A Light Transistor Based on Photons and Phonons

Tobias J. Kippenberg

Researchers at the Ecole Polytechnique Fédérale de Lausanne (EPFL), Switzerland and the Max Planck Institute of Quantum Optics (MPQ), Germany discover a novel way to switch light all-optically on a chip.

The ability to control the propagation of light is at the technological heart of today’s telecommunication society. Researchers in the Laboratory of Photonics and Quantum Measurement led by Prof. Tobias J. Kippenberg (now EPFL) have discovered a novel principle to accomplish this, which is based on the interaction of light (photons) with mechanical vibrations (phonons). As they report in a recent publication [1], this scheme allows to control the transmission of a light beam past a chip-based optical micro-resonator directly by a second, stronger light beam. The new device could have numerous applications in telecommunication and quantum information technologies.

So far, this effect has only been observed in the interaction of laser light with atomic vapours, based on an effect referred to as “electromagnetically induced transparency” (EIT). EIT has been used to manipulate light propagation at an impressive level: slowing of light pulses and even full storage has been achieved. However, EIT is restricted to light of wavelengths matching the natural resonances of atoms. Also, these technologies are hardly compatible with chip-scale processing.

The novel principle, discovered by a team of scientists including Dr. Albert Schliesser and Dr. Samuel Deléglise and doctoral students Stefan Weis and Rémi Rivière, is based on optomechanical coupling of photons to mechanical oscillations inside an optical micro-resonator. These optomechanical devices are fabricated using standard nanofabrication methods – drawing on the techniques used in semiconductor integrated circuit processing available in the cleanroom of EPFL. They can both trap light in orbits and act, at the same time, as mechanical oscillators, possessing well-defined mechanical vibrational frequencies just like a tuning fork.

If light is coupled into the resonator, the photons exert a force: radiation pressure. While this force has been used for decades to trap and cool atoms, it is only in the last five years that researchers could harness it to control mechanical vibrations at the micro- and nanoscale. This has led to a new research field: cavity optomechanics, which unifies photonics and micro- and nanomechanics. The usually small radiation pressure force is greatly enhanced within an optical microresonator,and can therefore deform the cavity, coupling the light to the mechanical vibrations. For the optomechanical control of light propagation, a second, “control” laser can be coupled to the resonator in addition to the “signal” laser. In the presence of the control laser, the beating of the two lasers causes the mechanical oscillator to vibrate – which in turn prevents the signal light to enter the resonator by an optomechanical interference effect, leading eventually to a transparency window for the signal beam.

For a long time the effect remained elusive, “We have known for more than two years that the effect existed,” says Dr. Schliesser, who theoretically predicted the effect early on. “Once we knew where to look it was right there,” says Stefan Weis, one of the lead authors of the paper. In the subsequent measurements, “the agreement of theory and experiment is really striking”, comments Dr. Deléglise.

In contrast to atoms, this novel form of induced transparency does not rely on naturally occurring resonances and could therefore also be applied to previously inaccessible wavelength regions such as the technologically important telecommunication window (near-infrared). Optomechanical systems allow virtually unlimited design freedom using wafer-scale nano- and microfabrication techniques. Furthermore, already a single optomechanical element can achieve unity contrast, which in the atomic case normally not is possible.

The novel effect, which the researchers have termed “OMIT” (optomechanically induced transparency) to emphasize the close relation to EIT, may indeed provide entirely new functionality to photonics. Future developments based on OMIT could enable the conversion of a stream of photons into mechanical excitations (phonons). Such conversion of radio frequency signals into mechanical vibrations is used in cell-phone receivers today for narrow-band filtering, a principle that could potentially be applied to optical signals as well.

Figure 1: False-colour scanning electron micrograph of the microresonator used in the study of OMIT. The red top part is a silica toroid; it is supported by a silicon pillar (gray) on a semiconductor chip. The silica toroid serves both, as an excellent optical resonator for photons, and it supports mechanical vibrations (phonons). The mutual coupling of photons and phonons can be harnessed to control the propagation of light all-optically.

Furthermore, using OMIT, novel optical buffers could be realized that allow storing optical information for up to several seconds. Finally, with research groups all over the world reaching for control of optomechanical systems at the quantum level, the switchable coupling demonstrated in this work could serve as an important interface in hybrid quantum systems.

Figure 2: Principle of optomechanically induced transparency (OMIT). a) The signal laser (red beam), incident on the cavity, gets coupled into the resonator, and gets dissipated there. No light is returned from the system. b) In the additional presence of a control laser (green beam), the radiation pressure of the two beams drives the boundary of the cavity into resonant oscillations, preventing most of the signal beam to enter the cavity by an interference effect. In this case, the signal beam is returned by the optomechanical system.

Reference
[1] S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, T.J. Kippenberg, "Optomechanically induced transparency", Science, Vol.330, pp.1520-1523 (Dec 10, 2010). Abstract.

A Large Faraday Effect Observed in An Atomically Thin Material

(From L to R): Dirk van der Marel, Alexey Kuzmenko, Julien Levallois and Iris Crassee of University of Geneva

A team of physicists from the University of Geneva (Switzerland) -- in collaboration with researchers in the University of Erlangen-Nuremberg (Germany) and Berkeley Advanced Light Source (USA) -- has recently measured the magnetically induced rotation of the polarization of light (Faraday rotation) [1] in graphene in the far-infrared range.

In contradiction to the common logics, the rotation angle, which is usually proportional to sample thickness, appears to be very strong – up to a few degrees in a single atomic layer. Such a large effect, which is due to the cyclotron resonance of ‘relativistic’ electrons in graphene, does not only provide a useful contact free tool to study the dynamics of the charge carriers in graphene, but also suggests that graphene can be used to manipulate the state of the optical polarization. This work is published in a recent issue of Nature Physics [2].

Graphene is a single layer of carbon atoms arranged in a honeycomb lattice. Electrons in graphene behave like massless relativistic particles moving with a velocity of about 300 times smaller than the speed of light [3]. A high mobility of charge carriers makes graphene potentially useful for electronics. Moreover, graphene shows unique optical properties such as the universal transparency [4], which in combination with excellent electrical conductivity favor its use in important optical applications, such as solar cells, infrared detection, computer screens and ultra fast lasers [5].

On the left: A schematic representation of the Faraday rotation. On the right: the Faraday rotation as a function of the photon energy and the magnetic field (This figure is reproduced from Reference [2]. We thank authors of the paper and 'Nature Physics' for their permission. -- 2Physics.com)

When an external magnetic field is applied over a medium it becomes magnetically polarized and the state of the optical polarization of light passing through the medium is affected: linearly polarized light is rotating gradually during its passage due to a difference in velocity and absorption of left- and right-handed polarized light. The rotation angle, also known as the Faraday angle, is proportional to the optical path length, to the applied magnetic field and a material specific parameter, the Verdet constant, which depends on the wavelength of the passing light. The ‘thickness’ of graphene is given by the inter atomic distance of graphite – stacked graphene layers; therefore an intriguing question is what happens to the optical polarization state if the optical path is as short as only one atom.

Iris Crassee, Julien Levallois, Dirk van der Marel and Alexey Kuzmenko at the University of Geneva have studied the Faraday rotation in the far-infrared range by graphene, epitaxially grown on SiC and characterized in the University of Erlangen-Nuremberg and Berkeley Advanced Light Source [2]. The experiments showed that even for such an extremely thin layer the Faraday rotation can reach 6 degrees in a moderate magnetic field of 7 Tesla (see the figure). If one could be able to stack several graphene layers at distances similar to interlayer spacing in graphite (about 0.35 nm) without changing their individual properties then the effective Verdet constant of such a material can in principle attain a few times of 10⁷ radian/(meter∙Tesla). For comparison, the Verdet constants of the magneto-optical materials used in the visible range, such as rare-earth garnets, are only of the order of 10²-10³ radian/(meter∙Tesla). A more appropriate, though, would be to compare the Faraday rotation in graphene and in the semiconductor-based two-dimensional electron gases (2DEGs) in the same spectral range (far-infrared and teraherz). The fact is that the effective Verdet constant in graphene is still at least one to two orders of magnitude larger!

The origin of the observed Faraday rotation is in a peculiar cyclotron orbital motion of nearly massless electrons in graphene in a magnetic field. A similar effect can also be observed in 2DEGs. However, the cyclotron mass and therefore the cyclotron frequency (at a given magnetic field) in 2DEGs are fixed. In graphene they can be varied with doping. Moreover, since graphene can be doped both positively and negatively either electrostatically or chemically, the cyclotron frequency, and therefore the direction of the Faraday rotation, can be inverted without changing the magnetic field.

The Faraday effect and the associated magneto-optical Kerr effect are already widely used in such vital applications as optical communications, data storage and laser systems, largely in the visible range. Although the Faraday rotation in graphene was shown to be strong in the by far less exploited far-infrared part of the electromagnetic spectrum, one can nevertheless think of using graphene for example, in ultrathin and ultra fast tunable ‘Faraday isolators’, in which light can travel in one direction, but is blocked in the other. In contrast to the existing devices, one should be able to tune the spectral range and also change the sign of the Faraday rotation in graphene by simply adjusting the gate voltage.

References
[1] M. Faraday, “On the magnetization of light and the illumination of magnetic lines of force”, Phil. Trans. R. Soc. 136, 104 (1846).
[2] I. Crassee, J. Levallois, A.L.Walter, M. Ostler, A. Bostwick, E. Rotenberg, Th. Seyller, D. van der Marel and A. B. Kuzmenko, “Giant Faraday rotation in single- and multi ayer graphene”, Nature Physics, 7, 48-51 (2011). Abstract.
[3] A. K. Geim and K. S. Novoselov, “The rise of graphene: Nature Materials, 6, 183 (2007). Abstract.
[4] R.R. Nair, P. Blake, A.N. Grigorenko, K.S. Novoselov, T.J. Booth, T. Stauber, N.M.R. Peres and A.K. Geim, “Fine structure constant defines visual transparancy of graphene”, Science 320, 1308 (2008). Abstract.
[5] F. Bonaccorso, Z. Sun, T. Hasan and A. C. Ferrari, “Graphene photonics and optoelectronics”, Nature Photonics, 4, 611 (2010). Abstract.

Metaflex: Flexible Metamaterial at Visible Wavelengths

A. Di Falco (left) and T. F. Krauss

[This is an invited article based on a recently published work by the authors -- 2Physics.com]

Authors: Andrea Di Falco and Thomas F. Krauss

Affiliation: School of Physics and Astronomy, Univ. of St Andrews, UK

Andrea Di Falco, Martin Plöschner and Thomas Krauss of the School of Physics and Astronomy of the Scottish University of St Andrews, in an article published by the New Journal of Physics [1], have recently reported on the fabrication of a key building block for flexible metamaterials for visible light, Metaflex.

Figure 1: Artist's impression of the Metaflex concept. The green sphere is made invisible and not reflected by the mirror.

Metamaterials have engineered properties that are not available with naturally occuring materials. For example, they can exhibit negative refraction, which means that light refracts in the opposite direction to the one we are used to. They can also be used to build superlenses, which are lenses that can form images with “unlimited” resolution, well beyond the diffraction limit and invisibility cloaks that can guide light around an object as if it did not exist. For these effects to take place, the smallest building blocks of metamaterials, called “meta-atoms”, have to be much smaller than the wavelength of the incident light. Therefore, at visible wavelengths, which are typically 400-600 nanometres, the meta-atoms have to be in the range of few tens of nanometers. For this reason, researchers have to employ the sophisticated techniques developed in the semiconductor industry, i.e. the same techniques that are used to densely pack the semiconductor circuits that are required in modern computer processors. As a result, most metamaterials are realised on flat and rigid substrates, which limits the range of applications that can be accessed.

The work carried out at St Andrews overcomes this limitation by demonstrating metamaterials on flexible substrates. This achievement can almost be understood as a transition from the hard and rigid “stone-age” of nanophotonics to a modern age marked by flexibility [2,3]. While some examples of stretchable and deformable metamaterials have previously appeared [4-6], the St Andrews researchers were the first to demonstrate such flexible metamaterials at visible wavelengths.

Metaflex consists of very thin, and self-supporting polymer membranes. The metamaterial property arises from an array of gold nanostructures that are resonant in the visible range. In particular, Di Falco et al. have “written” a nanometer sized gold fishnet pattern (in an area of few mm²), which interacts with light at a wavelength of 630 nm, i.e. the wavelength of red light. Because metaflex is so thin, multiple layers can be stacked together as well as wrapped around an object. Such multilayer metaflex will be demonstrated as the next step, which will allow the demonstration of more complex behaviors such as negative refraction in flexible substrates at optical wavelengths.

Metaflex is also a useful tool for exploring the paradigm of Transformation Optics, which is the concept behind the ideas of invisibility cloaks that are so inspiring [7]. Transformation Optics requires materials with “designer” refractive properties that go far beyond those available with natural materials, so are ideally suited to the application of metamaterials; flexibility then adds a key ingredient. Metaflex, being supple and modifiable, is the natural choice for applications where, for example, a curved geometry is required.

Figure 2 : A layer of Metaflex placed on a disposable contact lens to show its potential use in visual prostheses.

In addition to enabling such exciting ideas as invisibility cloaks, metaflex offers more immediately feasible and practical applications such as enhanced visual prostheses, whereby the designer refractive properties can be used to improve the performance of everyday objects such as contact lenses.



References
[1] Andrea Di Falco, Martin Ploschner and Thomas F Krauss, "Flexible metamaterials at visible wavelengths", New Journal of Physics, vol.12, 113006 (2010). Abstract.
[2] John A. Rogers, Takao Someya and Yonggang Huang, "Materials and Mechanics for Stretchable Electronics", Science, vol.327, 1603 (2010). Abstract.
[3] I. Park, S. H. Ko, H. Pan, C. P. Grigoropoulos, A. P. Pisano, J. M. J. Fréchet, E.-S. Lee, J.-H. Jeong, "Nanoscale patterning and electronics on flexible substrate by direct nanoimprinting of metallic nanoparticles", Advanced Materials, vol. 20, 489 (2008). Abstract.
[4] Hu Tao, A. C. Strikwerda, K. Fan, W. J. Padilla, X. Zhang and R. D. Averitt, "Reconfigurable Terahertz Metamaterials", Phys. Rev. Lett., vol. 103, 147401 (2009). Abstract.
[5] H.O. Moser, L.K. Jian, H.S. Chen, M. Bahou, S.M.P. Kalaiselvi, S. Virasawmy, S.M. Maniam, X.X. Cheng, S.P. Heussler, Shahrain bin Mahmood, and B.-I. Wu, "All-metal self-supported THz metamaterial - the meta-foil", Opt Express (2009) vol. 17, 23914 (2009). Abstract.
[6] Imogen M. Pryce, Koray Aydin, Yousif A. Kelaita, Ryan M. Briggs, and Harry A. Atwater, "Highly Strained Compliant Optical Metamaterials with Large Frequency Tunability", Nano Lett., vol. 10, 4222 (2010). Abstract.
[7] Ulf Leonhardt and Thomas Philbin, "Geometry and Light: The Science of Invisibility" (Mineola, NY: Dover, 2010)

Quantum Walks of Correlated Photons in Integrated Waveguide Arrays

Alberto Peruzzo

[This is an invited article based on a recently published work by the authors -- 2Physics.com]

Authors: Alberto Peruzzo and Jeremy L. O’Brien

Affiliation: Centre for Quantum Photonics, H. H. Wills Physics Laboratory and Dept of Electrical & Electronic Engineering, University of Bristol, UK

Since their initial development for studying the random motion of microscopic particles (such as those suspended in a fluid), random walks have been a successful model for random processes applied in many fields, from computer science to economics. Such processes are random in the sense that at a particular time the choice for a particle to make a particular step is probabilistic and decided by flipping a coin.

Past 2Physics articles based on works of this group:
Sep 20, 2009: "Shor's Quantum Factoring Algorithm Demonstrated on a Photonic Chip"
May 2, 2008: "Silicon Photonics for Optical Quantum Technologies"

In the quantum analogue – the quantum walk[1] – the walker is, at a given time, in a superposition of the possible states and different paths can interfere, exhibiting ballistic propagation with faster dynamics compared to the slow diffusion of classical random walks, prompting applications in quantum computer science and quantum communication. Indeed quantum walks have been shown to be universal for quantum computing, enable direct simulation of important physical, chemical and biological systems, and the possibility to study very large entangled states of several particles, with potential to investigate the existence of quantum- classical boundaries.

The first application of quantum walks was search algorithms on graphs (vertices connected by edges) and is more efficient than the classical search. Finding an element in a collection of N vertices using a quantum walk requires √N steps while the classical algorithm takes N steps to check all the vertices.

Quantum walks come in two types, the discrete time quantum walk (DTQW) and the continuous time quantum walk (CTQW). In a DTQW the step direction is specified by a coin and a shift operator, which are applied repeatedly, similarly to the classical random walk, but with the difference that now the coin flip is replaced by a quantum coin operation defining the superposition of the directions the step undertakes. The CTQW describes tunnelling of quantum particles through arrayed potential wells.

The theory of quantum walks have been extensively studied but only few experimental demonstration of several steps of single particle quantum walks with atoms, trapped ions, nuclear magnetic resonance and photons have been carried out so far.

Quantum walks are based on wave interference and require a stable environment to reduce the noise (decoherence) that would otherwise destroy the interference. Interferometric stability and miniaturization using phonics waveguide circuits have been shown to be a promising approach for quantum optics experiments, silica-on-silicon waveguides have been used to demonstrate high fidelity quantum information components [2, 3, 4] and a small scale quantum algorithm for prime number factorization [5].

We’ve implemented CTQW of photons designing periodic waveguide arrays in integrated photonic circuits that enable the injection of single photons and the coupling to single photon detectors at their output. The chips were fabricated in the high refractive index contrast material silicon oxynitride, enabling to quickly stop the coupling between neighbour waveguides so that high level of control over the propagation was possible.

Integrated quantum photonic circuit used to implement a continuous time quantum walk of two correlated photons.

In contrast to all previous demonstrations — which were restricted to single particle quantum walks that have exact classical counterparts — we have demonstrated the quantum walk of two identical photons spatially correlated within arrayed waveguide, observing uniquely quantum mechanical behaviour in the two-photon correlations at the outputs of this array [6]. Pairs of correlated photons were generated with a standard type I spontaneous parametric down-conversion process, a nonlinear process where a 402nm wavelength CW laser pumps a χ² nonlinear bismuth borate crystal generating pairs of photons at 804nm wavelength in conservation of energy and momentum. The correlated photons were coupled to the waveguide using fibre arrays and the correlations at the output were recorded by measuring two photon coincide events with a detection system of 12 avalanche single photons detectors and 3 programmable counting boards. The measured correlations fit with high similarity to our simulations.

Artist’s impression of the two-photon quantum walk.
Credit: Image by Proctor & Stevenson

We’ve shown that the results strongly depend on the input state and these correlations violate classical limits by 76 standard deviation, proving that such phenomena cannot be described using classical theory. This generalized form of quantum interference is similar to the Hong-Ou-Mandel dip effect in an optical beam splitter but in our case on a 21 mode system. Bunching of correlated photons reduces the probability of detecting two photons at the opposite sides of the array while enhancing the case of two particles at the same side.

Such two particle quantum walks have already been identified as a powerful computational tool for solving important problems such as graph isomorphism, and provide a direct route to powerful quantum simulations. Implementing new algorithms based on quantum walks will require integration of the single photon sources and detectors. These have already been showed to be compatible with integration, reducing coupling losses and considerably improving the overall performances. Reconfigurability and feedback will provide further necessary tools enabling to perform more challenging and interesting tasks.

Random walk is an extremely successful tool, employed in many scientific fields and their quantum analogues promise to be similarly powerful.

References:
[1] Y. Aharonov, L. Davidovich, N. Zagury, "Quantum Random Walks", Phys. Rev. A 48, 1687 (1993). doi:10.1103/PhysRevA.48.1687
[2] A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, J. L. O'Brien, "Silica-on-silicon waveguide quantum circuits", Science 320, pp. 646-649 (2008). doi:10.1126/science.1155441
[3] J. C. F. Matthews, A. Politi, A. Stefanov, J. L. O'Brien, "Manipulation of multiphoton entanglement in waveguide quantum circuits", Nature Photonics, 3, pp. 346-350 (2009). doi:10.1038/nphoton.2009.93
[4] A. Laing, A. Peruzzo, A. Politi, M. Rodas Verde, M. Halder, T. C. Ralph, M. G. Thompson, J. L. O'Brien, "High-fidelity operation of quantum photonic circuits", Quant. Phys., e-prints, arXiv:1004.0326v2.
[5] A. Politi, J. C. F. Matthews, J. L. O'Brien, "Shor's quantum factoring algorithm on a photonic chip", Science 325, no. 5945, pp. 1221, 2009. doi:10.1126/science.1173731.
[6] A. Peruzzo, M. Lobino, J.C.F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, J. L. O’Brien, "Quantum Walks of Correlated Photons", Science 329, pp. 1500-1503 (2010). doi:10.1126/science.1193515 .