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.

Quantum Tunneling of Water in Ultra-Confinement

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

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

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

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

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

Figure 1: The crystal structure of beryl

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

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

Figure 2: the measured momentum distribution n(p) in neutron Compton scattering experiments.

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

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

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

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.

Two dimensional Superconducting Quantum Interference Filter (SQIF) arrays using 20,000 YBCO Josephson Junctions

From Left to Right: (top row) Emma Mitchell, Jeina Lazar, Keith Leslie, Chris Lewis,
(bottom row) Alex Grancea, Shane Keenan, Simon Lam, Cathy Foley.

Authors: 
Emma Mitchell¹, Kirsty Hannam¹, Jeina Lazar¹, Keith Leslie¹, Chris Lewis¹, 
Alex Grancea², Shane Keenan¹, Simon Lam¹, Cathy Foley¹

Affiliation: 
¹CSIRO Manufacturing, Lindfield, NSW, Australia,
²CSIRO Data61, Epping, NSW, Australia.

Josephson junctions form the essential magnetic sensing element at the heart of most superconducting electronics. A Josephson junction consists of two superconducting electrodes separated by a thin barrier [1]. Provided the barrier width is less than the superconducting coherence length, Cooper pairs can tunnel quantum mechanically from one electrode to the other coherently when the temperature is below the critical temperature of the two electrodes. Due to the macroscopic quantum coherence of the Cooper pairs in the superconducting state, Josephson junctions not only detect magnetic fields and RF radiation over an extremely wide frequency band, but can also emit radiation. The highly sensitive response of the Josephson junction current to magnetic fields is the key to many of its applications, including magnetometers, absolute magnetic field detectors and low noise amplifiers. More recent applications also include small RF antennas which utilize the Josephson junction’s broadband (dc- THz) detection abilities.

The dc SQUID, or Superconducting Quantum Interference Device, consists of two Josephson junctions connected together in parallel via a superconducting loop. The SQUID is an extremely sensitive flux-to voltage transducer, but despite this simplicity, an exact solution of this problem can only be given in the case of negligible inductance of the loop containing the two junctions. When the SQUID is biased with a current and an external magnetic field is applied, the voltage response oscillates periodically with applied magnetic field (Figure 1a). The period of the oscillation is inversely proportional to the loop area. SQUIDs have been connected together into arrays of increasing size and complexity to improve device sensitivity.

Figure 1: Voltage responses for a (a) dc SQUID with two step-edge junctions (b) two dimensional SQIF with 20,000 step-edge junctions.

Feynman et al. (1966) first predicted [2] an enhancement in the SQUID interference effect by having multiple (identical) junctions in parallel, analogous to a multi-slit diffraction grating. This enhancement was originally observed using superconducting point contact junctions [3] and has been further developed using series arrays of low temperature superconducting (LTS) Nb SQUIDs. More recently 1D arrays of SQUIDs with incommensurate loop areas (non-identical and variable spread) with a non-periodic voltage response were suggested [4]. The voltage response of these superconducting quantum interference filters (SQIFs) is then analogous to a non-conventional optical grating where different periodic responses from individual SQUIDs with different loop areas are summed. This results in a voltage response to a magnetic field in which a dominant anti-peak develops at zero applied field due to constructive interference of the individual SQUID responses. Weaker non-periodic oscillations occur at non-zero fields where the individual SQUID responses destructively interfere. The magnitude and width of the anti-peak for a SQIF is governed by the range and distribution of SQUID loop areas and inductances.

In our recent work [5] we demonstrate high temperature superconducting (HTS) two dimensional SQIF arrays based on 20,000 YBCO step-edge Josephson junctions connected together in series and parallel (Figure 1b). The maximum SQIF response we measured had a peak-to-peak voltage of ~ 1mV and a sensitivity of (1530 V/T) using a SQIF design with twenty sub-arrays connected in series with each sub-array consisting of 50 junctions in parallel connected to 20 such rows in series. The variation in loop areas within each subarray had a pseudo- random distribution with a mean loop area designed to have an inductance factor β_L = 2LI_c/Φ₀ ~1 [6]. Figure 2a shows part of our array with four whole sub-arrays visible. At higher magnification the variation of individual loop areas is evident (Figure 2b) with the rows of step-edge junctions indicated by arrows.

Figure 2: (a) Part of the 20,000 YBCO step-edge junction SQIF array showing four complete sub-arrays of 1,000 junctions each (b) one sub-array at higher magnification showing rows of junctions (arrows) and variable loop areas (darker material is the YBCO).

The Josephson junctions in our samples are step-edge junctions formed when a grain boundary develops between the YBCO electrodes that grow epitaxially when a thin film is deposited over a small step approximately 400nm high with an angle of ~38^o, etched into the supporting MgO substrate [7, 8]. It is well documented that HTS Josephson junctions are difficult to fabricate in large numbers across a substrate. However, step-edge junctions have the advantage of being relatively simple and inexpensive to fabricate and can be placed, at high surface density almost anywhere on a substrate. To date, we have made 2D arrays showing a SQIF response with 20,000 up to 67,000 step-edge junctions on a 1cm² substrate.

Two dimensional SQIF arrays allow for large numbers of junctions to be placed in high density across a chip, enabling increases in the output voltage and sensitivity of the device. 2D arrays also allow for impedance matching of the array to external electronics by varying the ratio of junctions in parallel to those in series, by virtue of the junction normal resistance, R_n.

In addition, we demonstrated that the sensitivity of the SQIF depends strongly on the mean junction critical current, I_c, in the array, and the inductance (area) of the average loop in the array. In both cases keeping these parameters small such that β_L < 1 is necessary for improving the SQIF sensitivity, but can be difficult to achieve with HTS junctions in which the typical spread in I_c can be 30%. The SQIF response also depends on the number of junctions; a linear increase in the SQIF sensitivity with junction number was measured for our SQIF designs.

We were also able to demonstrate RF detection at 30 MHz using our HTS SQIFs at 77 K [5]. More recently a broadband SQIF response from DC to 140 MHz was demonstrated following improvements to our SQIF sensitivity (unpublished). This follows on from reports of near field RF detection to 180 MHz using 1000 low temperature superconducting (LTS) junctions [9], where more complex and expensive cryogenic requirements limit the LTS array applications outside the laboratory.

References:
[1] B.D. Josephson,  "Possible new effects in superconductive tunneling". Physics Letters, 1, 251 (1962). Abstract.
[2] Richard P. Feynman, Robert B. Leighton, Matthew Sands, “The Feynman lectures on Physics, Vol III” (Addison-Wesley, 1966).
[3] J.E. Zimmerman, A.H. Silver, "Macroscopic quantum interference effects through superconducting point contacts", Physical Review, 141, 367 (1966). Abstract.
[4] J. Oppenländer, Ch. Häussler, N. Schopohl, "Non-Φ_o periodic macroscopic quantum interference in one-dimensional parallel Josephson junction arrays with unconventional grating structures", Physical Review B, 63, 024511 (2000). Abstract.
[5] E.E. Mitchell, K.E. Hannam, J. Lazar, K.E. Leslie, C.J. Lewis, A. Grancea, S.T. Keenan, S.K.H. Lam, C.P. Foley, “2D SQIF arrays using 20,000 YBCO high RN Josephson junctions”, Superconductor Science and Technology, 29, 06LT01 (2016). Abstract.
[6] “The SQUID Handbook, Vol. I Fundamentals and technology of SQUIDs and SQUID systems", eds. John Clarke and Alex I. Braginski (Wiley, 2004).
[7] C.P. Foley, E.E. Mitchell, S.K.H. Lam, B. Sankrithyan, Y.M. Wilson, D.L. Tilbrook, S.J. Morris, "Fabrication and characterisation of YBCO single grain boundary step edge junctions", IEEE Transactions on Applied Superconductivity, 9, 4281 (1999). Abstract.
[8] E.E. Mitchell, C.P. Foley, “YBCO step-edge junctions with high IcRn”, Superconductivity Science and Technology, 23, 065007 (2010). Abstract.
[9] G.V. Prokopenko, O.A. Mukhanov, A. Leese de Escobar, B. Taylor, M.C. de Andrade, S. Berggren, P. Longhini, A. Palacios, M. Nisenoff, R. L. Fagaly, “DC and RF measurements of serial bi-SQUID arrays”, IEEE Transactions on Applied Superconductivity, 23, 1400607 (2013). Abstract.

Why Statistical Physics Should Be A Foundation For Materials Design

Marc Miskin

Author: Marc Miskin

Affiliation:
James Franck Institute and Department of Physics, The University of Chicago, USA.

The fact that major epochs in human history have been named after materials like bronze, steel, silicon, and stone expresses both how important materials are for technology and how long it can take before a new material is discovered. Even today, the timespan to convert materials' discoveries into functioning technologies takes upwards of 20 years. In part this is because creating technologically useful materials requires selecting a wide range of parameters to optimize the material’s performance. While tools like statistical physics are useful for describing a material’s behavior given a set of parameters, it remains unknown how to generally invert these relationships to target desired behavior. This task is called materials design and it is a new concept at the forefront of materials research.

Recently, several methods have emerged across disciplines that draw upon optimization and simulation to create computer programs that tailor material responses to specified behaviors. However, so far the methods developed either involve black-box techniques, in which the optimizer operates without explicit knowledge of the physical laws that underpin the material’s behavior, or require carefully tuned algorithms with applicability limited to a narrow subclass of materials.

Our recent publication titled “Turning Statistical Physics Models into Materials Design Engines” [1] presents a new perspective for material design. In contrast to prior approaches, it is broad enough to be applied without modification to any system that is well described by statistical mechanics and also retains much of the key insight that is at the heart of statistical physics. In short, our formalism allows a user to transform the capacity to predict material behavior into an optimizer that tunes it.

We achieved this by examining the fundamental relationship between microstate configurations and material properties. Statistical physics poses the idea that materials are intrinsically statistical objects: the properties a bulk material has are best calculated by averaging over all the possible configurations for the material's microscopic parts. Our insight was that design programs should focus on tailoring materials at the level of micro-states themselves, rather than simply focusing on the bulk emergent properties.

For instance, suppose that the pressure and temperature affect the stiffness of a given material and the goal is to set these two parameters to make the stiffest material. The black-box approach is to view this as an optimization problem with pressure and temperature as inputs and stiffness as an output. Yet this view completely ignores the micro-states. A better perspective is to treat the control parameters as means to alter the likelihood of micro-states. To design the material, an algorithm should tweak the parameters so that the material is more likely to be in micro-states with the target behavior.

This idea is the kernel of our approach: we built a formalism out of this concept and tackle materials' design at the level of micro-state information. This gave us a program that is broad enough to address the range of materials that are well described by statistical physics, and we achieve this with a boost in efficiency, thanks to the extra information extracted from the microstate configurations.

To test our approach, we constructed test problems that a good materials optimization scheme should be able to address by itself. Material scientists need optimizers that can solve problems where the search landscape has little variation between candidate materials, juggle multiple potentially competing physical effects, operate in high dimensional search spaces, tune the processing conditions that a material is subject to, and operate when on real-world scale optimization problems. We then translated these challenges into physical test problems, and compared our approach against optimization schemes that we have used successfully for materials design in the past. Given the criterion that the best optimizer is the one that has to make the fewest guesses to arrive at the material that performs a target function, our optimizer outperformed all of our old standards.

Probably the two most fascinating solutions presented in the paper [1] are the polymer folding problem and the directed self-assembly problem. In the polymer folding problem, we asked our optimizer to tune the interaction strengths between 6 beads attached to each other along a linear chain (Figure 1). Because the interactions are attractive, when they are strong enough the chain will fold itself up into a compact shape. The goal here was to make the chain fold into a specific shape: an octahedron. Its an interesting problem because it's well known that simply making all the interactions large will not produce an octahedral geometry. Instead, the interactions needed to be developed into three separate families to generate octahedron and it took hard work from the colloidal self-assembly community to show that this worked. So it was very exciting for us when our optimizer not only produced a virtually identical motif, but managed to yield the result in the span of hours.

Figure 1: Given a polymer of 6 beads each of different color, how should the strength of each short-ranged interaction be picked so that the polymer self-folds into an octahedron geometry? Each image shows a typical polymer configuration obtained at each stage in an optimization using our new approach. The optimizer essentially starts from random, chain like geometries and after ~200 cycles transforms them into the target shape.

There is a similar story behind our directed self-assembly problem. In this case, the material is a polymer made of two types of beads. The goal is to pattern a substrate with a thin strip that has an affinity for a particular one of those two beads (Figure 2). By setting the strip width and the strength of affinity just right, it is possible to make the polymer self-assemble into stripes containing only one polymer type followed by a stripe of the other polymer type and so on. This idea holds serious promise as a next-generation manufacturing technology for semiconductors because the sizes of these stripes are on the order of nanometers. By using the polymer stripes as stencils or masks, it is possible to make next generation circuits or hard drive media with features significantly smaller than what current processing techniques allow. What we found was that not only can our optimizer produce solutions to the problem of tailoring interaction strengths for this kind of directed self-assembly, but that it does so between 5-130X faster than approaches we had tried in the past. To put this into context, solving a directed self assembly problem in the past took us roughly 1 week. Now we can solve them in just under 12 hours.

Figure 2: Given melt of polymer chains each made from half a-type (red) and half b-type (blue) beads, how should one tune the interactions between the a and b beads and a substrate so that the polymer melt self-assembles into equally spaced stripes of a and b? On the top is an image of the original polymer melt configuration for randomly seeded interaction parameters. On the bottom shows the structures that result from using our algorithm to elicit self-assembly. Note the substrate has been colored based on the affinity for each type.

Speaking broadly, materials by design is a radical shift in how we transform bulk matter into useful technology. Historically materials have been either discovered by accident or appropriated from nature to perform technological functions. What we're after is the capacity to systematically identify which materials produce a target response. The benefit of this paradigm is that increasingly complex materials could be cooked up automatically to meet specific technological demands. Our algorithm is a small part of this growing field, but the hope is that it will inspire others to consider their expertise on materials within the new context of design.

Our experience in the past has been that it can be difficult to get started on building design engines for a new material. If the problem isn't posed the right way or the optimizer isn't appropriately tailored, it may require a substantial investment of time to construct an optimization scheme that actually works. What we tried to show in this paper is that our formalism works broadly over a range of very different physical problems without any need for additional modifications. It works out of the box, so to speak, for designing any material that can be simulated using a statistical physics approach. Our hope is that this robustness will translate into a reduction in the time researchers need to spend building design algorithms, and free them up to focus on the task of making exotic materials.

Some of our recent work along these lines can be found here:
[1] Marc Z. Miskin, Gurdaman Khaira, Juan J. de Pablo, Heinrich M. Jaeger, "Turning statistical physics models into materials design engines", Proceedings of the National Academy of Sciences, 113, 34-39 (2016). Full Text.
[2] Marc Z. Miskin, Heinrich M. Jaeger, "Adapting granular materials through artificial evolution", Nature Materials, 12, 326-331 (2013). Abstract.
[3] Marc Z. Miskin, Heinrich M. Jaeger, "Evolving design rules for the inverse granular packing problem", Soft Matter, 10, 3708-3715 (2014). Abstract.
[4] Jian Qin, Gurdaman S. Khaira, Yongrui Su, Grant P. Garner, Marc Miskin, Heinrich M. Jaeger, Juan J. de Pablo, "Evolutionary pattern design for copolymer directed self-assembly", Soft Matter, 9, 11467–11472 (2013). Abstract.

Single-Photon Sources Combine High Purity, Indistinguishability and Efficiency All Together

From left to right: Chao-Yang Lu, Jian-Wei Pan, Sven Höfling and Christian Schneider.

Authors: Chao-Yang Lu¹, Christian Schneider², Sven Höfling^1,2,3,  Jian-Wei Pan¹

Affiliation:
¹CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, China.
²Technische Physik, Physikalisches Institat and Wilhelm Conrad Rontgen-Center for Complex Material Systems, Universitat Wurzburg, Germany.
³SUPA, School of Physics and Astronomy, University of St. Andrews, UK.

One-sentence summary: A single-photon source has been demonstrated which, for the first time, combines the features of high efficiency and near-perfect levels of purity and indistinguishabilty, opening the way to scalable multi-photon experiments on a semiconductor chip.

Spontaneous parametric down conversion has served as an excellent workhorse for fundamental test of quantum mechanics, quantum teleportation and optical quantum computing [1]. In this nonlinear optics process, the emission of photon pairs is probabilistic (with a probability of p) and inevitably accompanied by higher-order emission events (on the order of p²), which strongly limit the scalability for optical quantum information processing. So far, up to eight-photon entanglement—created from four independent photon pairs—have been demonstrated [2].

Past 2Physics article by Chao-Yang Lu and/or Jian-Wei Pan :
March 22, 2015: "Quantum Teleportation of Multiple Properties of A Single Quantum Particle" by Chao-Yang Lu and Jian-Wei Pan
January 04, 2015: "Achieving 200 km of Measurement-device-independent Quantum Key Distribution with High Secure Key Rate" by Yan-Lin Tang, Hua-Lei Yin, Si-Jing Chen, Yang Liu, Wei-Jun Zhang, Xiao Jiang, Lu Zhang, Jian Wang, Li-Xing You, Jian-Yu Guan, Dong-Xu Yang, Zhen Wang, Hao Liang, Zhen Zhang, Nan Zhou, Xiongfeng Ma, Teng-Yun Chen, Qiang Zhang, Jian-Wei Pan
June 30, 2013: "Quantum Computer Runs The Most Practically Useful Quantum Algorithm" by Chao-Yang Lu and Jian-Wei Pan.

In an attempt to overcome this obstacle, increasing attention has turned to single quantum emitters, such as self-assembled semiconductor quantum dots (QD), trapped atoms or ions, single defects in diamond or monolayer, and single molecules. In the past two decades, although many previous proof-of-principle experiments have established photon antibunching — an unambiguous evidence for single-photon emission, a scalable extension to multiple photonic quantum bits remain elusive.

To be useful for multi-photon applications such as Boson sampling, a perfect single quantum emitters should fulfill the following wish list: (1) High quantum efficiency: The decay of excited states should predominantly result in an emitted photon. (2) Deterministic generation: Upon a pulsed excitation, the source should deterministically emit one photon in a push-button fashion. (3) High purity: The emission should have a vanishing multi-photon probability. (4) High indistinguishability: Individual photons emitted at different trials should be quantum mechanically identical to each other. (5) High collection efficiency: The radiated photons should be extracted with a high efficiency to a single spatial mode.

Past 2Physics article by Sven Höfling :
May 17, 2015: "A Current Out Of Fluctuations" by Pierre Pfeffer, Fabian Hartmann, Sven Höfling, Martin Kamp, Lukas Worschech.

Among the discovered single quantum emitters so far, QDs have the highest quantum efficiency in solid state and narrowest linewidth at cryogenic temperature, and thus are promising as deterministic single-photon emitters. However, despite the extensive efforts, simultaneously fulfilling all the five criteria in the wish list proved challenging. Most previous experiments either relied on non-resonant excitation of a QD-microcavity that degraded the photon purity and indistinguishability [3,4], or used resonant excitation of a QD in a planar cavity that limited the extraction efficiency [5].

Figure 1: (a) Scanning electron microscopy image of a typical QD micropillar. (b) Numerical simulation of the photon emission from the QD-micropillar. (c) The photons collected into the first lens per pulse versus single-photon purity versus pump power.

Recently, the USTC-Wurzburg joint team exploited s-shell pulsed resonant excitation of a Purcell-enhanced QD-micropillar to deterministically generate resonance fluorescence single photons [6] which for the first time combines all the features in the wish list. The experiments were performed on an InAs/GaAs QD embedded inside a 2.5 micron diameter micropillar cavity (see Fig.1a) with a quality factor of 6124 and a Purcell factor of 6.3. Great efforts are made to find a single perfect QD at a sweet point where at 7.8 K the QD is to spatially coupled and spectrally resonant to the micropillar. At pi pulse, we detect 3.7 million single photon counts per second. The overall system efficiency is 4.6%. After correcting for detection efficiency and optical loss, we estimate that 66% of the generated single photons are collected into the first objective lens. Figure 1c summarizes the combined performance of the efficiency and single-photon purity as a function of pump power. It should be noted that the high generation and extraction efficiency are obtained with little compromise of the single-photon purity (g²(0) ≤ 0.009).

The overall system efficiency 4.6% — the highest reported in QDs — can be improved using techniques such as orthogonal excitation and detection of RF, near-unity-efficiency superconducting nanowire single-photon detection, and antireflection coatings of the optical elements. At this stage already, the performance of the single-photon source is already about ten time brighter than the triggered single-photon source used in eight-photon entanglement, but requires a pump power that is 7 orders of magnitude lower.

Figure 2: Quantum interference between two single photons separated by ~13 ns where the photon polarization set at cross (a) and parallel (b). A zoom-in near the zero time delay is shown in (c).

Another crucial demand is that the photons should possess a high degree of indistinguishability. We note that the pulsed resonant excitation is more critically needed for QDs with large Purcell factors where the reduced radiative lifetime approaches the time jitter. The single photons' indistinguishability is tested using two-photon Hong-Ou-Mandel interference. Figure 2a and 2b show histograms of normalized two-photon counts for orthogonal and parallel polarization at an emission time separation of ~13 ns, respectively. An almost vanishing zero-delay peak is observed for two photons with identical polarization (see Fig. 2c for a zoom-in). We obtain a degrees of indistinguishability to be 0.978.

Such a single-photon source can be readily used to perform multi-photon experiments on a solid-state platform. Immediate applications include implementation of Boson sampling [7] — an intermediate quantum computation where it is estimated that with 20-30 single photons one can demonstrate complex tasks that is difficult for classical computers. In addition to the photonic applications, the high-efficiency fluorescence extraction would also allow a fast high-fidelity single-shot readout of single electron spins, and efficiently entangling distant QD spins.

References:
[1] Jian-Wei Pan, Zeng-Bing Chen, Chao-Yang Lu, Harald Weinfurter, Anton Zeilinger, Marek Żukowski, "Multi-photon entanglement and interferometry", Review of Modern Physics, 84, 777–838 (2012). Abstract.
[2] Xing-Can Yao, Tian-Xiong Wang, Ping Xu, He Lu, Ge-Sheng Pan, Xiao-Hui Bao, Cheng-Zhi Peng, Chao-Yang Lu, Yu-Ao Chen, Jian-Wei Pan, "Observation of eight-photon entanglement", Nature Photonics, 6, 225–228 (2012). Abstract.
[3] Charles Santori, David Fattal, Jelena Vučković, Glenn S. Solomon, Yoshihisa Yamamoto, "Indistinguishable photons from a single-photon device", Nature, 419, 594–597 (2002). Abstract.
[4] Stefan Strauf, Nick G. Stoltz, Matthew T. Rakher, Larry A. Coldren, Pierre M. Petroff, Dirk Bouwmeester, "High-frequency single-photon source with polarization control", Nature Photonics, 1, 704 (2007). Abstract.
[5] Yu-Ming He, Yu He, Yu-Jia Wei, Dian Wu, Mete Atatüre, Christian Schneider, Sven Höfling, Martin Kamp, Chao-Yang Lu, Jian-Wei Pan, "On-demand semiconductor single-photon source with near-unity indistinguishability", Nature Nanotechnology, 8, 213–217 (2013). Abstract.
[6] Xing Ding, Yu He, Z.-C. Duan, Niels Gregersen, M.-C. Chen, S. Unsleber, S. Maier, Christian Schneider, Martin Kamp, Sven Höfling, Chao-Yang Lu, Jian-Wei Pan, "On-Demand Single Photons with High Extraction Efficiency and Near-Unity Indistinguishability from a Resonantly Driven Quantum Dot in a Micropillar", Physical Review Letters, 116, 020401 (2016). Abstract.
[7] Scott Aaronson, Alex Arkhipov, The computational complexity of linear optics, Proceedings of the 43rd annual ACM symposium on Theory of computing, 2011, San Jose (ACM, New York, 2011), p. 333. Full Article.

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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