Inspiration from Nature: Ultralight Fractal Designs for High Mechanical Efficiency

[From Left to Right] Daniel Rayneau-Kirkhope, Robert Farr, Yong Mao



Authors: Daniel Rayneau-Kirkhope¹, Robert Farr^2,3, Yong Mao⁴

Affiliation:
¹Open Innovation House, School of Science, Aalto University, Finland,
²Unilever R&D, Colworth House, Sharnbrook, Bedford, UK
³London Institute for Mathematical Sciences, Mayfair, London, UK
⁴School of Physics and Astronomy, University of Nottingham, UK

Hierarchical design is ubiquitous in nature [1]. Material properties can be tailored by having structural features on many length scales. The gecko, a lizard ranging from 2 to 60 cm in length, has a remarkable ability to walk on vertical walls and even upside-down on ceilings. This ability is brought about through the repeated splitting of the keratinous fibres on the bottom of the gecko’s foot, which increases the contact area so effectively that even the very weak van der Waals interactions can support the entire weight of the gecko [2].

A more specific form of hierarchical design is self-similar design, where one structural feature is found to be repeated on a number of different length scales. A natural example is the trabecular or spongy bone found around the joints in animals [3]. Here, a series of small beams are arranged in such a way that the stiffness and strength requirements are met while using minimal material. Regardless of the level of magnification, the same patterns are found in the structure. Interestingly, the exact configuration of the constituent beams in the trabecular bone is constantly changing: it is the result of a continuous opitimisation process that goes on throughout the lifetime of the bone and responds to change in stress levels [4]. It is found that when the animal’s bones support only small loads, many very slender pillars are present, and when the loading increases, fewer but stouter pillars are employed [5].

In our recently published work [6], we demonstrate that through the use of hierarchical, self-similar design principles, advantageous structural properties can be obtained. We show that the scaling of the amount of material required for stability against the loading can be altered in a systematic manner. A particular structure is fabricated through rapid prototyping, and we obtain the optimal generation number (for our specific structure) for any given value of loading.

Scaling

The volume of material required for stability can be related to the loading through a simple power law relationship. That is, the volume required is given by a dimensionless loading parameter raised to some power with a pre-factor (that is dependent only on material properties and specifics of the geometry). When the loading is small, it is the scaling (power) of the loading that dominates the relationship. Under tension, this power is one and a structure requires an amount of material that is proportional to the loading it must withstand; for a solid beam under compression, due to elastic buckling, the power is one-half. Given, for all realistic applications, the non-dimensional loading parameter is much less than 1, this means more material is required to support compressive than tensional loads. This one-half power law has direct consequences when one considers optimal structure: if a beam is bearing a compressive load, it is more efficient to use one beam rather than two, whereas in the case of tension, due to the linear relationship, splitting a tension member into more than one piece has no effect on the volume required for stability.

Fractal design

Our work centers on a very simple, iterative procedure that can be used to create designs of great complexity. The “generation” of a structure describes the number of iterations used to create the geometry. The simplest compression bearing structure is a solid slender beam. When loaded with a gradually increasing force, the beam will eventually buckle into a sinusoidal shape known as an “Euler buckling mode”. We can suppress this by using a hollow tube, but we introduce a second mode of a local failure of the tube wall – Koiter buckling. After optimizing for tube diameter and thickness, it is found that the scaling power increases to two-thirds, and the volume of material required for stability is reduced.

Figure 1: Showing the iterative process from low generation numbers to higher for structures bearing compression along their longest axis. At each step, all beams that are compressively loaded are replaced by a (scaled) generation-1 frame.

The next step is to replace the hollow beam with a space frame of hollow beams. The space frame used here is made up of n octahedra and two end tetrahedra. Optimising the number of octahedra, the radius and the wall thickness of the component beams (which are all assumed be identical) we find a new power law, and again, an improvement over the hollow beam design.

Continuing this procedure of replacing all beams under compressive load with (scaled) space frames constructed from hollow beams (figure 1), we find that the scaling law is always improved by the increased level of hierarchy. In general, the scaling is described by a (G+2)/(G+3) power-law relating non-dimensional volume to non-dimensional loading. Thus, as the generation number tends to infinity, the scaling relating material required for stability to loading approaches that of the tension member.

3D Printing

Working with Joel Segal, of the University of Nottingham, we fabricated an example of a generation-2 structure with solid beams, shown in figure 2. This was done through rapid prototyping technologies: micrometer-layer-by-micrometer-layer the structure was printed in a photosensitive polymer with each beam a fraction of a millimeter in radius. This structure shows the plausibility of the design and the extent to which modern manufacturing techniques allow for an increased creativity in design geometry. Through a process of 3-d printing and electro less deposition, it is believed that a metallic, hollow tubed structure could be created.

Figure 2: Showing a structure fabricated through rapid prototyping techniques. The inset shows the layering effect of the 3D printing technique. The structure shown in constructed in RC25 (Nanocure) material from envisionTEC on an envisionTEC perfactory machine.

Optimal generations

Although the scaling is always improved by increasing the generation number of the structure, the prefactor isn’t. The optimal structure is then obtained by balancing the scaling relationship with the prefactor in the expression. Generally, as the loading decreases (or the size of the structure increases), the scaling becomes more important and the optimal generation number increases. For large loads (or small structures) it can even be the case a simple, solid, beam is optimal.

Our work also formalises this relationship, for a long time engineers have created chair legs from hollow tubes or cranes out of space frames, Gustave Eiffel used three levels of structural hierarchy in designing the Eiffel tower. We show formally, that the optimal generation number has a set dependence on the loading conditions and allow future structures to be designed with this in mind. A further consequence of the alteration of the scaling law is that the higher the generations, the less difference it makes as to whether you have one structure holding a given load or two structures holding half the load each.

Reference:
[1] Robert Lakes, "Materials with structural hierarchy", Nature, 361, 511 (1993). Abstract.
[2] Haimin Yao, Huajian Gao, "Mechanics of robust and releasable adhesion in biology: Bottom–up designed hierarchical structures of gecko", Journal of the Mechanics and Physics of Solids, 54,1120 (2006). Abstract.
[3] Rachid Jennanea, Rachid Harbaa, Gérald Lemineura, Stéphanie Bretteila, Anne Estradeb, Claude Laurent Benhamouc, "Estimation of the 3D self-similarity parameter of trabecular bone from its 2D projection", Medical Image Analysis, 11, 91 (2007). Abstract.
[4] Rik Huiskes, Ronald Ruimerman, G. Harry van Lenthe, Jan D. Janssen, "Effects of mechanical forces on maintenance and adaptation of form in trabecular bone", Nature, 405, 704 (2000). Abstract.
[5] Michael Doube, Michał M. Kłosowski, Alexis M. Wiktorowicz-Conroy, John R. Hutchinson, Sandra J. Shefelbine, "Trabecular bone scales allometrically in mammals and birds", Proceedings of the Royal Society B, 278, 3067 (2011). Abstract.
[6] Daniel Rayneau-Kirkhope, Yong Mao, Robert Farr, "Ultralight Fractal Structures from Hollow Tubes", Physical Review Letters, 109, 204301 (2012). Abstract.

Observation of Entanglement Between a Quantum Dot Spin and a Single Photon

[From left to right] Parisa Fallahi, Atac Imamoglu, Javier Miguel-Sanchez, Wei-bo Gao, Emre Togan















Authors: Wei-bo Gao, Parisa Fallahi, Emre Togan, Javier Miguel-Sanchez, Atac Imamoglu

Affiliation: Institute of Quantum Electronics, ETH Zurich, Switzerland

Entanglement deepens our understanding of fundamental physics. A well-known example is the study of non-local interpretations of quantum mechanics by testing the violation of Bell’s inequality [1]. In the practical side, an interface between a stationary qubit (spin) and a flying qubit (photon) is a basic element to build a distributed quantum network. Moreover, such a network can be used for building a quantum computer, that offers significant speedups in solving certain technologically relevant classes of problems. A realization of distributed quantum computation will use few-qubit quantum processor nodes (spins) connected by photons [2]. A particularly interesting platform is a spin based semiconductor system in which photonic circuits that interconnect the nodes can be fabricated on the same semiconductor chip [3].

In the past few years, considerable efforts have been made to demonstrate entanglement between a spin and a photon. In 2004, the first observation of entanglement between a single trapped atom and a single photon was realized in the group of C. Monroe in Michigan [4]. In 2006 and 2007, the entanglement between a neutral atom and a single photon was realized in the groups of H. Weinfurter [5] G. Rempe [6] in Germany. In 2010, entanglement between an N-V center and a single photon was reported [7]. Despite the appeal of semiconductor based systems the realization of spin-photon entanglement in these systems had been very challenging mainly due to fast transitions and strong decoherence of the quantum dot spins and has only been achieved in 2012. In our work as well as the complementary work of the Yamamoto group at Stanford, the difficulty of measurement was overcome and the first semiconductor spin-photon entanglement was reported [8, 9].

Our experiment focuses on a single electron spin trapped in an InGaAs self-assembled quantum dot. A magnetic field of 0.7 Tesla applied perpendicular to the sample growth direction. The ground states of the quantum dot are identified by the orientation of the electron spin. The basic principle behind the deterministic generation of a spin–photon entangled state is straightforward: following the excitation of the quantum dot into an excited (trion) state, radiative recombination will project the system into an entangled state where the color and polarization of the emitted photon are entangled with the spin of the electron in the ground state. Our measurement process entails suppression of the laser background using cross polarized excitation and collection, thus erasing the polarization information of the quantum dot photons. We therefore focus on the entanglement between the spin qubit and the color (frequency) of the photonic qubit.

To demonstrate entanglement we measure both classical and quantum correlations between the electron spin and the color of the emitted photon. Quantum correlations are demonstrated through observation of oscillations in the emitted photon counts conditioned on detecting a spin in a superposition of up and down spins. By reversing the spin projection direction, we observe a Pi-phase change in the oscillation. These oscillations originate from a phase shift between the two components of the entangled state as the time between photon emission and spin measurement is changed. We calculate an overall entanglement fidelity with a lower bound of 0.67±0.05 , which is above 0.5 and thus constitutes a proof for entanglement in our system.

Semiconductor quantum dots have many advantages compared to the other candidates for optically accessible qubits. For example, majority of the photons are emitted into the zero phonon line making them bright, narrow bandwidth single-photon sources. Also fast spin manipulation of the spin states (~4ps) is possible, and the spontaneous emission time is short (~600ps), making a repetition rate of 76MHz possible in our experiment. There are, however, also drawbacks: the dephasing time of the spin states is about 1ns, limiting the useful time window in the entanglement generation. Moreover, lack of a cycling transition, reduces the likelihood of being able to determine the spin state at a single experimental run, limiting efficient scaling to more spins. Luckily these drawbacks can be overcome by using coupled quantum dot systems that have much richer transition structure and the spin qubits can be more robust against the noisy environment [10]. We aim to achieve spin-spin entanglement in the coupled quantum dot systems in the near future.

References:
[1] Alain Aspect, Philippe Grangier, and Gérard Roger, "Experimental realization of Einstein-Podolsky-Rosen-Bohm gedanken experiment: a new violation of Bell’s inequalities", Physical Review Letters, 49, 91–94 (1982). Abstract.
[2] H. J. Kimble, "Quantum Internet", Nature 453, 1023 (2008). Abstract.
[3] K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, A. Imamoğlu, "Quantum nature of a strongly coupled single quantum dot-cavity system", Nature, 445, 896–899 (2007). Abstract.
[4] B. B. Blinov, D. L. Moehring, L.-M. Duan, C. Monroe, "Observation of entanglement between a single trapped atom and a single photon", Nature 428, 153–157 (2004). Abstract.
[5] Jürgen Volz, Markus Weber, Daniel Schlenk, Wenjamin Rosenfeld, Johannes Vrana, Karen Saucke, Christian Kurtsiefer, Harald Weinfurter, "Observation of entanglement of a single photon with a trapped atom", Physical Review Letters, 96, 030404 (2006). Abstract.
[6] Tatjana Wilk, Simon C. Webster, Axel Kuhn, Gerhard Rempe, "Single-atom single-photon quantum interface", Science, 317, 488–490 (2007). Abstract.
[7] E. Togan, Y. Chu, A. S. Trifonov, L. Jiang, J. Maze, L. Childress, M. V. G. Dutt, A. S. Sørensen, P. R. Hemmer, A. S. Zibrov, M. D. Lukin, "Quantum entanglement between an optical photon and a solid state spin qubit", Nature, 466, 730–734 (2010). Abstract.
[8] W. B. Gao, P. Fallahi, E. Togan, J. Miguel-Sanchez, A. Imamoglu, "Observation of entanglement between a quantum dot spin and a single photon", Nature, 491, 426–430 (2012). Abstract.
[9] Kristiaan De Greve, Leo Yu, Peter L. McMahon, Jason S. Pelc, Chandra M. Natarajan, Na Young Kim, Eisuke Abe, Sebastian Maier, Christian Schneider, Martin Kamp, Sven Höfling, Robert H. Hadfield, Alfred Forchel, M. M. Fejer, Yoshihisa Yamamoto, "Quantum-dot spin–photon entanglement via frequency down conversion to telecom wavelength", Nature, 491, 421–425 (2012). Abstract.
[10] K. M. Weiss, J. M. Elzerman, Y. L. Delley, J. Miguel-Sanchez, A. Imamoğlu, "Coherent Two-Electron Spin Qubits in an Optically Active Pair of Coupled InGaAs Quantum Dots", Physical Review Letters, 109, 107401 (2012). Abstract.

Quantum Statistics From Outside Space And Time

[From left to right] 
Front row: Yeong-Cherng Liang (Geneva), Jean-Daniel Bancal (then Geneva, now Singapore); 
Middle row: Antonio Acin (Barcelona), Nicolas Gisin (Geneva); 
Back row: Valerio Scarani (Singapore), Stefano Pironio (Brussels).







Authors:
Jean-Daniel Bancal^1,5, Stefano Pironio², Antonio Acin^3,4, Yeong-Cherng Liang¹, Valerio Scarani⁵, Nicolas Gisin¹

Affiliations:
¹Group of Applied Physics, University of Geneva, Switzerland
²Laboratoire d’Information Quantique, Université Libre de Bruxelles, Belgium
³ICFO-Institut de Ciències Fotòniques, Castelldefels (Barcelona), Spain
⁴ICREA-Institució Catalana de Recerca i Estudis Avançats, Barcelona, Spain
⁵Centre for Quantum Technologies and Department of Physics, National University of Singapore, Singapore

Quantum theory predicts what nature does with unparalleled scope and accuracy. In the new perspective of quantum information, one can add that quantum theory predicts what nature can do for you. But the theory is silent about how nature does it. This silence is at the heart of the uneasiness that some scientists and most laypersons have felt, and continue feeling, when confronted with quantum physics.

Einstein, for one, believed that this silence was only a temporary feature of the then-newly born formalism. He was confident that, with time, someone would find an explanation for quantum phenomena in terms of mechanisms in space-time. However, the passing of time brought physics further from Einstein’s wishes: in 1964, John Bell proved that quantum theory is incompatible with pre-established agreement. Indeed, some predictions of the theory violate a criterion called Bell inequality. Whenever this happens, we are certain that the results of measurements were certainly not pre-recorded in the physical systems. This violation has been clearly observed in several experiments, since Aspect’s pioneering one in 1982.

Past 2Physics article by Antonio Acín:
August 19, 2012: "Testing the Dimension of Classical and Quantum Systems" by Martin Hendrych, Rodrigo Gallego, Michal Mičuda, Nicolas Brunner, Antonio Acín, Juan P. Torres

The violation of Bell inequalities puts severe constraints on Einstein’s hope: any mechanism in space-time that reproduces quantum predictions must involve superluminal influences – exactly what Einstein wanted to avoid at all cost! The faster-than-light character comes from the fact that the predictions of quantum theory, as well as the observed experimental results, are unchanged if the measurement events are space-like separated.

For many physicists, once the obscene word “superluminal” is uttered, all speech must cease. Others, less definite at the moment of telling nature how to behave, were ready to give some credit to a mechanistic explanation, but under one condition: it must not be possible for us to use these influences to send actual messages faster than light. In other words, to be acceptable by the physics community, the hypothetical influences must at least be “hidden”. Abner Shimony coined the expression “peaceful coexistence” between relativity and the violation of Bell inequalities. There did not seem to be much more to be said on the topic, apart from noticing that the Bohmian presentation of quantum theory uses precisely hidden influences in the updating of its “quantum potential”.

In our recent work, we show that the constraint can be strengthened to the extreme: any finite-speed influence would lead to the possibility of sending messages faster than light, in blatant violation of relativity. The price to pay for peaceful coexistence is to accept influences that propagate at infinite speed, making the quantum universe fully connected, while conspiring to remain hidden from us.

In order to understand the generality of our result, let us first stress one point: if the goal would be to reproduce all the predictions of quantum theory as we know it, it is already obvious that the speed must be infinite. Indeed, finite-speed influences would certainly lead to deviations from quantum predictions, depending on the space-time configuration: for instance, if the measurement events cannot be connected by the influence, one should never observe a violation of Bell inequalities. In this work, we decided not to erect quantum theory to the rank of untouchable truth: we accepted finite-speed influences as working assumption, together with the required deviations from the predictions of our present-day formalism. We only assumed that, if the influences have the time to propagate from one measurement event to the next, quantum statistics are produced (because this is what is observed). Even in such a flexible scenario, we were able to prove that ultimately finite-speed influences cannot be hidden. Further, the conclusion can be reached using only observable statistics: it is not only theory-independent, but also “device-independent”.

Illustration of how to obtain a constraint on finite-speed models with three particles

The trick consists in devising a suitable multi-partite configuration, because no conclusion can be reached in the more familiar bipartite scenario. The idea of the argument can be sketched with three parties (see figure). The diagrams are drawn in the preferred frame in which the hypothetical influences propagate. Configuration (a) is such that the influences propagate from A to B, then from B to C: in this case, we request that quantum statistics are recovered. In configuration (b), A and B do not receive each other’s influence, while C receives the influences from both A and B. Now:

• On the one hand, according to the role of influences in this model, a possible violation of Bell inequalities by A and B in configuration (a) should cease if the observers change to configuration (b) e.g. by advancing B’s measurement. 
• On the other hand, for the influences to be hidden, the statistics AC and BC must be the same in both configurations.

The contradiction can be reached by finding marginal statistics AC and BC, whose possible three-partite extension are necessarily such that AB violates some Bell inequality. As it turns out, we have not found such an example with three parties, but a similar one involving four particles.

In conclusion: assuming that some quantum statistics can be observed, a classical mechanism that explains them must not only use superluminal influences: either it uses infinite-speed influences, or it allows us to send messages faster than light. Both alternatives are mind-boggling? Well, there is a reason why physicists prefer to skip the issue of “how nature does it”.

The history of an idea, with three references:

•  The idea is already ten years old, but at that time we did not have the mathematical tools to find a complete proof: Valerio Scarani, Nicolas Gisin, "Superluminal influences, hidden variables, and signaling", Physics Letters A, 295, 167 (2002). Abstract.
• We resumed working on this project in February 2011. Two weeks later appeared in the arXiv a nice breakthrough: Sandro Coretti, Esther Hänggi, Stefan Wolf, "Nonlocality is transitive", Physical Review Letters, 107, 100402 (2011).  Abstract. Wolf and coworkers had found a proof for “no-signaling statistics”. Those statistics cannot be obtained with quantum physics, so the final challenge remained open; nevertheless, this work showed that there is real hope of finding a proof. 
• Our proof for quantum statistics is: J-D. Bancal, S. Pironio, A. Acín, Y-C. Liang, V. Scarani, N. Gisin, "Quantum non-locality based on finite-speed causal influences leads to superluminal signaling", Nature Physics, 8, 867 (2012). Abstract.

Disordered photonics: A New Strategy for Light Trapping in Thin Films

Left to right: Kevin Vynck, Matteo Burresi, Francesco Riboli, and Diederik S. Wiersma

Authors: 
Kevin Vynck, Matteo Burresi, Francesco Riboli, and Diederik S. Wiersma

Affiliation: 
European Laboratory for Non-linear Spectroscopy (LENS) &
National Institute of Optics (CNR-INO), Florence, Italy

Thin-film solar cells nowadays represent a promising alternative to more conventional, thick, silicon panels. Using less material for solar cells allows for a significant saving of natural resources and a lowering of the production costs. A counter-effect of using thinner films is that the amount of light that is absorbed and eventually converted into electricity is significantly reduced. For this reason, improving the absorption of light by thin dielectric films constitutes a challenge of paramount importance in the development of high-efficiency, cost-effective, photovoltaic technologies [1].

Significant efforts have been made in recent years to design structures on the scale of the wavelength that are able to efficiently “trap” light in thin films. Among the various techniques proposed [2], great attention has been given to so-called photonic crystals, made, for instance, by creating a periodic array of holes in the film. At well-defined frequencies and angles of incidence, light impinging on the film can couple to the optical modes created by the nanostructuring and be trapped in the absorbing medium for a long time, thereby significantly increasing the light absorption [3]. Alternatively, randomly textured surfaces have been designed to efficiently spread light in the film on broad spectral and angular ranges, leading as well to an overall increase of the light absorption [4].

In a recent Letter published in Nature Materials [5], our team has presented a new strategy for light trapping thin films that takes advantage of both the efficient light trapping of photonic structures and the broadband/wide-angle properties of random media. The solution that we proposed relies on the use of two-dimensional disordered photonic structures, such as that shown in Figure 1 (higher panel), which exhibit complex electromagnetic modes to which coupling from free space is possible.

Figure 1: (Upper panel) Schematic view of a thin film containing a random pattern of holes. (Lower panel) Top and side views of the electromagnetic energy density in a randomly-nanopatterned film at two different frequencies (where t is the film thickness and λ, the wavelength of light). Light is efficiently trapped in the film, due to the light coupling to disordered optical modes. (Figures adapted from Ref. [5])

To understand the physical process involved, it is instructive to consider how light behaves in such a film. The dielectric film naturally acts as a waveguide for light, confining it in the plane of the film and preventing any out-of-plane loss. Placing holes at random positions in the film makes such that light is multiply-scattered in the plane, in a similar way as a two-dimensional random walk. Multiple scattering and wave interference lead to the formation of optical modes, the characteristics of which (e.g., their spatial extent) are intimately related to the structural properties of the disordered system. A key feature of these modes is that they are leaky, due to the finite thickness of the film, meaning that they are accessible from the third dimension, and thus, can be used for light trapping purposes.

For illustration, the electromagnetic energy density produced by a plane wave at normal incidence on a thin film containing a random pattern of holes (air filling fraction of 30%) is shown in Figure 1 (lower panel) at two different frequencies. The very high energy density in the film is a clear indication of an efficient light trapping effect. The speckle patterns observed arise from the interference between the multiply-scattered waves in the plane of the film, as described above.

The main results of our work are given in Figure 2, showing the absorption spectra of a bare (unpatterned) film with a moderate absorption efficiency (< 5%) and of the same film containing the random pattern of holes considered above. A strong enhancement of the absorption efficiency is observed over a broad range of frequencies, as well as for wide incidence angles and both polarizations of light (see the inset). These are very important properties for solar panels since they should ideally be efficient in all circumstances.

Figure 2: Absorption spectra of the bare (unpatterned) film (black curve) and the films containing random and amorphous patterns of holes (blue and gray curves, respectively). The inset shows the angular dependence of the absorption of the randomly-nanopatterned film at t/λ=0.15 for both polarizations of light. The random pattern of holes leads to a large absorption of the incident light over broad spectral and angular ranges. Disorder correlations in the amorphous pattern allow for a fine-tuning of the absorption spectrum. (Figure adapted from Ref. [5])

Since, as stated above, the coupling process is mediated by the optical modes, which intrinsically depend on the type of disorder considered, we further investigated the possibility to tune the light absorption by engineering the disorder. More particularly, we considered the case of an “amorphous” structure, characterized by a short-range correlation in the position of the holes, as periodic patterns, yet lacking any long-range order. The results on the absorption efficiency, shown in Figure 2, are remarkable: while the absorption is diminished at lower frequencies, becoming quite close to that of the bare slab, it is significantly increased at higher frequencies. The absorption enhancement occurs when the wavelength in the material approximately equals the typical distance between holes, proving that disorder correlations provide us with an important degree of control over the light absorption spectrum.

A final test to conclude our work has been to simulate the absorption of a film of amorphous silicon in the red part of the solar spectrum, where efficient light trapping is generally needed. We observed that the absorption efficiency of the films containing the disordered hole patterns (random and amorphous) was at least as high as that of the film containing the periodic hole pattern. This is an important result as it shows that periodic nanostructuring does not necessarily guarantee the best possible outcome. The lack of periodicity in photonic structures and the robustness of the properties of the films to structural imperfections could lead to the development of low-cost solar panels with a higher efficiency.

References:
[1] Albert Polman and Harry A. Atwater, "Photonic design principles for ultrahigh-efficiency photovoltaics", Nature Materials, 11, 174-177 (2012). Abstract.
[2] Shrestha Basu Mallick, Nicholas P. Sergeant, Mukul Agrawal, Jung-Yong Lee and Peter Peumans, "Coherent light trapping in thin-film photovoltaics", MRS Bulletin 36, 453-460 (2011). Abstract.
[3] Xianqin Meng, Guillaume Gomard, Ounsi El Daif, Emmanuel Drouard, Regis Orobtchouk, Anne Kaminski, Alain Fave, Mustapha Lemiti, Alexei Abramov, Pere Roca i Cabarrocas, Christian Seassal, "Absorbing photonic crystals for silicon thin-film solar cells: design, fabrication and experimental investigation", Solar Energy Materials and Solar Cells, 95, S32-S38 (2011). Abstract.
[4] C. Rockstuhl, S. Fahr, K. Bittkau, T. Beckers, R. Carius, F.-J. Haug, T. Söderström, C. Ballif, F. Lederer, "Comparison and optimization of randomly textured surfaces in thin-film solar cells", Opics Express, 18, A335-A341 (2010). Abstract.
[5] Kevin Vynck, Matteo Burresi, Francesco Riboli, Diederik S. Wiersma, "Photon management in two-dimensional disordered media", Nature Materials, 11, 1017-1022 (2012). Abstract.

Qubits Have Got A Bus Service

(left) Jason Petta of Princeton University  and (right) Jacob Taylor of the Joint Quantum Institute (JQI), USA

Scientists working at Princeton University and the Joint Quantum Institute (JQI) have shown how a major hurdle in transferring information from one quantum bit, or qubit, to another might be overcome [1] . Their so-called "quantum bus" provides the link that would enable quantum processors to perform complex computations. [The JQI is a collaborative institute of the National Institute of Standards and Technology (NIST) and the University of Maryland at College Park].

Qubits are unlike a classical bit because they can be not only a 1 or 0 but also both, simultaneously. Qubit-based computing exploiting spooky quantum effects like entanglement and superposition will speed up factoring and searching calculations far above what can be done with mere zero-or-one bits in conventional computers. But these quantum states are fragile and short-lived, which makes designing ways for them to perform basic functions, such as getting qubits to talk to one another—or "coupling"—difficult. To domesticate quantum weirdness, however, to make it a fit companion for mass-market electronic technology, many tricky bi-lateral and multi-lateral arrangements---among photons, electrons, circuits, cavities, etc.---need to be negotiated.

A new milestone in this forward march is this work by a Princeton-Joint Quantum Institute (JQI) collaboration which could successfully excite a spin qubit using a resonant cavity. The circuit, via the cavity, senses the presence of the qubit as if it were a bit of capacitance. This result, published in Nature [1], points toward the eventual movement of quantum information over “bus” conduits much as digital information moves over buses in conventional computers.

Qubit Catalog

A qubit is an isolated system---a sort of toggle---which is maintained simultaneously in a mixture of two quantum states. Qubits come in many forms, such as photons in either of two polarization states, or atoms oriented in either of two states, or superconducting circuits excited in either of two ways.

One promising qubit platform is the quantum dot, a tiny speck of semiconducting material in which the number of electrons allowed in or out can be severely controlled by nearby electrodes. In a charge qubit the dot can co-exist in states where one or zero electrons are in the dot. In a spin qubit, two electrons (sitting in two neighboring dots), acting like a molecule, possess a composite spin which can be up or down.

Quantum dots are easy to fabricate using established semiconductor technology. This gives them an advantage over many other qubit modes, especially if you want to build an integrated qubit chip with many qubits in proximity. One drawback is that qubits in a dot are harder to protect against outside interference, which can ruin the delicate quantum processing of information. An example of this unwanted decoherence is the magnetic interaction of the electron “molecule” with the nuclei of the very atoms that make up the dot.

Another challenge is to control or excite the qubit in the first place. That is, the qubit must be carefully incited into its two-states-at-once condition, the technical name for which is Rabi oscillation. The Princeton-JQI work artfully addresses all these issues.

Circuit QED

Indeed, the present work is another chapter in the progress of knowledge about electromagnetic force. In the 19th century James Clerk Maxwell set forth the study of electrodynamics in its classic form. In the early and mid 20th century a quantum version of electrodynamics (QED) was established which also, incidentally, accommodated the revolutionary idea of antimatter and of the creation and destruction of elementary particles.

More recently QED has been extended to the behavior of electromagnetic waves within metal circuits and resonant cavities. This cavity-QED or circuit-QED (cQED), provides a handy protocol for facilitating a traffic between qubits and circuits: excitations, entanglement, input and readout, teleportation (movement of quantum information), computational logic, and protection against decoherence.

Forty years ago this effort to marry coherent quantum effects with electronics was referred to as quantum electronics. The name used nowadays has shifted to quantum optics. “With the advent of the laser, the focus moved into the optical domain,” says Jacob Taylor, a JQI fellow and NIST physicist. “It is only in the past few years that the microwave domain – where electronics really function – has come into its own, returning quantum optics to its roots in electrical circuits.”

Cavities are essential for the transportation of quantum information. That’s because speed translates into distance. Qubits are ephemeral; the quantum information they encode can dissipate quickly (over a time frame of nanoseconds to seconds) and all processing has to be done well before then. If, moreover, the information has to be moved, it should be done as quickly as possible. Nothing goes faster than light, so transporting quantum information (at least for moving it from one place to another within a computer), or encoding the information, or entangling several qubits should be done as quickly as possible. In this way information or processing in more distant nodes can take place.

Hybrid quantum dot-superconducting resonator device. Note the Princeton tiger is 1 mm from head to tail. The spin-orbit qubits are located at the nexus of the seven gate electrodes. (a) Circuit schematic and micrograph of the hybrid device design. Scanning electron micrograph (b) and cross-sectional schematic view (c) of the nanowire double quantum dot (DQD). The left and right barrier gates (BL and BR), left and right plunger gates (L and R), and middle gate (M) are biased to create a double-well potential within the nanowire. The drain contact of the nanowire, D, is grounded, and the source contact, S, is connected to an antinode of the resonator, oscillating at a voltage VCavity. [Image credit: K. Petersson, Princeton University]

Spin-Orbit Coupling

The JQI part of this spin-qubit collaboration, Jacob Taylor, earlier this year participated in research that established a method for using a resonant cavity to excite a qubit consisting of an ion held simultaneously in two spin states. The problem there was a mismatch between the frequency at which the circuit operated and the characteristic frequency of the ion oscillating back and forth between electrodes. The solution was to have the circuit and ion speak to each other through the intermediary of an acoustic device [2].

The corresponding obstacle in the JQI-Princeton experiment is that the circuit (in effect a microwave photon reflecting back and forth in a resonant cavity) exerts only a weak magnetic effect upon the electron doublet in the quantum dot. The solution: have the cavity influence the physical movement of the electrons in the dot---a more robust form of interaction (electrical in nature)---rather than the interact with the electrons’ spin (magnetic force).

Next this excitation is applied to the spin of the electron doublet (the aspect of the doublet which actually constitutes the quantum information) via a force called spin-orbit coupling. In this type of interaction the physical circulation of the electrons in the dot (the “orbit” part) tangles magnetically with the spins of the nuclei (the “spin” part of the interaction) in the atoms composing the dot itself.

It turns out this spin-orbit coupling is much stronger in indium-arsenide than in the typical quantum dot material of gallium-arsenide. This it was that material science was an important ingredient in this work, in addition to contributions from the physics and electrical engineering departments at Princeton.

To recap: an electrical circuit excites the dot electrically but the effect is passed along magnetically to the qubit in the dot when the electrons in the dot move past and provoke an interaction with the nuclei in the InAs atoms. Thus these qubits deserve to be called the first spin-orbit qubits in a quantum dot.

The influence works both ways. Much as the presence of a diver on the end of a diving board alters the resonant frequency of the board, so the presence of the spin qubit alters the resonant frequency of the cavity, and so its presence can be senses. Conversely, the alteration, effected by the spin-orbit interaction, can be used to excite the qubit, at rates of a million per second or more.

Previously a quantum-dot-based charge qubit was excited by a cavity. So why was it important to make a quantum-dot qubit based on spin? "The spins couple weakly to the electrical field, making them much harder to couple to than a charge,” said Taylor. “However, it is exactly this property which also makes them much better qubits since it is precisely undesired coupling to other systems, which destroys quantum effects. With a spin-based qubit, this is greatly suppressed."

References:
[1] K.D. Petersson, L.W. McFaul, M.D. Schroer, M. Jung, J.M. Taylor, A.A. Houck and J.R. Petta. "Circuit quantum electrodynamics with a spin qubit". Nature, 490, 380–383 (2012). Abstract.
[2] D. Kielpinski, D. Kafri, M. J. Woolley, G. J. Milburn, and J. M. Taylor, "Quantum Interface between an Electrical Circuit and a Single Atom", Physical Review Letters, 108, 130504 (2012). Abstract.

First Demonstration of Spin-Orbit Coupling in Ultracold Fermi Gases

Photo: Jing Zhang of Shanxi University

Authors: Hui Zhai¹ and Jing Zhang²
Affiliation:
¹Institute for Advanced Study, Tsinghua University, Beijing, China
²State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan, China

Photo: Hui Zhai of Tsinghua University

In 1995, scientists successfully cooled bosons to Bose-Einstein condensate, and later on in 1999, quantum degenerate Fermi gas could also be demonstrated in experiment. These degenerate atomic gases have the advantage that both their single particle motion and the interaction between atoms can be manipulated and well controlled by light or magnetic field. Utilizing these advantages -- during the last decade -- many exciting experiments have been carried out, which either simulate interesting models for condensed matter systems or reveal interesting new many-body quantum phases or quantum phenomena.

However, in all these studies, an important ingredient has not been included until very recently, that is, the coupling between the atomic spin degree of freedom and its orbital motion. This is because for neutral atoms, unlike charged electrons, there is no intrinsic spin-orbit coupling. Nevertheless, in reality, spin-orbit coupling plays a very important role in determining electron structure in solid and the nuclear structure. Spin-orbit coupling is also the key ingredient giving birth to some new states of matters such as topological insulators and topological superfluids. Therefore, for the purposes of both quantum simulation and discovering new state of matter, it is desirable to introduce spin-orbit coupling into the field of ultracold quantum gases.

In 2011, Ian Spielman’s group in NIST first generated spin-orbit coupling in Bose gases [1]. In that experiment, two counter-propagating laser beams are applied to the Bose condensate of Rubidium atoms. One of the two lasers is linearly polarized and the other is circularly polarized. Thus, when an atom absorbs a photon from one beam and then emits a photon to the other laser beam, their spin is flipped and also their momentum is also changed by the momentum difference of these two lasers. That is to say, the spin flip process is always accompanied by the change of momentum. In this way, the spin and their motion are locked together and a synthetic spin-orbit coupling is added into the motion of atoms. Such a coupling changes the single particle spectrum dramatically and the energy minimum is shifted from zero-momentum to finite momentum, which gives rise to unconventional condensate with intriguing phase or density patterns [2].

In our recent paper [3] we have for the first time applied the similar scheme to create spin-orbit coupling and demonstrate its effect in ultracold Fermi gases of Potassium-40. Fermi gas differs from Bose gas because fermions should obey Pauli exclusion principle, and therefore they have to occupy different momentum states and form a Fermi surface at low temperature. This also leads to the major difference for the manifestation of the spin-orbit coupling effects in a Fermi gas compared to in a Bose condensate. We have demonstrated several effects in our work.

Fig. 1: Spin oscillation under spin-orbit coupling. Different curves represent Fermi gases with different density.

First, if one starts with a fully polarized Fermi gas and applies a pulse of Raman coupling, the whole system will start Rabi oscillation. If all atoms oscillate with the same frequency, the Rabi oscillation will remain coherent for long time. However, in this system, atoms occupy different momenta and because of spin-orbit coupling, atoms with different momenta have different energies. Thus, different atoms oscillate with different periods, which leads to strong dephasing. This simulates spin-orbit coupling induced spin diffusion process of a spin polarized current in semiconductors. In our work, we also provide strong evidence for the topology change of Fermi surface. Using the momentum resolved radio-frequency spectroscopy, the single dispersion is also mapped out, where the effects of spin-orbit coupling is clearly demonstrated. Later on, MIT group led by Martin Zwierlein also studied spin-orbit coupled Fermi gas with lithium-6 atoms, and they measured spin-resolved single particle dispersion using spin-injection spectroscopy [4].

Fig 2: single particle dispersion measured by momentum resolved radio-frequency spectroscopy

In the near future, we plan to bring the system nearby a magnetic Feshbach resonance, and utilize the strong attraction there to create a fermion superfluid in the presence of spin-orbit coupling. Such a superfluid, when confined into one-dimensional geometry by optical lattices, becomes topological and displays Majorana edge mode, as discovered in nanowire recently [5]. Realizing such a topological phase in cold atom setup will allow us to study its properties in a more controllable way.

To reach this goal, we also need to overcome several challenges. One major challenge is the heating due to spontaneous mission in the Raman process. For instance, for our experiment with Potassium-40, the temperature of the Fermi gases increases from around 0.2 of Fermi temperature to around 0.5 of Fermi temperature after Raman laser is turn on for around 100 ms. The heating is more profound for light atoms like Lithium. Such a problem may be overcome by further cooling fermions with very low temperature boson bath or by choosing other atoms like Yb or Dy, which have excited level with very narrow linewidth, and the spontaneous mission rate can be greatly suppressed.

The spin-orbit coupling generated in current experiment is a special type, which can be viewed as equal weight of Rashba and Dresselhaus. Another direction for future studies is to generate more complicated spin-orbit coupling, and one of the most interesting forms is pure Rashba because of the higher symmetry of this type of coupling. Such a coupling increases the single particle ground state degeneracy and the low-energy density-of-state, and thus it leads to many profound many-body quantum phenomena, as predicated by many of recent theoretical studies [6]. It is exciting to discover them in experiments.

References:
[1] Y. J. Lin, K. Jimenez-Garcia and I. B. Spielman, "Spin–orbit-coupled Bose–Einstein condensates", Nature, 471, 83 (2011). Abstract. 2Physics Article.
[2] Chunji Wang, Chao Gao, Chao-Ming Jian, and Hui Zhai, "Spin-Orbit Coupled Spinor Bose-Einstein Condensates", Physical Review Letters, 105, 160403 (2010). Abstract;   Tin-Lun Ho and Shizhong Zhang, "Bose-Einstein Condensates with Spin-Orbit Interaction", Physical Review Letters, 107, 150403 (2011). Abstract.
[3] Pengjun Wang, Zeng-Qiang Yu, Zhengkun Fu, Jiao Miao, Lianghui Huang, Shijie Chai, Hui Zhai, and Jing Zhang, "Spin-Orbit Coupled Degenerate Fermi Gases", Physical Review Letters, 109, 095301 (2012). Abstract.
[4] Lawrence W. Cheuk, Ariel T. Sommer, Zoran Hadzibabic, Tarik Yefsah, Waseem S. Bakr, and Martin W. Zwierlein, "Spin-Injection Spectroscopy of a Spin-Orbit Coupled Fermi Gas", Physical Review Letters, 109, 095302 (2012). Abstract.
[5] V. Mourik, K. Zuo, S. M. Frolov, S. R. Plissard, E. P. A. M. Bakkers, and L. P. Kouwenhoven, "Signatures of Majorana Fermions in Hybrid Superconductor-Semiconductor Nanowire Devices", Science, 336, 1003 (2012). Abstract. 2Physics Article.
[6] For a review, see Hui Zhai, "Spin-orbit coupled quantum gases", International Journal of Modern Physics, 26, 1230001 (2012). Full Article.

Measurement of Photon Statistics with Live Photoreceptor Cells

Leonid Krivitsky

Author: Leonid Krivitsky

Affiliation: Data Storage Institute, Agency for Science Technology and Research (A*STAR), Singapore

Conventional light sources, such as lamps, stars, laser pointers etc. are known to exhibit intrinsic photon fluctuations. This means that the number of photons emitted by the source is not strictly defined but is given by a specific statistical distribution. For example, the photon number distribution of a laser obeys a Poisson distribution, whilst the photon number distribution of a thermal source (lamp, star) obeys an exponential distribution.

The question which we address in this work is how fluctuations of various light sources are perceived by visual systems of living organisms [1]. A simple analogy which illustrates this is our human perception of the stars in the night sky. It is known that faint stars blink because of the atmospheric turbulence, which disturbs the star light on its way to the eye. At the same time, we may notice that bright stars, e.g. Polaris, observed under the same conditions, seem almost stable. This observation suggests that the ability of the eye to perceive blinking (fluctuating) lights is related to the brightness of the source. This scenario can be carefully reproduced in the lab by interfacing photosensitive eye cells, known as photoreceptors, with flashes of light from sources with different photon statistics.

Photoreceptor cells within the eye, known as retinal rods, are responsible for vision under low light conditions [2]. They are capable of detecting light down to the single photon level. When stimulated by light, the cells respond in ways that can be measured. In particular, the electrical activity of the cell, which is driven by the absorption of individual photons by the cells, can be measured by using fine glass microelectrodes. Moreover, since the cell is constrained within the recording microelectrode, moving the microelectrode allows us to position the cell close to the tip of an optical fiber, which is used to perform targeted light delivery into the cell (see Fig. 1) [3].

Fig.1 Microscope image of the retinal rod cell constrained in a glass suction pipette (on the right) and a tapered optical fiber (on the left) used for light delivery to the cell.

In our experiment, we send flashes of light into the cell by feeding flashes of light from the laser and pseudo-thermal light source into an optical fiber. We then measure the average and standard deviation of the cell response to repetitive light flashes at different flash intensities. The relation between the average <A> and the standard deviation ΔA of the amplitude of the cell response is characterized by a signal-to-noise ratio SNR= <A>/√ΔA.

It turns out that the fluctuation of the cell’s response depends crucially on the saturation of the cell response. Firstly, the dependence of the average cell response on the number of impinging photons behaves differently for light sources with different photon statistics (see Fig.2). As we can see, for the case of the pseudo-thermal light source (open symbols) the saturation is considerably smoother than for the laser light (solid symbols). This is explained by the fact that for bright (on average) pseudo-thermal light source there is always a considerable chance of observing flashes with low photon numbers, which prevents sharp saturation of the average response.

Fig.2 Dependence of the average normalized amplitude of the cell response on the normalized number of impinging photons for laser (solid symbols, solid lines) and pseudo-thermal (open symbols, dashed lines) light sources. Lines are results of theoretical modelling. Typical values of saturation amplitudes are in the range of 18-25 pA, and of photon numbers are in the range of 700-2500 photons per pulse. Saturation of the response is different for the two sources due to the difference in their photon statistics.

Secondly, the saturation of the cell at relatively bright flashes leads to a sharp increase of the SNR (see Fig.3). Indeed, if the cell is saturated by bright lights, its response does not fluctuate and this automatically results in a high value of SNR since ΔA becomes vanishingly small. This may be the reason why we are able to see fluctuating dim stars, but the bright stars in the night sky appear almost stable.

Fig.3 Dependence of the Signal to Noise Ratio (SNR) on the normalized number of impinging photons for laser (solid symbols, solid lines) and pseudo-thermal (open symbols, dashed lines) light sources. Lines are results of theoretical modelling. Sharp increase of SNR is a signature of the bleaching of the cell.

In conclusion, this work contributes to a better understanding of the sensitivity of retinal rod cells to photo-stimulation. It shows that under certain conditions, the cell can, like other man-made photodetectors, be used to measure the photon statistics of various light sources. It is of further interest to us to investigate how the cell interacts with sources of non-classical light and this study is currently in progress. More practical applications of the above work could include building a detector with retinal rods that can mimic the natural detection of light by our eyes.

References:
[1] "Measurement of Photon Statistics with Live Photoreceptor Cells", Nigel Sim, Mei Fun Cheng, Dmitri Bessarab, C. Michael Jones, Leonid A. Krivitsky, Physical Review Letters, 109, 113601 (2012). Abstract.
[2] "Single-photon detection by rod cells of the retina", F. Rieke and D. A. Baylor, Review of Modern Physics, 70, 1027 (1998). Abstract.
[3] "Method of targeted delivery of laser beam to isolated retinal rods by fiber optics", Nigel Sim, Dmitri Bessarab, C. Michael Jones, Leonid Krivitsky, Biomedical Optics Express, 2, 2926 (2011). Abstract.

Quantum Teleportation Over 143 Kilometers

From left to right: Anton Zeilinger, Xiao-song Ma, Rupert Ursin, Bernhard Wittmann, Thomas Herbst, Sebastian Kropascheck of Institute for Quantum Optics and Quantum Information (IQOQI), Vienna, Austria.

Authors: Xiao-song Ma^1,2, Johannes Kofler³, Rupert Ursin^1,2, Anton Zeilinger^1,2

Affiliation:
¹Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Vienna, Austria.
²Vienna Center for Quantum Science and Technology, Faculty of Physics, University of Vienna, Austria.
³Max Planck Institute of Quantum Optics (MPQ), Garching, Germany.

Johannes Kofler of Max Planck Institute of Quantum Optics (MPQ), Germany

The so-called "quantum internet” is envisaged as a revolutionary platform for information processing. It is not based anymore on classical computer networks but on the current developments of modern quantum information, where individual quantum particles are the carriers of information. Quantum networks promise absolutely secure communication and enhanced computation power for decentralized tasks compared to any conceivable classical technology. Due to the intrinsic transmission losses in conventional glass fibers a global quantum network will likely base on the free-space transfer of quantum states, e.g., between satellites and from satellites to ground. The now realized quantum teleportation [1] over a distance of 143 kilometers [2], beating a just one-month old record of 97 kilometers set by a group of physicists from China [3], is a significant step towards this future technology.

Past 2Physics articles by Rupert Ursin and/or Anton Zeilinger:

May 30, 2009: "Transmission of Entangled Photons over a High-Loss Free-Space Channel" by Alessandro Fedrizzi, Rupert Ursin and Anton Zeilinger,

June 08, 2007: "Entanglement and One-Way Quantum Computing "
by Robert Prevedel and Anton Zeilinger

On the island of La Palma our team produced entangled pairs of particles of light (photons 2 and 3, see figure 1). Quantum entanglement means that none of the photons taken by itself has a definite polarization but that, if one measures the polarization of one of the photons and obtains a random result, the other photon will always show a perfectly correlated polarization. This type of quantum correlation cannot be described by classical physics and Albert Einstein therefore called it “spooky action at a distance”. Photon 3 was then sent through the air to Tenerife, across the Atlantic Ocean at an altitude of about 2400 meters and over a distance of 143 kilometers, where it was caught by a telescope of the European Space Agency. Photon 2 remained in the laboratory at La Palma. There, we created additional particles of light (photon 1) in a freely selectable polarization state which we wanted to teleport.

Figure 1: Schematic illustration of the teleportation experiment. The polarisation state of particles of light was teleported over a distance of 143 kilometres from the Canary Island La Palma to Tenerife. Graphic: IQOQI Vienna & MPQ Garching.

This was achieved in several steps: First, a special kind of joint measurement, the so-called Bell measurement (“BM”), was performed on photons 1 and 2, which irrevocably destroys both photons. Two possible outcomes of this measurement were discriminated, and the corresponding classical information was sent via a conventional laser pulse (violet in the figure) to Tenerife. There, depending on which of the outcomes of the Bell measurement had been received, the polarization of photon 3 was transformed accordingly. This transformation (“T”) completed the teleportation process, and the polarization of photon 3 on Tenerife was then identical with the initial polarization of photon 1 on La Palma.

Figure 2: Long time exposure photography viewing from La Palma to Tenerife. A green laser beam indicates the free-space link between the two laboratories [Graphic: IQOQI Vienna].

The complexity of the setup and the environmental conditions (changes of temperature, sand storms, fog, rain, snow) constituted a significant challenge for the experiment. They also demanded a combination of modern quantum optical technologies concerning the source of entangled particles of light, the measurement devices, and the temporal synchronization of the two laboratories (see Figure 2 for the experimenter’s view from La Palma to Tenerife). The experiment therefore represents a milestone, which demonstrates the maturity and applicability of these technologies in real-world outdoor conditions and hence paves the way for future global quantum networks. For the next step of satellite-based quantum teleportation an international collaboration of the Austrian and Chinese Academy of Sciences plans to shoot a satellite into space in the foreseeable future.

References
[1] “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels”, Charles H. Bennett, Gilles Brassard, Claude Crépeau, Richard Jozsa, Asher Peres, William K. Wootters, Physical Review Letters, 70, 1895 (1993). Abstract.
[2] “Quantum teleportation over 143 kilometres using active feed-forward”, Xiao-Song Ma, Thomas Herbst, Thomas Scheidl, Daqing Wang, Sebastian Kropatschek, William Naylor, Bernhard Wittmann, Alexandra Mech, Johannes Kofler, Elena Anisimova, Vadim Makarov, Thomas Jennewein, Rupert Ursin, Anton Zeilinger, Nature 489, 269 (2012). Abstract.
[3] “Quantum teleportation and entanglement distribution over 100-kilometre free-space channels”, Juan Yin, Ji-Gang Ren, He Lu, Yuan Cao, Hai-Lin Yong, Yu-Ping Wu, Chang Liu, Sheng-Kai Liao, Fei Zhou, Yan Jiang, Xin-Dong Cai, Ping Xu, Ge-Sheng Pan, Jian-Jun Jia, Yong-Mei Huang, Hao Yin, Jian-Yu Wang, Yu-Ao Chen, Cheng-Zhi Peng, Jian-Wei Pan, Nature 488, 185 (2012). Abstract.

Topological States and Adiabatic Pumping in Quasicrystals

Left to right: Kobi E. Kraus, Oded Zilberberg, Yoav Lahini, Zohar Ringel and Mor Verbin

Authors: 
Yaacov E. Kraus¹, Yoav Lahini^2,3, Zohar Ringel¹, Mor Verbin², Oded Zilberberg¹

Affiliation:
¹Dept. of Condensed Matter Physics, Weizmann Institute of Science, Israel
²Dept. of Physics of Complex Systems, Weizmann Institute of Science, Israel
³Department of Physics, Massachusetts Institute of Technology, USA

The materials that make up our world have a variety of electrical properties. Some materials, such as metals, conduct electricity extremely well, while others are insulators, and are very efficient as shields from electric currents.

Recently, a new discovery revolutionized the prevailing paradigm of electrical properties of materials, when a new type of material was discovered [1, 2]. These materials are termed “topological insulators”, and have very unique electrical properties. For example, electricity would flow smoothly on the surface of a topological insulator, while the interior will be completely insulating. Interestingly, if one would cut this material in half, the new surface that is created, which was previously buried within the insulating interior, will suddenly become conducting. If the material is cut repeatedly, the same will happen each time.

Past 2Physics article by Yoav Lahini:
November 07, 2010: "Hanbury Brown and Twiss Interferometry with Interacting Photons"
by Yoav Lahini, Yaron Bromberg, Eran Small and Yaron Silberberg

In addition to this peculiar property, the electrical behavior on the surface itself reveals unique phenomena that are even expected to simulate bizarre new particle excitations [3]. As a result, these fascinating materials generated much activity in the condensed matter physics community, in an attempt to find new topological materials and to study their intriguing properties.

In a recent paper [4], we found that other unconventional materials, known as quasicrystals, are in fact also members of the topological materials family. Moreover, the topological behavior that they exhibit is similar to that of usual topological materials in some aspects, but differs from them in others.

Quasicrystals are materials in which the atoms are arranged in a distinct way. In most solid materials, the atoms are arranged in space either periodically or in a completely random fashion. Quasicrystals are an intermediate type of solid - they are neither periodic nor random. Rather, there is some non-repeating (i.e. non periodic) but well defined rule to the arrangement of their atoms [5, 6]. Despite the fact that quasicrystals have been experimentally observed already in 1982 [5], for a long time there was a debate between crystallographers whether they exist at all, as it was assumed that all crystalline materials are necessarily periodic. The conclusion that quasicrystals are a new type of solid revolutionized material science, updated the physical definition of what is a crystal, and culminated in the awarding of the Nobel Prize in Chemistry to its discoverer, Dan Shechtman from the Technion - Israel Institute of Technology [7].

Yet, many of the physical properties of quasicrystals, such as their electrical conductance, are not fully understood. The work recently published by our group in Physical Review Letters [4], discusses the electrical properties of surfaces of quasicrystals, and finds a new and surprising connection between quasicrystals and topological states of matter. Specifically, we show that a one-dimensional quasicrystal behaves, to some extent, like two-dimensional topological matter known as quantum Hall systems. We prove this claim theoretically and measure it experimentally.

The experiments were done on a novel type of quasicrystals, known as photonic quasicrystals [8, 9]. These systems are made of quasi-periodic arrangements of transparent materials, rather than atoms. In these systems, one studies the optical properties, rather than the electrical, but the underlying physics is very much the same. A major advantage of using photonic quasicrystals is the ability to fabricate one-dimensional materials, and to directly image the propagation of light within them.

In our experiments, we have realized a one-dimensional photonic quasicrystal, and measured the boundary (the surface of a one-dimensional system) properties of these quasicrystals. We found that the photonic states that reside at the boundary are localized -- meaning that light that is injected to that boundary will stay there. This is analogous to the electric currents on the surface of topological matter, which do not penetrate the interior of the material, but remain confined to the surface. This finding was surprising, as common wisdom was that -- generally, such a behavior is not supposed to occur in one-dimensional systems.

Our theory explains how that becomes possible in quasicrystals. In brief, the arrangement of atoms in a quasicrystal can be mathematically described as some type of projection of a periodic system on a system of lower dimension – for example, projection of a two-dimensional square lattice onto a one-dimensional line [10]. Note that this description defines the position of the atoms of the quasicrystal, but do not imply the properties of any electrons (or photons) moving through it. In our case, the one-dimensional quasicrystalline models we worked with can be described as another type of one-dimensional projection of a quantum Hall system, known as “dimensional reduction” [3]. Most importantly, the novel projection used to define our one-dimensional quasicrystals preserves the topological properties! Thus, we find that beyond their mere structure, quasicrystals can, in some sense, also “inherit” nontrivial topological properties from their higher-dimensional periodic “ancestors”.

Taking things a step forward, we have shown that the boundary states observed in the experiments indeed possess nontrivial topological properties, by demonstrating a topological “pumping” of light from one side of the quasicrystal to the other [4].

Figure 1: Experimental observation of adiabatic pumping via topologically protected boundary states in a photonic quasicrystal. (a) An illustration of the adiabatically modulated photonic quasicrystal, constructed by slowly varying the spacing between the waveguides along the propagation axis z. Consequently, the injected light is pumped across the sample. (b) Experimental results: Light was injected into the rightmost waveguide. The measured intensity distributions as a function of the position are presented at different stages of the adiabatic evolution, i.e., different propagation distances. It is evident that along the adiabatic evolution the light crossed the lattice from right to left.

This fascinating discovery appears to be just the beginning. Our results suggest that additional quasicrystals should exhibit topological states [11, 12], and that these states will always be linked to systems of a higher dimension. This approach might mean that three-dimensional quasicrystalline materials -- either photonic or electronic -- would exhibit strange surface properties, which can be explained as originating from a six-dimensional topological system. These subjects are currently under active investigation.

References:
[1] “Colloquium: Topological Insulators”, M.Z. Hasan and C.L. Kane, Reviews of Modern Physics, 82, 3045 (2010). Abstract.
[2] “Topological insulators and superconductors”, Xiao-Liang Qi and Shou-Cheng Zhang , Reviews of Modern Physics, 83, 1057 (2011). Abstract.
[3] “Topological field theory of time-reversal invariant insulators”, Xiao-Liang Qi, Taylor L. Hughes, and Shou-Cheng Zhang, Physical Review B 78, 195424 (2008). Abstract.
[4] "Topological States and Adiabatic Pumping in Quasicrystals”, Yaacov E. Kraus, Yoav Lahini, Zohar Ringel, Mor Verbin, and Oded Zilberberg, Physical Review Letters, 109, 106402 (2012). Abstract.
[5] “Metallic Phase with Long-Range Orientational Order and No Translations Symmetry”, D. Shechtman, I. Blech, D. Gratias, and J.W. Cahn, Physical Review Letters, 53, 1951 (1984). Abstract.
[6] "Quasicrystals: A New Class of Ordered Structures", Dov Levine and Paul Joseph Steinhardt, Physical Review Letters, 53, 2477 (1984). Abstract.
[7] See http://www.nobelprize.org/nobel_prizes/chemistry/laureates/2011/press.html .
[8] “Wave and defect dynamics in nonlinear photonic quasicrystals”, Barak Freedman, Guy Bartal, Mordechai Segev, Ron Lifshitz, Demetrios N. Christodoulides and Jason W. Fleischer, Nature, 440, 1166 (2006). Abstract.
[9] “Observation of a Localization Transition in Quasiperiodic Photonic Lattices”, Y. Lahini, R. Pugatch, F. Pozzi, M. Sorel, R. Morandotti, N. Davidson and Y. Silberberg, Physical Review Letters, 103, 013901 (2009). Abstract.
[10] “Algebraic theory of Penrose's non-periodic tilings of the plane”, N.G. de Bruijn, Kon. Nederl. Akad. Wetensch. Proc. Ser. A (1981).
[11] “Topological Equivalence Between The Fibonacci Quasicrystal and The Harper Model”, Yaacov E. Kraus and Oded Zilberberg, Physical Review Letters, 109, 116404 (2012). Abstract.
[12] “Observation of Topological Phase Transitions in One-Dimensional Photonic Quasicrystals”, M. Verbin, Y. E. Kraus, O. Zilberberg, Y. Lahini and Y. Silberberg, in preparation.