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2Physics Quote:
"While silicon is bulky and rigid, plastic electronics is soft, deformable and lightweight. Flexible electronic devices like rollable displays, conformable sensors, plastic solar cells and flexible batteries could enable applications that would be impossible to achieve by using the hard electronics of today. So far, the effective commercialization of such technology has been mainly prevented by cost and performance constraints. However, for some applications, the specific functionalities provided by flexible, biocompatible, conformable and light plastic electronics are much more important than the aforementioned obstacles and future scenarios can be realistically foreseen."
-- Giovanni A. Salvatore, Niko Münzenrieder, Gerhard Tröster
(Read their full article: "Trasparent Electronics Wrapped Around Hairs and Transferred on Plastic Contact Lens" )

Sunday, April 20, 2014

A Cosmic Web Filament Revealed in Lyman α Emission around a Luminous High-redshift Quasar

[Left to Right] Sebastiano Cantalupo, Fabrizio Arrigoni-Battaia, J. Xavier Prochaska, Joseph F. Hennawi, Piero Madau.

Authors: Sebastiano Cantalupo1,2, Fabrizio Arrigoni-Battaia2, J. Xavier Prochaska1,2, Joseph F. Hennawi2, Piero Madau1

1Department of Astronomy and Astrophysics & UCO/Lick Observatory, University of California, Santa Cruz, USA
2Max-Planck-Institut für Astronomie, Heidelberg, Germany

Galaxies are believed to be embedded in a “cosmic web”, the three-dimensional cellular foam arrangement of matter in the Universe predicted by the standard cold dark matter cosmological paradigm [1]. Most of the baryons do not reside in galaxies, but are spread along this web in highly ionized gaseous medium [2] that is too rarefied to form stars. While intergalactic gas may have been observed as absorption features in the spectra of background sources [3], direct constraints on the three-dimensional properties and morphology of the cosmic web are still missing. Limited by the rarity of bright background sources, absorption studies are only able to provide one-dimensional skewers of the cosmic web that are typically separated by several tens of Mpc. Direct detection of intergalactic gas in emission would instead provide a full three-dimensional image significantly improving our understanding of cosmological structure formation and the cycle of baryons in and out of galaxies.

Despite the predicted low surface brightness, there have been attempts to detect the cosmic web in Lyman α emission, e.g., by means of low-resolution spectroscopy [4] to search blindly for fluorescence generated by optically thick gas illuminated by the cosmic UV background [5]. Achieving a very deep flux limit of 8x10-20erg s-1 cm-2 arcsec-2, these observations failed to reveal the cosmic web. Positive fluctuations in the ionizing background may be used to increase the expected fluorescent signal [6]. In a pilot survey obtained in 2010 using a custom-built, narrow-band (NB) filter on the VLT-FORS we demonstrated indeed that bright quasars can, like a flashlight, “illuminate” the densest knots in the surrounding cosmic web and boost fluorescent Lyman α emission to detectable levels [7]. In this survey we found several compact ”dark galaxies” and extended nebulae (up to 65 physical kpc) around star forming galaxies, but none of them extending on intergalactic scales. Following the same experiment, we have initiated in 2012 a NB imaging campaign on Keck/LRISb centered on z~2 bright quasars and we have reported in a recent Nature letter [8] the first result of this new imaging survey.
Figure 1 : Processed and combined images of the field surrounding the quasar UM287. Each image is 2 arcmin on a side and the quasar is located at the center. In the narrow-band (NB3985) image (panel 'a'), which is tuned to the Lyman α line of the systemic redshift for UM287, one identifies very extended (≈ 55 arcsec across) emission – that we named "Slug Nebula". The deep V-band image (panel 'b') does not show any extended emission associated with UM287. This requires the Slug Nebula to be line-emission, and we identify it as Lyman α at the redshift of the quasar.

On November 12 and 13, 2012, we imaged the field of the quasar UM 287 with a custom NB filter tuned to Lyman α at z = 2.279 inserted into the Keck/LRISb camera on the 10m Keck-I telescope. We acquired 10 hours of integration in a series of dithered, 1200s exposures in clear conditions. In parallel (enabled by a dichroic), we obtained broad-band V images with the LRISr camera. Figure 1 presents the processed and combined images, centered on UM287. The V -band image is very deep and hundreds of compact sources are present in the field. We expect the majority of these are background galaxies, unrelated to the system. In the NB3985 image, however, one identifies a very extended source originating near the quasar with a projected size of about 1 arcmin (500kpc physical or 1.6 Mpc co-moving). We will refer to this extended emission as the ”Slug Nebula” in the reminder of this article. Within the nebula, very few sources are identified in the broad-band images nor is any extended emission observed. This requires the narrow-band light to be line-emission, and we identify it as Lyman α at the redshift of UM287.
Figure 2 : Lyman α image of the Slug Nebula. We subtracted from the NB image the continuum contribution estimated from the broad-band images. The location of the quasar UM287 is labeled with the letter “a”. The color map and the contours indicates, respectively, the Lyman α surface brightness and the signal-to-noise ratio (S/N) per arcsec2 aperture. The extended emission spans a projected angular size of ≈ 55 arcsec (about 460 physical kpc), measured from the 2σ (~10−18 erg s-1 cm-2 arcsec-2) contours. Object “b” is an optically faint (g~23AB) quasar at the same redshift of UM287. The Nebula appears broadly filamentary and asymmetric, extending mostly on the eastern side of quasar “a” up to a projected distance of about 35 arcsec (~285 physical kpc) measured from the 2σ isophotal.

Figure 2 presents the NB3985 image, continuum subtracted using standard techniques [8]. One identifies several compact sources including UM287 (labeled “a” in the figure) with excess Lyman α emission. The second brightest compact emitter (indicated by the letter “b”) is an optically faint (g~22 AB) quasar at the same redshift of UM287. The image is dominated, however, by the filamentary and asymmetric Slug Nebula. Although Lyman α nebulae extending up to about 250 kpc have been previously detected [9-13], the Slug Nebula represents so far a unique system as we show in Figure 3: with a size of about 55” or 460 physical kpc, it extends well beyond the virial radius of any plausible dark matter halo associated with UM287. Indeed, in order to be fully contained within the virial radius of a dark matter halo centered on UM287, the quasar host halo should have a total halo mass of 1013.5 Msun. This is ten times larger than the typical value associated with radio-quiet quasars (1012.5 Msun, see [8] for discussion) and it would make the host halo of UM287 one of the largest know at z > 2. However, this possibility is clearly excluded by the absence of an excess of Lyman α emitting galaxies around UM287 compared to other radio-quiet quasars. Our analysis of the galaxy distribution around UM287 suggests instead that this quasar is residing in a typical or under-dense environment for radio-quiet quasars and that its total halo mass therefore does not exceed 1012.5 Msun. Differently from any previous detection, the Slug Nebula is therefore the first possible image of intergalactic gas at z > 2 extending beyond any individual, associated dark matter halo. The rarity of these systems may be explained by the combination of anisotropic emission from the quasars (typically only about 40% of the solid angle around a bright, high-redshift quasar is unobstructed [14]), the anisotropic distribution of dense filaments and light travel effects that, for quasar ages younger than a few Myr, further limit the possible ”illuminated” volume.
Figure 3 : Luminosity-size relations for previously detected, bright Lyman α nebulae and the Slug Nebula around the quasar UM287. The plot includes nebulae surrounding AGN and Lyman α blobs (LAB). The dashed line indicates the virial diameter of a dark matter halo with total mass M ~ 1012.5 Msun, the typical host of radio-quiet quasars including UM287, as confirmed by the analysis of the galaxy overdensity in our field. The Slug Nebula, differently from any previous detection, extends on Intergalactic Medium scales that are well beyond any possible associated dark matter halo. Note that, even if we restrict the size measurement of the UM287 Nebula to the 4 × 10−18 erg s-1 cm-2 arcsec-2 isophotal to be comparable with the majority of the previous surveys, the measured apparent size of the Slug Nebula will be reduced only by about 20%.

In order to constrain the physical properties of this, so far, unique system, we use a set of Lyman α radiative transfer calculations [15] combined with hydrodynamical simulation of cosmological structure formation around a quasar halo host similar to UM287. We consider two possible, extreme scenarios for the Lyman α emission mechanism of the intergalactic gas associated with the Slug Nebula: a) the gas is mostly ionized and the Lyman α emission is mainly produced by hydrogen recombinations. b) the gas is mostly neutral and the emission is mainly due to scattering of the Lyman α and continuum photons produced by the quasar Broad Line Region (BLR). In both cases, we performed a full three dimensional Lyman α radiative transfer calculation including gas temperature and velocity field effects on Lyman α scattering within the Nebula. The models are used to obtain the scaling relations between the observable Lyman α surface brightness from the intergalactic gas surrounding the quasar and the hydrogen column densities. Through these relations, we converted the observed SB into an estimated gas column density for the two extreme scenarios. Note that the estimated column densities for case ”a” are degenerate with the ionized gas clumping factor (C =2
>/2, where n is the electron density) below the simulation resolution scale, ranging from ~10 proper kpc for diffuse intergalactic gas to ~100 pc for the densest regions within galaxies.

The results, using the observed BLR Lyman α luminosity and C = 1, are presented in Fig.4. The observed Lyman α emission from the intergalactic gas associated with the Slug Nebula requires very large column density of ”cold” (T < 5 x 104 K) gas to be matched by current simulations. The implied total, cold gas mass ”illuminated” by the quasar is Mgas ~1011.4±0.6 Msun for the ”mostly neutral” case (”b”) and Mgas ~1012±0.5Msun for the ”mostly ionized” case (”a”) and C = 1. Note that the total estimated mass for the case ”a” scales as C1/2. For comparison, a typical simulated filament in our cosmological simulation of structure formation with size and morphology similar to the Slug Nebula around a similar halo has a total gas mass of about 1011.3 Msun, but only about 15% of this gas is ”cold” (T < 5x104 K), i.e. 1010.5 Msun and therefore able to emit substantial Lyman α emission. These estimates are consistent with other recent, grid-based hydrodynamical simulations of structure formation [16].

Figure 4 : Inferred hydrogen column densities associated with the Slug Nebula. We have converted the observed Lyman α Surface Brightness into gas column densities using a set of scaling relations obtained with detailed radiative transfer simulations. We have explored two extreme cases: a) the gas is mostly ionized by the quasar radiation (panel “a”), b) the gas is mostly neutral (panel “b”). Two circular regions with a diameter of 7 arcsec (~ 8 times the seeing radius) have been masked at the location of the quasars (black circles). The inferred hydrogen column density in panel “a” scales as C−1/2, where C is the gas clumping factor below a spatial length of up to about 10 physical kpc at moderate overdensities (less than about 40 times the mean density of the Universe at z~2). The implied column densities and gas masses, in both cases, are at least a factor of ten larger than what is typically observed within cosmological simulations around massive haloes, suggesting, e.g., that a large number of small clumps within the diffuse Intergalactic medium may be missing within current numerical models.

How one can explain the large differences between the estimated, cold gas mass of the Slug Nebula and the available amount of cold gas predicted by numerical simulations on similar scales? The Slug Nebula seems to point in the direction of a second, fainter quasar companion of UM287. However, because of the large distance from UM287 -- at least 200 proper kpc and up to 4 proper Mpc considering the 1σ redshift error, and the morphology of the Nebula we can exclude that the UM287 Nebula is the result of tidal interaction due to a merging event between the two quasar hosts. Indeed, such a large separation would imply that any possible encounter between the two quasars is likely a high velocity interaction or an encounter with large impact parameter. We note that it is not impossible but extremely difficult to produce a long and massive tidal tail during a ”fast” encounter but the amount of gas stripped by the quasar host galaxies in the best scenario would likely be a very small fraction (< 10%) of its total ISM and certainly cannot account for the total amount of gas detected in the Nebula. Irrespective of the details of the possible interaction between the two quasar host galaxies, any resulting, long tidal tail would be very thin with sizes of the order of few kpc or less while the observed Nebula has a thickness of at least 100 physical kpc in its widest point.

Similarly, it would be very difficult to explain the properties of the Nebula assuming a galactic gas outflow origin produced by possible quasar feedback events. Indeed, although radio-quiet quasar outflows are highly unconstrained from current observations and poorly understood theoretically, the large size of the Nebula, extending well beyond the virial radius of the quasar host halo, would require a high velocity outflow that is incompatible with the “cold” temperature of the gas required by the Lyman α emission. A recent spectroscopic follow-up (Cantalupo et al., in preparation) provides additional evidences that the Nebula is kinematically quiet and therefore that it cannot be generated by “quasar feedback”. The size, morphology and kinematical properties of the gas are instead broadly consistent with our expectations from a filament of the “cosmic web”.

How one can then reconcile the intergalactic nature of the Slug Nebula with the large mass discrepancy with intergalactic gas simulations? One possibility is to assume that the simulations are not resolving a large population of small, cold gas clumps within the low-density Intergalactic medium that are illuminated and ionized by the intense radiation of the quasar. In this case, an extremely high clumping factor, namely C ~1000, on scales below few kpc would be required in order to explain the large luminosity of the Slug Nebula with the cold gas mass within the intergalactic filaments predicted by the simulations. On the other hand, if some physical process that is not fully captured by current grid-based simulations increases the fraction of cold gas around the quasar, e.g. a proper treatment of metal mixing, a smaller clumping factor may be required. In the extreme – and rather unrealistic - case that all the hot gas is turned into a cold phase, the required clumping factor would be C ~20. Even if the gas is not ionized by the quasar (case ”b” above), the simulations are able to reproduce the observed mass only if a substantial amount of hot gas is converted into a cold phase. Incidentally, this is exactly the same result found comparing the properties of Lyman α absorption systems around a large statistical sample of quasars with simulations [17].

The discovery of the Slug Nebula represents both a unique laboratory and a challenge for our knowledge of cosmological structure formation on Intergalactic scales around massive haloes. On one hand, it provides a fundamental confirmation that specifically designed, deep narrow-band surveys centered on bright quasars are able to provide - for the first time - an image of cosmic gas on intergalactic scales. The rarity of such detection however, may imply that several conditions regarding, e.g. the geometry of the quasar "illumination" are met arguing for the necessity of a very large sample of quasars. On the other hand, our observation indicates that current models of cosmological structure formation (at least numerical methods based on Adaptive Mesh Refinement algorithms) are far from providing an accurate picture of the gas properties - not only within galaxies - but also for diffuse Intergalactic gas within several hundreds of physical kpc from massive haloes at z ~2. In particular, the size and luminosity of the Slug Nebula suggest that a large population of cold, sub-kpc scale clumps may be present within the diffuse Intergalactic medium in proximity of quasars. Proper modeling of this gas phase will require a new generation of numerical models that are able - simultaneously - to spatially resolve these small intergalactic clumps within large simulation boxes, treat the multiphase nature of this gas and its interaction with galaxies and quasars.

[1] J. Richard Bond, Lev Kofman, Dmitry Pogosyan, "How filaments of galaxies are woven into the cosmic web". Nature, 380, 603–606 (1996). Abstract. arXiv:astro-ph/9512141.
[2] Renyue Cen, Jordi Miralda-Escude, Jeremiah P. Ostriker, Michael Rauch, "Gravitational collapse of small-scale structure as the origin of the Lyman-alpha forest". Astrophysical Journal Letters, 437, L9–L12 (1994). arXiv:astro-ph/9409017.
[3] Michael Rauch, "The Lyman Alpha Forest in the Spectra of QSOs". Annual Reviews of Astronomy and Astrophysics, 36, 267–316 (1998). Abstract. arXiv:astro-ph/9806286.
[4] Michael Rauch, Martin Haehnelt, Andrew Bunker, George Becker, Francine Marleau, James Graham, Stefano Cristiani, Matt Jarvis, Cedric Lacey, Simon Morris, Celine Peroux, Huub Röttgering, Tom Theuns, "A Population of Faint Extended Line Emitters and the Host Galaxies of Optically Thick QSO Absorption Systems". Astrophysical Journal, 681, 856–880 (2008). Full Text.
[5] Andrew Gould, David H. Weinberg, "Imaging the Forest of Lyman Limit Systems". Astrophysical Journal, 468, 462 (1996). arXiv:astro-ph/9512138.
[6] Sebastiano Cantalupo, Cristiano Porciani, Simon J. Lilly, Francesco Miniati, "Fluorescent Lyα Emission from the High-Redshift Intergalactic Medium". Astrophysical Journal, 628, 61–75 (2005). Full Text.
[7] Sebastiano Cantalupo, Simon J. Lilly, Martin G. Haehnelt, "Detection of dark galaxies and circum-galactic filaments fluorescently illuminated by a quasar at z = 2.4". Monthly Notices of the Royal Astronomical Society, 425, 1992–2014 (2012). Abstract. arXiv:1204.5753 [astro-ph.CO].
[8] Sebastiano Cantalupo, Fabrizio Arrigoni-Battaia, J. Xavier Prochaska, Joseph F. Hennawi, Piero Madau, "A Cosmic Web Filament revelead in Lyman-α emission around a luminous high-z quasar". Nature, 506, 63 (2014). Abstract.
[9] T.M. Heckman, G.K. Miley, M.D. Lehnert, W. van Breugel, "Spatially resolved optical images of high-redshift quasi-stellar objects". Astrophysical Journal, 370, 78–101 (1991).
[10] Patrick J. McCarthy, "High redshift radio galaxies". Annual Reviews of Astronomy and Astrophysics, 31, 639–688 (1993). Abstract.
[11] Charles C. Steidel, Kurt L. Adelberger, Alice E. Shapley, Max Pettini, Mark Dickinson, Mauro Giavalisco, "Lyα Imaging of a Proto-Cluster Region at =3.09". Astrophysical Journal, 532, 170–182 (2000). Full Article.
[12] Michiel Reuland, Wil van Breugel, Huub Röttgering, Wim de Vries, S. A. Stanford, Arjun Dey, Mark Lacy, Joss Bland-Hawthorn, Michael Dopita, George Miley, "Giant Lyα Nebulae Associated with High-Redshift Radio Galaxies". Astrophysical Journal, 592, 755–766 (2003). Full Text.
[13] Y. Matsuda, T. Yamada, T. Hayashino, R. Yamauchi, Y. Nakamura, N. Morimoto, M. Ouchi, Y. Ono, K. Kousai, E. Nakamura, M. Horie, T. Fujii, M. Umemura, M. Mori, "The Subaru Ly-alpha blob survey: a sample of 100-kpc Ly-alpha blobs at z= 3". Monthly Notices of the Royal Astronomical Society, 410, L13–L17 (2011). arXiv:1010.2877 [astro-ph.CO].
[14] M. Polletta, D. Weedman, S. Hönig, C. J. Lonsdale, H. E. Smith, J. Houck, "Obscuration in Extremely Luminous Quasars". Astrophysical Journal, 675, 960–984 (2008). Full Text.
[15] Sebastiano Cantalupo, Cristiano Porciani, "RADAMESH: cosmological radiative transfer for Adaptive Mesh Refinement simulations". Monthly Notices of the Royal Astronomical Society, 411, 1678–1694 (2011). Full Article.
[16] Michele Fumagalli, Joseph F. Hennawi, J. Xavier Prochaska, Daniel Kasen, Avishai Dekel, Daniel Ceverino, Joel Primack, "Confronting Simulations of Optically Thick Gas in Massive Halos with Observations at z=2-3"
. arXiv:1308.1669 [astro-ph.CO].

[17] J. Xavier Prochaska, Joseph F. Hennawi, Khee-Gan Lee, Sebastiano Cantalupo, Jo Bovy, S. G. Djorgovski, Sara L. Ellison, Marie Wingyee Lau, Crystal L. Martin, Adam Myers, Kate H. R. Rubin, Robert A. Simcoe, "Quasars Probing Quasars VI. Excess HI Absorption within One Proper Mpc of z~2 Quasars". Astrophysical Journal, 776, 136 (2013). Abstract.

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Sunday, April 13, 2014

Dropleton – The New Semiconductor Quasiparticle

From Left to Right: (top row) Andrew E. Almand-Hunter, Hebin Li, Steven T. Cundiff, (bottom row) Martin Mootz, Mackillo Kira, Stephan.W. Koch

Authors: Andrew E. Almand-Hunter1,2, Hebin Li1, Steven T. Cundiff1,2, Martin Mootz3, Mackillo Kira3, Stephan.W. Koch3

1JILA, University of Colorado & National Institute of Standards and Technology, Boulder, CO, USA
2Department of Physics, University of Colorado, Boulder, CO, USA
3Department of Physics, Philipps-University Marburg, Germany.

The description of many-particle systems becomes significantly simplified if stable configurations of subsets of the particles can be identified, particularly when the particles are interacting with one another. Examples of stable configurations range from solar systems and galaxies on an astronomical scale [1] to atoms and nuclei on a microscopic scale [2]. In solid-state systems [3], the stable configurations are referred to as “quasiparticles” that have several particle-like features, even though their physical properties are influenced by the interactions. The dropleton is the latest addition to the “periodic table” of quasiparticles in solids, as reported in our recent publication [4].

Extended crystalline solids typically contain more than 1020 interacting electrons per cm3, which makes the quantum many-body problem unsolvable based on overwhelming dimensionality. Therefore, finding quasiparticles is not only extremely useful but also instrumental in order to describe and understand the physics of solids. The “crystal electron’’ – or “Bloch electron’’ – is the simplest quasiparticle of solids. One can attribute a varying mass to an electron inside a crystal, in the same way as a swimmer’s bodyweight seems to change in water. As a quantum feature, crystal electron's effective mass not only depends on the electron-crystal interaction but also on its velocity [3]. When a single electron is removed from an ensemble of many electrons, the missing electron is also a quasiparticle called the “hole’’. The hole simply has the properties of the missing electron, such as a positive elementary charge and a negative effective mass. Conceptually, a hole resembles a bubble, i.e. particle vacancy, in water; its motion is clearly much simpler to track than that of remaining particles.

The quantum mechanically allowed electron-energy regions in solids are commonly known as energy bands and they can be separated by forbidden regions, the band gaps [3]. Without any doping and at low temperatures, a semiconductor is an insulator where all energetically low-lying bands are fully occupied by electrons and all energetically higher bands are completely free. The absorption of light transfers semiconductor electrons from the energetically highest fully occupied band – the valence band – into the originally unoccupied conduction band. Due to their opposite charge, the optically excited conduction-band electron and the simultaneously generated valence-band hole experience an attractive Coulomb interaction which may bind them to a new quasiparticle known as an exciton [5,6]. An exciton is similar in many ways to a hydrogen atom; however, it has a relatively short lifetime since the electron can return from the conduction into the valence band. In this electron-hole recombination process, the excess energy can be emitted as light or it can be transferred to the host crystal as heat.

Under suitable conditions, two excitons can bind into a molecule referred to as biexciton[7,8] which has strong analogies to the hydrogen molecule. Generally, it is an interesting open question if and in which form electron-hole pairs can form even larger clusters with quasiparticle character and how these clusters can be identified spectroscopically. One may distinguish the presence of distinct quasiparticles by the different color resonance they absorb or emit light [9-15], in the same way as atoms and molecules have distinct resonances in the absorption spectrum as fingerprints that provide a positive identification of the “culprit”.

However, identification of semiconductor quasiparticles from light absorption is not as simple as it seems. In general, an ordinary laser pulse only induces electron-hole-pair excitations whereas the more complex quasiparticles are created by the quantum mechanical many-particle interactions, yielding several possible outcomes [16] that blur the quasiparticle resonances. Since the state and the characteristic features of the excited state are very complex and depend sensitively on the detailed excitation conditions, it is generally very difficult to identify the quasiparticle signatures in spectra as long as “only” classical spectroscopy is used.

Figure 1: Classical vs. quantum-optical spectroscopy. In classical spectroscopy (left), the photons (wave symbols) are uncorrelated and they create unbound pairs of electrons (spheres) and holes (open circles). In quantum spectroscopy (right), the photons are correlated (yellow ellipse) such that they directly excite a correlated electron-hole cluster (yellow circle).

To overcome this problem, we developed the concept of quantum-optical spectroscopy [16,17] based on fundamental quantum properties of light. In general, quantized light can be described in terms of photons, i.e. the energy quanta of light. Whereas classical laser light basically contains isolated photons, i.e. no specific photon clusters, such clusters are characteristic for quantum light sources. Most important for our quasiparticle search, the cluster characteristics of the exciting light is directly transferred to the optically generated electron-hole excitations. Consequently, suitable quantum-light sources can e.g. generate predominantly excitons, or biexcitons, or even larger clusters [16,17]. In other words, one can directly excite new quasiparticles with a quantum-light source whose photon clusters match the cluster characteristics of the desired quasiparticle state. Figure 1 illustrates this main difference of classical and quantum-optical laser spectroscopy.

Even though freely adjustable quantum-light sources do not yet exist, we have demonstrated [18] that a large set of classical pump-probe spectra can be robustly projected into the desired quantum-optical spectra. To collect the data, we used short pulses to generate electrons and holes faster than they can decay. In our quasiparticle-search experiments [4], we actually apply pulses of light, produced by a laser, that are only 100 femtoseconds (1fs=10-15s) in duration. To study the types of quasiparticles that can occur in a semiconductor, beyond just electrons, holes and excitons, we use a strong pulse, known as the “pump” pulse to excite a desired number of electrons and holes. We then monitor how a weak subsequent pulse, known as the “probe” pulse, is absorbed. To observe different types of quasiparticles, we perform these measurements very carefully as we slowly increase the intensity of the pump pulse. Then each pump-pulse intensity labels a probe-absorption spectrum within the massive set of raw data that is the input to the projected quantum-optical spectrum.

When we did this experiment, we noticed already in the raw data that the light began to be absorbed at a new color as the intensity of the pump pulse increased. This new color was distinct from the color corresponding to the creation of an exciton, or of unbound pairs of electrons and holes. We initially ascribed this observation to the formation of a biexciton. However, increasing the intensity of the pump caused this new absorption feature to change color, but very surprisingly, it did so in the wrong direction, namely opposite to the shift of the absorption due to the exciton. This gave us the hint that the new quasiparticles could be dormant underneath the blurred and shifted “biexciton” resonance.

Figure 2: Revealing new energy resonances of Dropletons. Dropleton's binding energy is determined from the light absorption that is sensitive to three-photon correlations. The spectra are plotted as a function of pump pulse's photon number. The red color denotes regions with high absorption.

To reveal which quasiparticle explains this curious behavior, we projected the raw data to an absorption spectrum that is sensitive to three-photon clusters; the quantum-optical absorption spectra are shown Fig. 2 as function of pump power. The energy is expressed in terms of binding energy with respect to exciton resonance. For low photon numbers, we observed only a biexciton resonance that had a fixed binding energy around 2.2meV, as intuitively expected. By increasing the number of photons in the pump pulse, we surprisingly observed that the semiconductor starts to absorb light at completely new colors identified by the steps. We also performed measurements that could reject molecular electron-hole states as an explanation for energy quantization, and demonstrated that the new quasiparticle evolves coherently living up to 25 picoseconds (1ps=10-12s) [4].

After discovering these new energy resonances, we proceeded to identify the exact form of the new quasiparticle that matches the measured “fingerprints”. Since the quasiparticle has a stronger binding than biexciton it must contain more electron-hole pairs than biexciton, i.e. two. However, there is no quantum theory that can exactly solve the corresponding many-body problem. Therefore, we had to develop a new approach[19] to identify the new quasiparticles. More specifically, we expressed the system energy exactly in terms of pairwise electron-hole correlation function, instead of electron and hole densities that is the basis of the density functional theory [20]. Since the correlations uniquely define complicated quasiparticles, we could precisely determine the energies of different possible electron-hole configurations.

Figure 3: Illustration of a dropleton. In a dropleton, the probability distribution of the electrons and holes forms a ring-like pattern; a representative pair-correlation function is shown as a function of the electron-hole separation. The shell defines the size of the dropleton; roughly one electron-hole pair resides within each ring.

After a thorough search, all experimental observations were explained [4] only by a configuration where electrons and holes are not bound into excitons, but they rather are loosely organized, much like particles in a liquid. However, the liquid was confined inside a small bubble, which directly explained the quantization as a confinement effect. Due to liquid characteristics, quantization, and small size, we called the new quasiparticle a dropleton. The jumps in the dropleton energy levels were shown [4] to correspond to adding a new electron-hole pair to the dropleton. In total, we could detect dropletons with four, five, six, and seven electron-hole pairs and conclude that the quantum droplet size was in the range of 200nm (1nm=10-9m) in diameter.

The discovery of dropleton is the first tangible demonstration that the quantum-optical spectroscopy excites and controls quasiparticles with unprecedented accuracy. To make full use of this encouraging advancement, it will be an important future goal to develop ultrafast and strong light sources whose quantum fluctuations can be freely adjusted. Since the dropletons are brand new addition to the quasiparticle family, it is not predictable how and when they can be seen in practical use. However, all quasiparticles also influence the operation of optoelectronic devices such as laser diodes which are already used in DVD readers/writers and in optical communications. Thus, the improved control of quasiparticles will certainly enhance our ability to design these types of devices. In addition, dropletons couple strongly with quantum light, which should be extremely useful when designing lasers and devices capable of encoding and processing quantum information. This level of control of light-matter interaction will provide intriguing possibilities to test foundations of quantum mechanics as well as introduce new ways to utilize them to build devices with an incredible performance.

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[2] Yu. Ts. Oganessian, A. V. Yeremin, A. G. Popeko, S. L. Bogomolov, G. V. Buklanov, M. L. Chelnokov, V. I. Chepigin, B. N. Gikal, V. A. Gorshkov, G. G. Gulbekian, M. G. Itkis, A. P. Kabachenko, A. Yu. Lavrentev, O. N. Malyshev, J. Rohac, R. N. Sagaidak, S. Hofmann, S. Saro, G. Giardina, K. Morita "Synthesis of nuclei of the superheavy element 114 in reactions induced by 48Ca". Nature, 400, 242 (1999). Abstract.
[3] Charles Kittel, "Introduction to solid state physics" (Wiley & Sons, 8th Ed., 2005). 
[4] A.E. Almand-Hunter, H. Li, S.T. Cundiff, M. Mootz, M. Kira, S.W. Koch, "Quantum droplets of electrons and holes". Nature, 506, 471 (2014). Abstract.
[5] J. Frenkel, "On the transformation of light into heat in solids. I". Physical Review, 37, 17 (1931). Abstract.
[6] Gregory H. Wannier, "The structure of electronic excitation levels in insulating crystals". Physical Review, 52, 191 (1937). Abstract.
[7] Murray A. Lampert, "Mobile and immobile effective-mass complexes in nonmetallic solids". Physical Review Letters, 1, 450 (1958). Abstract.
[8] J.R. Haynes, "Experimental observation of the excitonic molecule". Physical Review Letters, 17, 860 (1966). Abstract.
[9] A.G. Steele, W.G. McMullan, and M.L.W. Thewalt, "Discovery of polyexcitons". Physical Review Letters, 59, 2899 (1987). Abstract.
[10] Daniel B. Turner, Keith A. Nelson, "Coherent measurements of high-order electronic correlations in quantum wells". Nature, 466, 1089 (2010). Abstract.
[11] Carson D. Jeffries, "Electron–hole condensation in semiconductors". Science 189, 955 (1975). Abstract.
[12] Takeshi Suzuki, Ryo Shimano, "Time-resolved formation of excitons and electron–hole droplets in Si studied using terahertz spectroscopy". Physical Review Letters, 103, 057401 (2009). Abstract.
[13] R.A. Kaindl, M.A. Carnahan, D. Hagele, R. Lovenich, D.S. Chemla, "Ultrafast terahertz probes of transient conducting and insulating phases in an electron–hole gas". Nature, 423, 734 (2003). Abstract.
[14] R. P. Smith, J. K. Wahlstrand, A. C. Funk, R. P. Mirin, S. T. Cundiff, J. T. Steiner, M. Schafer, M. Kira, S. W. Koch, "Extraction of many-body configurations from nonlinear absorption in semiconductor quantum wells". Physical Review Letters, 104, 247401 (2010). Abstract.
[15] R. Huber, F. Tauser, A. Brodschelm, M. Bichler, G. Abstreiter, A. Leitenstorfer, "How many-particle interactions develop after ultrafast excitation of an electron–hole plasma". Nature, 414, 286 (2001). Abstract.
[16] Mackillo Kira, Stephan W. Koch, "Semiconductor quantum optics" (Cambridge University Press, 2011).
[17] M. Kira and S.W. Koch, "Quantum-optical spectroscopy in semiconductors". Physical Review A, 73, 013813 (2006). Abstract.
[18] M. Kira, S.W. Koch, R.P. Smith, A.E. Hunter, S. T. Cundiff, "Quantum spectroscopy with Schrödinger-cat states". Nature Physics, 7, 799 (2011). Abstract.
[19] M. Mootz, M. Kira and S.W. Koch, "Pair-excitation energetics of highly correlated many-body states", New J. Phys. 15, 093040 (2013). Full Article.
[20] David Sholl and Janice A. Steckel, "Density Functional Theory: A Practical Introduction" (Wiley, 2009).

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Sunday, April 06, 2014

Entangled Photons are Used to Enhance the Sensitivity of Microscope.

(From left to right) Ryo Okamoto, Shigeki Takeuchi, Takafumi Ono

Authors: Takafumi Ono, Ryo Okamoto, Shigeki Takeuchi

Research Institute for Electronic Science, Hokkaido University, Japan,
The Institute of Scientific and Industrial Research, Osaka University, Japan.

We demonstrated a microscope whose sensitivity is enhanced by using quantum entanglement -- over the limit set by the conventional (classical) light illumination. This is the first experimental demonstration of the application of entangled photons for microscopy.

Quantum entanglement is a unique feature of quantum particles, like photons, electrons, and so on. Quantum entanglement was first introduced by Schrödinger, and later a famous debate on it occurred between Einstein and Bohr; Einstein called it `spooky action at a distance’. Now, quantum entanglement is attracting attention as the resources for quantum information technologies like quantum cryptography and quantum computation. We demonstrated that quantum entanglement is not only useful for such information technologies, but also in other broader fields, like microscopy.

Figure 1: A schematic image of the entanglement-enhanced microscope.

Some years ago, we reported the experiment of four photon interference with high visibility -- enough to beat the standard quantum limit for the phase sensitivity [2]. In that experiment, we used so called `NOON’ state, a path-entangled state where N-photon state is either in one of the two paths (and 0 photons in the opposite path). We demonstrated the quantum interference fringe using a four-photon NOON state with a high-visibility (91%) that was enough to beat the standard quantum limit of the phase sensitivity.

Perhaps the next natural step is to demonstrate entanglement-enhanced metrology. Among the applications of optical phase measurement, the differential interference contrast microscope (DIM) is widely used for the evaluation of opaque materials or biological tissues. The depth resolution of such measurements is determined by the signal-to-noise ratio (SNR) of the measurement, and the SNR is in principle limited by the standard quantum limit. In the advanced measurements using DIM, the intensity of the probe light is tightly limited for a non-invasive measurement, and the limit of the SNR has become a critical issue.

In our recent work [1], we proposed and demonstrated an entanglement-enhanced microscope, which is a confocal-type DIM where an entangled photon pair source is used for illumination. An image of a glass plate sample, where a Q shape is carved in relief on the surface with a ultra-thin step of ~17 nm, is obtained with better visibility than with a classical light source. The signal-to-noise ratio is 1.35±0.12 times better than that limited by the standard quantum limit. The success of this research will enable more highly sensitive measurements of living cells and other objects, and it has the potential for application in a wide range of fields, including biology and medicine.
Figure 2: (a) Atomic force microscope (AFM) image of a glass plate sample (BK7) on whose surface a Q shape is carved in relief with an ultra-thin step using optical lithography. (b) The section of the AFM image of the sample, which is the area outlined in red in a. The height of the step is estimated to be 17.3nm from this data. (c) The image of the sample using an entanglement-enhanced microscope where two-photon entangled state is used to illuminate the sample. (d) The image of the sample using single photons (a classical light source).

We believe this experimental demonstration is an important step towards entanglement- enhanced microscopy with ultimate sensitivity, using a higher NOON state or other quantum states of light. There are some other related works harnessing such nonclasical light for metrology[3-5].

[1] Takafumi Ono, Ryo Okamoto, Shigeki Takeuchi, “An entanglement-enhanced microscope”. Nature Communications, 4, 2426 (2013). Abstract.
[2] Tomohisa Nagata, Ryo Okamoto, Jeremy L. O'Brien, Keiji Sasaki, Shigeki Takeuchi, “Beating the standard quantum limit with four-entangled photons”. Science, 316, 726–729 (2007). Abstract.
[3] Andrea Crespi, Mirko Lobino, Jonathan C. F. Matthews, Alberto Politi, Chris R. Neal, Roberta Ramponi, Roberto Osellame, Jeremy L. O’Brien, “Measuring protein concentration with entangled photons”. Applied Physics Letters, 100, 233704 (2012). Abstract.
[4] Florian Wolfgramm, Chiara Vitelli, Federica A. Beduini, Nicolas Godbout, Morgan W. Mitchell, “Entanglement- enhanced probing of a delicate material system”. Nature Photonics, 7, 28–32 (2013). Abstract.
[5] Michael A. Taylor, Jiri Janousek, Vincent Daria, Joachim Knittel, Boris Hage, Hans-A. Bachor, Warwick P. Bowen, “Biological measurement beyond the quantum limit”. Nature Photonics, 7, 229–233 (2013). Abstract.

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Sunday, March 30, 2014

Polarization-controlled Photon Emission
from Site-controlled InGaN Quantum Dots

Left to Right: (top row) Chih-Wei Hsu, Anders Lundskog, K. Fredrik Karlsson, Supaluck Amloy. (bottom row) Daniel Nilsson, Urban Forsberg, Per Olof Holtz, Erik Janzén.

Authors: Chih-Wei Hsu1, Anders Lundskog1, K. Fredrik Karlsson1, Supaluck Amloy1,2, Daniel Nilsson1, Urban Forsberg1, Per Olof Holtz1, Erik Janzén1

1Department of Physics Chemistry and Biology (IFM), Linköping University, Sweden.
2Department of Physics, Faculty of Science, Thaksin University, Phattalung, Thailand.

A common requirement to realize several optoelectronic applications, e.g. liquid-crystal displays, three-dimensional visualization, (bio)-dermatology [1] and optical quantum computers [2], is the need of linearly-polarized light for their operation. For existing applications today, the generation of linearly-polarized light is obtained by passing unpolarized light through a combination of polarization selective filters and waveguides, with an inevitable efficiency loss as the result. These losses could be drastically reduced by employment of sources, which directly generate photons with desired polarization directions.

Quantum dots (QDs) have validated their important role in current optoelectronic devices and they are also seen as promising as light sources for generation of “single-photons-on-demand”. Conventional QDs grown via the Stranski-Krastanov (SK) growth mode are typically randomly distributed over planar substrates and possess different degrees of anisotropies. The anisotropy in the strain field and/or the geometrical shape of each individual QD determines the polarization performance of the QD emission. Accordingly, a cumbersome post-selection of QDs with desired polarization properties among the randomly-distributed QDs is required for device integration [3]. Consequently, an approach to obtain QDs with controlled site and polarization direction is highly desired.
Figure 1. Magnified SEM images of GaN EHPs with various α. The values of α are defined as the angles between the long axis of EHPs and the underlying GaN template.

Here, we demonstrate an approach to directly generate a linearly-polarized QD emission by introducing site-controlled InGaN QDs on top of GaN-based elongated hexagonal pyramids (GaN EHPs). The polarization directions of the QD emission are demonstrated to be aligned with the orientations of the EHPs (Figure 1). The reliability and consistency for this architecture are tested by a statistical analysis of InGaN QDs grown on GaN EHP arrays with different in-plane orientations of the elongations. Details of the process and optical characterizations can be found in our resent publication [4].

Figure 2. a) µPL spectra of EHPs with the polarization analyzer set to θmaxmin), by which the maximum (minimum) intensity of sharp emission peaks are detected. b) Distribution histograms of measured polarization directions from the GaN EHPs for various α.

Figure 2a shows representative polarization-dependent micro-photoluminescence (µPL) spectra from a EHP measured at 4o K. A broad emission band peaking at 386 nm and several emission peaks in the range between 410 and 420 nm are observed. These sharp emission lines are originating from the multiple QDs formed on top of the GaN EHP. Despite the formation of multiple QDs on a GaN EHP, the emission peaks from all QDs tend to be linearly-polarized in the same direction as revealed in Figure 3a and all peaks have their maximum and minimum intensities in the same direction, θ. The correlation between the outcome of the polarization-resolved measurements and the orientations of GaN EHPs (as defined by α) reveals that the polarization direction is parallel to the elongation (α≅φ in Figure 2b). A polarization guiding (α≅φ) is unambiguously revealed for GaN EHPs with α = 0o, 60o and 120o. For the remaining group of GaN EHPs with α = 30o, 90o and 150o, preferential polarization directions are seemly revealed, but α≅φ is less strictly obeyed. The polarization guiding effect and the high degree of polarization are further elucidated in the following.

Figure 3. a) Statistical histogram showing the overall measured degree of polarization from GaN EHPs. b) The computed degree of polarization plotted as a function of the split-off energy. The QD shape is assumed to be lens-shaped with an in-plane asymmetry of b/a= 0.8. The single particle electron (hole) eigenstates are obtained from an effective mass Schrödinger equation (with a 6 band k•p Hamiltonian), discretized by finite differences. The Hamiltonians include strain and internal electric fields originating from spontaneous and piezoelectric polarizations. The polarized optical transitions are computed by the dipole matrix elements.

The polarization direction of the ground-state-related emission from the QDs reflects the axis of the in-plane anisotropy of the confining potential, concerning both strain and/or QD shape [5]. The same polarization direction monitored for the different QDs indicates that all grown QDs possess unidirectional in-plane anisotropy. The polarization control observed in our work can be explained in three ways: (1) the GaN EHPs transfer an anisotropic biaxial strain field to the QDs resulting in the formation of elongated QDs. The direction of the strain field in the EHPs should be strongly correlated with α. (2) Given that the top parts of the GaN EHPs are fully strain relaxed, as concluded for the GaN SHPs [6], the asymmetry induced by a ridge will result in an anisotropic relaxation of the in-plane strain of the QDs on the ridge. The degree of relaxation is higher along the smallest dimension of the top area, i.e. along the direction perpendicular to the ridge elongation, resulting in a ground state emission of the QD being polarized in parallel with the ridge. (3) The edges of the ridges form a Schwoebel–Ehrlich barrier, which prevents adatoms of diffusing out from the (0001) facet [7,8]. Since the adatoms have larger probability to interact with an edge barrier parallel rather than orthogonal to the ridge elongation, the adatoms will preferentially diffuse parallel to the ridge. As the strain and the shape of the QDs are not independent factors and accurate structural information of the QDs is currently unavailable, the predominant factors determining the polarization is to be verified.

The polarization degree of the III-Ns is more sensitive to the in-plane asymmetry compared to other semiconductor counterparts due to the significant band mixing and the identical on-axis effective masses of the A and B bands in the III-N [5]. A statistical investigation of the value of P performed on 145 GaN EHPs reveals that 93% of the investigated GaN EHPs possess P > 0.7 with an average value of P = 0.84 (Figure 3a). The polarization of the emissions is related to the QD asymmetry determined by the anisotropy of the internal strain and electric fields, as well as by the structural shape of the QD itself [5]. Numerical computations predict a high degree of polarization for small or moderate in-plane shape anisotropies of GaN and InGaN QDs [9]. This is related to the intrinsic valence band structure of the III-Ns. In particular, the split-off energy has been identified as the key material parameter determining the degree of polarization for a given asymmetry. Figure 3b shows the computed degree of polarization plotted against a variation of the split-off energy. Given a fixed asymmetry of the QDs, it is concluded that the material with the smallest split-off energy exhibits the highest degree of polarization. The high degree of polarization observed for InGaN QDs can be rationalized by the small split-off energies of InN and GaN, resulting in an extreme sensitivity to the asymmetry. Such a characteristic implies its inherent advantage for the generation of photons possessing a specific polarization.

In summary, we have demonstrated an effective method to achieve site-controlled QDs emitting linearly-polarized emission with controlled polarization directions by growing InGaN QDs on top of elongated GaN pyramids in a MOCVD (metal organic chemical vapor deposition) system. The polarization directions of the QD emission can be guided by the orientations of the underlying elongated GaN pyramids. Such an effect can be realized as the elongated GaN pyramids provide additional in-plane confinement for the InGaN QDs implanting unidirectional in-plane anisotropy into the QDs, which subsequently emit photons linearly-polarized along the elongated direction of the GaN EHPs.

[1] Zeng Nan, Jiang Xiaoyu, Gao Qiang, He Yonghong, Ma Hui, "Linear polarization difference imaging and its potential applications". Applied Optics, 48, 6734-6739 (2009). Abstract.
[2] E. Knill, R. Laflamme, G.J. Milburn, "A scheme for efficient quantum computation with linear optics". Nature, 409, 46-52 (2001). Abstract.
[3] Robert J. Young, D.J.P. Ellis, R.M. Stevenson, Anthony J. Bennett, "Quantum-dot sources for single photons and entangled photon pairs". Proceedings of the IEEE, 95, 1805–1814 (2007). Abstract.
[4] Anders Lundskog, Chih-Wei Hsu, K Fredrik Karlsson, Supaluck Amloy, Daniel Nilsson, Urban Forsberg, Per Olof Holtz, Erik Janzén, "Direct generation of linearly-polarized photon emission with designated orientations from site-controlled InGaN quantum dots". Light: Science & Applications 3, e139 (2014). Full Article.
[5] R. Bardoux, T. Guillet, B. Gil, P. Lefebvre, T. Bretagnon, T. Taliercio, S. Rousset, F. Semond, "Polarized emission from GaN/AlN quantum dots: single-dot spectroscopy and symmetry-based theory". Physical Review B, 77, 235315 (2008). Abstract.
[6] Q.K.K. Liu, A. Hoffmann, H. Siegle, A. Kaschner, C. Thomsen, J. Christen, F. Bertram, "Stress analysis of selective epitaxial growth of GaN". Applied Physics Letters, 74, 3122-3124 (1999). Abstract.
[7] O. Pierre-Louis, M.R. D’Orsogna, T.L. Einstein, "Edge diffusion during growth: The kink Schwoebel-Erhlich effect and resulting instabilities". Physical Review Letters, 82, 3661-3664 (1999). Abstract.
[8] S.J. Liu, E.G. Wang, C.H. Woo, Hanchen Huang, "Three-dimensional Schwoebel–Ehrlich barrier". Journal of Computer-Aided Materials Design, 7, 195–201 (2001). Abstract.
[9] S. Amloy, K.F. Karlsson, T.G. Andersson, P.O. Holtz, "On the polarized emission from exciton complexes in GaN quantum dots". Applied Physics Letters, 100, 021901 (2012). Abstract.

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Sunday, March 23, 2014

Invisibility Cloak Goes Three-Dimensional for Heat

Authors: Hongyi Xu1, Xihang Shi1, Fei Gao1, Handong Sun1,2, Baile Zhang1,2

1Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore.
2Centre for Disruptive Photonic Technologies, Nanyang Technological University, Singapore.

While the topic of invisibility has long been investigated in optics-related topics, it is for the first time that invisibility cloaking is realized for heat in a three-dimensional (3D) thermal space, according to a recent research result[1] published by our group at Nanyang Technological University, Singapore.

Thermal invisibility was initially inspired by the concept of Transformation Optics [2, 3], a method that can control light propagation with a coordinate transformation in a 3D optical space, which in general requires optical metamaterials with exotic constitutive parameters (e.g. extremely large or extremely small anisotropic permittivity and permeability). Despite the inspiring elegance of 3D optical invisibility cloaking theory, its experimental realizations have been mainly limited to two dimensions (2D), because of the widely acknowledged tremendous difficulties in constructing optical metamaterials with stringent parameters in 3D.

Similarly, the recent development of thermal invisibility cloaking based on transformation thermodynamics were firstly demonstrated in 2D [4, 5]. The method, similar to transformation optics, requires thermal metamaterials with anisotropy and inhomogeneity, being difficult in 3D.

Researchers in Nanyang Technological University successfully bypassed the problem by taking advantage of the difference between heat (a diffusion phenomenon) and light (a wave phenomenon), and experimentally demonstrated the world’s first ultra-thin 3D thermal cloak that shields an air bubble in a stainless steel from external conductive heat flux [1]. The technology can protect a 3D object from heat flux without distorting the external temperature distribution by simply using an ultra-thin layer of thermal metamaterial made of copper with carefully designed thickness.

The implementation process of thermal cloak is illustrated in Fig.1. A hemi-spherical hole with radius of 0.51 cm was drilled by electrical discharge machining in a half stainless steel block with dimension of 2×2×1 cm. A thin disk of copper was punched into the hemi-spherical hole by a molding rod (Fig 1a), to form a copper shell (Fig. 1b) with homogeneous thickness of 100 μm. Two identical half blocks were further combined together to form a complete 3D thermal cloak (Fig. 1c), with dimension of 0.5/0.51 cm for the inner/outer radius of the copper spherical layer, and 2×2×2 cm for the complete stainless steel block.

Figure 1. Illustration of the Fabrication of a 3D thermal cloak. a, Molding process of half of the 3D thermal cloak: (a) Thin copper disk is punched into the hemispherical hole in the stainless steel block. (b) Illustration and snapshot of half of the thermal cloak after molding. (c) Illustration and snapshot of the full cloak by combining two half blocks. The red/blue plate represents high/low temperature at the bottom/top surface [1].

In the experimental characterization, a hot plate (red color, Fig. 1c) and an ice tank (blue color, Fig. 1c) were closely attached to the bottom and top surface of the thermal cloak. When heat diffused from bottom to top, the temperature at the cross-section surface was captured by a thermal camera. The dynamic process of heat transfer from the beginning to the moment near thermal equilibrium was recorded in a movie clip:

The temperature distributions at the beginning time and at the moment near thermal equilibrium are shown in Fig. 2. In Fig. 2a and 2d (cases of background), the temperature distribution is homogeneous across the entire surface, indicating that heat diffuses through the stainless steel smoothly. In Fig. 2b and 2e (cases without thermal cloak), the distribution of temperature is distorted (being ‘bent’ towards the air bubble) and a relatively cool region is left behind the air bubble, indicating that part of heat flux has been blocked by the air bubble. In Fig. 2c and Fig. 2f (cases with thermal cloak), the temperature distribution outside the air bubble is restored to norm, as if the air bubble did not exist, indicating the cloaking effect for heat flux.
Figure 2. Characterization of conductive thermal cloaking for transient homogeneous thermal flux. (a-c) Temperature distributions for the moment of 0.5 min at the beginning of heat transfer. (d-f) Temperature distributions for the moment of 4.5 min close to thermal equilibrium. (a&d) Temperature distributions in the pure background without any air bubble or cloak. (b&e) Temperature distributions when an air bubble without the cloak is present. (c&f) Temperature distributions when the air bubble is cloaked by the ultra-thin cloak. In b-c and e-f, the dotted circles indicate the position of the air bubble, while the dotted circles in a and d are merely for comparison [1].

This thermal invisibility cloak is the first demonstration in 3D that heat flux can be effectively controlled by thermal metamaterials. Application wise, effective control of heat is an important subject in modern semiconductor industries, where the exponential increase of package density is generating more and more heat in a unit space. The heat generated jeopardized the performance and lifetime of semiconductor devices, accounting for over 50 percent of electronic failures [6]. With effective heat control technologies based on thermal metamaterials, it is possible to develop efficient heat dissipation solutions to thermal problems in semiconductor industries.

[1] Hongyi Xu, Xihang Shi, Fei Gao, Handong Sun, Baile Zhang, "Ultrathin Three-Dimensional Thermal Cloak", Physical Review Letters, 112, 054301 (2014). Abstract.
[2] Ulf Leonhardt, "Optical Conformal Mapping", Science, 312, 1777-1780 (2006). Abstract.
[3] J. B. Pendry, D. Schurig, D. R. Smith, "Controlling Electromagnetic Fields", Science, 312, 1780-1782 (2006). Abstract.
[4] Supradeep Narayana, Yuki Sato, "Heat Flux Manipulation with Engineered Thermal Materials", Physical Review Letters, 108, 214303 (2012). Abstract.
[5] Robert Schittny, Muamer Kadic, Sebastien Guenneau, Martin Wegener, "Experiments on Transformation Thermodynamics: Molding the Flow of Heat", Physical Review Letters, 110, 195901 (2013). Abstract.
[6] Shanmuga Sundaram Anandan, and Velraj Ramalingam, "Thermal Management of Electronics: A Review of Literature," Thermal Science, 12, 5-26 (2008). Full Article.


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