fig 1(c)).

LICIs are particularly attractive for future quantum control experiments due to their high degree of controllability using the polarization and frequency of the laser. The interaction is not limited to just a single LICI, and allows control of the timing of its appearance as well. Understanding the dynamics induced by LICIs will facilitate understanding and applicability to systems of higher complexity. Implementing and understanding LICIs in more complex systems will open the way to novel spectroscopy techniques in physics and chemistry.

References:
[1] Dario Polli, Piero Altoè, Oliver Weingart, Katelyn M. Spillane, Cristian Manzoni, Daniele Brida, Gaia Tomasello, Giorgio Orlandi, Philipp Kukura, Richard A. Mathies, Marco Garavelli, Giulio Cerullo, "Conical intersection dynamics of the primary photoisomerization event in vision", Nature, 467, 440 (2010). Abstract.
[2] B. K. McFarland, J. P. Farrell, S. Miyabe, F. Tarantelli, A. Aguilar, N. Berrah, C. Bostedt, J. D. Bozek, P. H. Bucksbaum, J. C. Castagna, R. N. Coffee, J. P. Cryan, L. Fang, R. Feifel, K. J. Gaffney, J. M. Glownia, T. J. Martinez, M. Mucke, B. Murphy, A. Natan, T. Osipov, V. S. Petrović, S. Schorb, Th. Schultz, L. S. Spector, M. Swiggers, I. Tenney, S. Wang, J. L. White, W. White, M. Gühr, "Ultrafast X-ray Auger probing of photoexcited molecular dynamics", Nature Communications, 5, 4235 (2014). Abstract.
[3] Nimrod Moiseyev, Milan Šindelka, Lorentz S. Cederbaum, "Laser-induced conical intersections in molecular optical lattices", Journal of Physics B,  41, 221001 (2008). Full Article.
[4] Milan Šindelka, Nimrod Moiseyev, Lorentz S. Cederbaum, "Strong impact of light-induced conical intersections on the spectrum of diatomic molecules", Journal of Physics B, 44, 045603 (2011). Abstract.
[5] Nimrod Moiseyev, Milan Šindelka, "The effect of polarization on the light-induced conical intersection phenomenon", Journal of Physics B, 44, 111002 (2011). Abstract.
[6] Gábor J. Halász, Ágnes Vibók, Nimrod Moiseyev, Lorenz S. Cederbaum, "Nuclear-wave-packet quantum interference in the intense laser dissociation of the D₂⁺ molecule", Physical Review A, 88, 043413 (2013). Abstract.
[7] Gábor J Halász, Ágnes Vibók, Nimrod Moiseyev, Lorenz S Cederbaum, "Light-induced conical intersections for short and long laser pulses: Floquet and rotating wave approximations versus numerical exact results", Journal of Physics B, 45, 135101 (2012). Abstract.
[8] Gábor J. Halász, Ágnes Vibók, Milan Šindelka, Lorenz S. Cederbaum, Nimrod Moiseyev, "The effect of light-induced conical intersections on the alignment of diatomic molecules", Chemical Physics, 399, 146 (2012). Abstract.
[9] G.J. Halász, A. Vibók, L.S. Cederbaum, "Direct Signature of Light-Induced Conical Intersections in Diatomics", Journal of Physical Chemistry Letters, 6, 348 (2015). Abstract.
[10] Adi Natan, Matthew R. Ware, Vaibhav S. Prabhudesai, Uri Lev, Barry D. Bruner, Oded Heber, Philip H. Bucksbaum, "Observation of Quantum Interferences via Light-Induced Conical Intersections in Diatomic Molecules", Physical Review Letters, 116, 143004 (2016). Abstract.

Polarized Light Modulates Light-Dependent Magnetic Compass Orientation in Birds

From Left to Right: Rachel Muheim, Sissel Sjöberg, Atticus Pinzon-Rodriguez

Authors: Rachel Muheim, Sissel Sjöberg, Atticus Pinzon-Rodriguez

Affiliation: Department of Biology, Lund University, Sweden.

Magnetic compass orientation of birds depends on polarization of light

A wide range of animals, including birds, use directional information from the Earth’s magnetic field for orientation and navigation [1]. The magnetic compass of birds is light dependent and suggested to be mediated by light-induced, biochemical reactions taking place in specialized photoreceptors [2,3]. The photopigment molecules form magnetically sensitive radical-pair intermediates upon light excitation. The ratio of the spin states of the radical pairs (i.e., singlet vs. triplet state) is affected by Earth-strength magnetic fields, which thereby alters the response of the photopigments to light. In birds, such magneto-sensitive photoreceptors have been proposed to be arranged in an ordered array in the eye. Depending on their alignment to the magnetic field, they would show an increased or decreased sensitivity to light [2,3]. The animals would thereby perceive the magnetic field as a magnetic modulation pattern centered on the magnetic field lines, either superimposed on the visual field or mediated by a separate channel [4]. Cryptochromes have been proposed as putative candidate receptor molecules and found to be expressed in the retinas of birds exhibiting magnetic orientation behavior [2,5–7].

Hitherto, the majority of biophysical models on magnetic field effects on radical pairs have assumed that the light activating the magnetoreceptor molecules is non-directional and unpolarized, and that light absorption is isotropic. Yet, natural skylight enters the avian retina unidirectionally, through the cornea and the lens, and is often partially polarized. Also, the putative magnetoreceptor molecules, the cryptochromes, absorb light anisotropically, i.e., they preferentially absorb light of a specific direction and polarization. This implies that the light-dependent magnetic compass is intrinsically polarization sensitive [8,9].

Zebra Finch Bird

We developed a behavioural training assay to test putative interactions between the avian magnetic compass and polarized light. Thereby, we trained zebra finches to magnetic and/or overhead polarized light cues in a 4-arm “plus” maze to find a food reward with the help of their magnetic compass [10]. We found that overhead polarized light affected the birds’ ability to use their magnetic compass. The birds were only able to reliably find the food reward when the polarized light was aligned parallel to the magnetic field, but not when it was aligned perpendicular to the magnetic field [10]. We found this effect when using both 100% and 50% polarized light.

4-arm “plus” maze.

Our findings demonstrate that the magnetic compass of birds, and likely other animals, is polarization sensitive, which is a fundamentally new property of the light-dependent magnetic compass. Thus, the primary magnetoreceptor is photo- and polarization selective, as recently suggested by biophysical models [9]. The magnetic compass thus seems to be based on light-induced rotational order, thereby relaxing the requirement for an intrinsic rotational order of the receptor molecules (as long as rotational motion is restricted). The putative cryptochrome magnetoreceptors may therefore be distributed in any, also non-randomly oriented, cells in the avian retina [9]. Similar effects are expected to occur also in other organisms orienting with a light-dependent magnetic compass based on radical-pair reactions. Our findings thereby add a new dimension to the understanding of how not only birds, but animals in general, perceive the Earth’s magnetic field.

It remains to be shown to what degree birds in nature are affected by different alignments of polarized light and the Earth’s magnetic field. It could be a mechanism to enhance the magnetic field around sunrise and sunset, when polarized light is aligned roughly parallel to the magnetic field and when many migratory songbirds are believed to determine their departure direction and calibrate the different compasses with each other for the upcoming night’s flight. During midday, when polarized light and the magnetic field are aligned roughly perpendicular to each other, the magnetic field would be less prominent, thus would be less likely to interfere with visual tasks like foraging and predator detection [10].

References:
[1] Roswitha Wiltschko, Wolfgang Wiltschko, "Magnetic Orientation in Animals" (Springer, 1995).
[2] Thorsten Ritz, Salih Adem, Klaus Schulten, "A model for photoreceptor-based magnetoreception in birds", Biophysics Journal, 78, 707–718 (2000). Article.
[3] Christopher T. Rodgers, P. J. Hore, "Chemical magnetoreception in birds: The radical pair mechanism", Proceedings of the National Academy of Sciences, 106, 353–360 (2009). Abstract.
[4] Ilia A. Solov'yov, Henrik Mouritsen, Klaus Schulten, "Acuity of a cryptochrome and vision-based magnetoreception system in birds", Biophysics Journal, 99, 40–49 (2010). Article.
[5] Miriam Liedvoge, Henrik Mouritsen, "Cryptochromes—a potential magnetoreceptor: what do we know and what do we want to know?" Journal of Royal Society Interface, 7, S147 –S162 (2010). Abstract.
[6] Christine Nießner, Susanne Denzau, Julia Christina Gross, Leo Peichl, Hans-Joachim Bischof, Gerta Fleissner, Wolfgang Wiltschko, Roswitha Wiltschko, "Avian ultraviolet/violet cones identified as probable magnetoreceptors", PLOS ONE, 6, 0020091 (2011). Abstract.
[7] Kiminori Maeda, Alexander J. Robinson, Kevin B. Henbest, Hannah J. Hogben, Till Biskup, Margaret Ahmad, Erik Schleicher, Stefan Weber, Christiane R. Timmel, P.J. Hore, "Magnetically sensitive light-induced reactions in cryptochrome are consistent with its proposed role as a magnetoreceptor", Proceedings of the National Academy of Sciences, 109, 4774–4779 (2012). Abstract.
[8] Rachel Muheim,  "Behavioural and physiological mechanisms of polarized light sensitivity in birds", Philosophical Transactions of the Royal Society B : Biological Sciences, 366, 763 –771 (2011). Abstract.
[9] Jason C.S. Lau, Christopher T. Rodgers, P.J. Hore, "Compass magnetoreception in birds arising from photo-induced radical pairs in rotationally disordered cryptochromes", Journal of Royal Society Interface, 9, 3329–3337 (2012). Abstract.
[10] Rachel Muheima, Sissel Sjöberga, Atticus Pinzon-Rodrigueza, "Polarized light modulates light-dependent magnetic compass orientation in birds", Proceedings of the National Academy of Sciences, 113, 1654-1659 (2016). Abstract.

Discovery of Weyl Fermions, Topological Fermi Arcs and Topological Nodal-Line States of Matter

Princeton University group (click on the picture to view with higher resolution), From left to right: Guang Bian, M. Zahid Hasan (Principal investigator), Nasser Alidoust, Hao Zheng, Daniel S. Sanchez, Suyang Xu and Ilya Belopolski. 

Author: M. Zahid Hasan

Affiliation: Department of Physics, Princeton University, USA

Link to Hasan Research Group: Laboratory for Topological Quantum Matter & Advanced Spectroscopy >>

The eponymous Dirac equation describes the first synthesis of quantum mechanics and special relativity in describing the nature of electron. Its solutions suggest three distinct forms of relativistic particles - the Dirac, Majorana and Weyl fermions [1-3]. In 1929, Hermann Weyl proposed the simplest version of the equation, whose solution predicted massless fermions with a definite chirality or handedness [3]. Weyl’s equation was intended as a model of elementary articles, but in nearly 86 years, no candidate Weyl fermions have ever been established in high-energy experiments. Neutrinos were once thought to be such particles but later found to possess a small mass. Recently, analogs of the fermion particles have been discovered in certain electronic materials that exhibit strong spin-orbit coupling and topological behavior. Just as Dirac fermions emerge as signatures of topological insulators [4], researchers have shown that electronic excitations in semimetals such as tantalum or niobium arsenides (TaAs and NbAs) behave like Weyl fermions [5-7]. And such a behavior is consistent with their topological semimetal bandstructures [8,9].

Past 2Physics article by M. Zahid Hasan:
July 18, 2009: "Topological Insulators : A New State of Quantum Matter"

In 1937 physicist Conyers Herring considered under what conditions electronic bands in solids have the same energy by accident in crystals that lack certain symmetries [10]. Near these accidental band touching points, the low-energy excitations, or electronic quasiparticles can be described by an equation that is essentially identical to the 1929 Weyl equation. In recent times, these touching points have been theoretically studied in the context of topological materials and are referred to as Weyl points and the quasiparticles near them are the emergent Weyl fermions [11]. In these solids, the electrons’ quantum-mechanical wave functions acquire a phase, as though they were moving in a superficial magnetic field that is defined in momentum space. In contrast to a real magnetic field, this fictional field (known as a Berry curvature) admits excitations that behave like magnetic monopoles. These monopoles are topological defects or singularities that locate at the Weyl points. So the real space Weyl points are associated with chiral fermions and in momentum space they behave like magnetic monopoles [11-17]. The fact that Weyl nodes are related to magnetic monopoles suggests they will be found in topological materials that are in the vicinity of a topological phase transition [14,15]. The surface of a topological insulator has a Fermi surface that forms a closed loop in momentum space; in a Weyl semimetal, these loops become non-closed arcs as some symmetry is lifted [11,12]. These Fermi arcs terminate at the location of the bulk Weyl points ensuring their topological nature [12]. Theory had suggested that Weyl semimetals should occur in proximity to topological insulators in which inversion or time-reversal symmetry was broken [12,14,16].

Building on these ideas, researchers, including the Princeton University group, used ab initio calculations to predict candidate materials [8,9] and perform angle-resolved photoemission spectroscopy to detect the Fermi arcs, characteristic of Weyl nodes, on the surface of TaAs and NbAs [5-7]. ARPES is an ideal tool for studying such a topological material as known from the extensive body of works on topological insulators [4]. The ARPES technique involves shooting high-energy photons on a material and measuring the energy, momentum and spin of the ejected electrons both from the surface and the bulk. This allows for the explicit determination of both bulk Weyl nodes and the Fermi-arc surface states (Figure 1).

Figure 1: (click on the image to view with high resolution) Weyl fermion and Fermi arcs (a) Schematic of the band structure of a Weyl fermion semimetal. (b) Correspondence of the bulk Weyl fermions to surface Fermi arc states. (c) ARPES mapping of TaAs Fermi surface. (d) Fermi arc surface states and Weyl nodes on the (001) surface of TaAs. (e) Linear dispersion of Weyl quasi-particles in TaAs. (Adapted form Ref. [5])

In the absence of spin-orbit coupling, the tantalum arsenide material is a nodal-line semimetal in which the bulk Fermi surface is a closed loop in momentum space [8,17,18]. With spin-orbit coupling turned on, the loop-shaped nodal line condenses into discrete Weyl points in momentum space [8]. In this sense the topological nodal-line semimetal can be thought of as a state where the Weyl semimetals originate from by further symmetry breaking (Figure 2). Such a state has been considered in theory previously [17] but it lacked concrete experimental realizations. Very recently, the first example of a topological nodal-line semimetal in the lead tantalum selenide (PbTaSe₂) materials has been reported experimentally [18]. Even though many predictions existed, no concrete experimentally realizable material was found. These findings suggest that Weyl semimetals [5-7] and nodal-line semimetals [17-18] are the first two examples of topological materials that are intrinsically gapless in contrast to topological insulators [4].

Figure 2: (click on the image to view with high resolution) Topological nodal-line semimetals (a) Schematic of a Weyl semimetal and a topological nodal-line semimetal. (b) ARPES mapping and theoretical simulation of (001)-surface band structure of PbTaSe₂ showing the loop-shaped bulk Fermi surface. (c) ARPES spectrum and theoretical band structure along some momentum space directions. (e) Calculated iso-energy band contour showing the nodal line and topological surface states. (Adapted from Ref. [18])

In the 1980s, Nielsen and Ninomiya suggested that exotic effects, like the ABJ (Adler-Bell-Jackiw) chiral anomaly—in which the combination of an applied electric and magnetic fields generates an excess of quasiparticles with a particular chirality—were associated with Weyl fermions and could be observable in 3D crystals [13]. A further correspondence has been established more recently with the increased understanding of materials with band structures that are topologically protected [11-17]. Unusual transport properties that are associated with Weyl fermions, such as a reduction of the electrical resistance in the presence of an applied magnetic field, have already been reported in the TaAs class of materials [19,20] (Figure 3). Weyl materials can also act as a novel platform for topological superconductivity leading to the realization of Weyl-Majorana modes potentially opening a new pathway for investigating qubit possibilities [21]. Weyl particles have also been observed in photonic (bosonic) crystals. In these systems the number of optical modes has an unusual scaling with the volume of the photonic crystal, which may allow for the construction of large-volume single-mode lasers [22]. Development in the last few months seems to suggest that Weyl particles are indeed associated with a number of unexpected quantum phenomena and these findings may lead to applications in next-generation photonics and electronics.

Figure 3: (click on the image to view with high resolution) Signature of the chiral anomaly in the Weyl fermion semimetal TaAs. (a) Magneto-resistance (MR) data of the Weyl semimetal TaAs in the presence of parallel electric and magnetic fields at T = 2 K. The MR decreases as one increases the magnetic field. (b) MR as a function of angle between the electric and the magnetic fields. The negative magneto-resistance is quickly suppressed as one varies the direction of the magnetic ~B field away from that of the electric ~E field. The observed negative MR and its angular dependence serve as the key signature of the chiral anomaly. (c,d) Landau energy spectra of the left- and right-handed Weyl fermions in the presence of parallel electric and magnetic fields. (Adapted from Ref. [20])

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