Search

We propose an atomic grating based on an electromagnetically induced transparency phenomenon that switches between zeroth-order diffraction to a distinct higher-order diffraction pattern by driving a planar gaseous medium of a four-level tripod ( ⋔ ) atoms with three laser beams: modulation of standing wave control beam propagating nearly perpendicular to the planar medium, while vortex and weak plane probe beams directed perpendicular to the medium. We numerically investigate the behavior of the amplitude, phase modulations, and probe field diffraction intensities of different orders by the variation of the field detunings and orbital angular momentum number of the composite vortex light beam. Specifically, in the off-resonant case, the interplay between a square lattice of the control and an additional spatial variation of the vortex beam allows the emergence of higher diffraction orders and variable gain due to double transparency windows in this complex optical system. We believe that our proposed scheme might be useful in optical memory devices via the storage of information to diffraction orders of the atomic grating.

We introduce unitary-gate randomized benchmarking (URB) for qudit gates by extending single-and multi-qubit URB to single- and multi-qudit gates. Specifically, we develop a qudit URB procedure that exploits unitary 2-designs. Furthermore, we show that our URB procedure is not simply extracted from the multi-qubit case by equating qudit URB to URB of the symmetric multi-qubit subspace. Our qudit URB is elucidated by using pseudocode, which facilitates incorporating into benchmarking applications., Comment: 14 pages. Comments are welcome!

Quantum computer technology is progressing rapidly with dozens of qubits and hundreds of quantum logic gates now possible. Although current quantum computer technology is distant from being able to solve computational problems beyond the reach of non-quantum computers, experiments have progressed well beyond simply demonstrating the requisite components. We can now operate small quantum logic processors with connected networks of qubits and quantum logic gates, which is a great stride towards functioning quantum computers. This book aims to be accessible to a broad audience with basic knowledge of computers, electronics and physics. The goal is to convey key notions relevant to building quantum computers and to present state-of-the-art quantum-computer research in various media such as trapped ions, superconducting circuits, photonics and beyond.

Our aim is to formulate continuous-variable quantum secret sharing as a continuous-variable ramp quantum secret sharing protocol, provide a certification procedure for it and explain the criteria for the certification. Here we introduce a technique for certifying continuous-variable ramp quantum secret-sharing schemes in the framework of quantum interactive-proof systems. We devise pseudocodes in order to represent the sequence of steps taken to solve the certification problem. Furthermore, we derive the expression for quantum mutual information between the quantum secret extracted by any multi-player structure and the share held by the referee corresponding to the Tyc-Rowe-Sanders continuous-variable quantum secret-sharing scheme. We solve by converting the Tyc-Rowe-Sanders position representation for the state into a Wigner function from which the covariance matrix can be found, then insert the covariance matrix into the standard formula for continuous-variable quantum mutual information to obtain quantum mutual information in terms of squeezing. Our quantum mutual information result quantifies the leakage of the ramp quantum secret-sharing schemes.

Quantum control for error correction is critical for the practical use of quantum computers. We address quantum optimal control for single-shot multi-qubit gates by framing as a feasibility problem for the Hamiltonian model and then solving with standard global-optimization software. Our approach yields faster high-fidelity ($>$99.99\%) single-shot three-qubit-gate control than obtained previously, and our method has enabled us to solve the quantum-control problem for a fast high-fidelity four-qubit gate.

My interest in scientific visualization began when I was an undergraduate student at the University of Calgary and saw the film "Powers of 10" for the first time. The film begins and ends with the image of a man asleep at a picnic. In between the first and last scene, we zoom out from the picnic to the vast reaches of space, changing the distance scale by leaps of powers of 10. After reaching the size of the observable universe, at 1024 m, the view zooms back to the picnicker and into his hand, ultimately focusing down to the level of a single carbon nucleus, at the scale of 10−16 m.

We study collective spontaneous emission from arbitrary distributions of N two-state atoms using quantum trajectory theory and without an a priori single-mode assumption. Assuming a fully excited initial state, we calculate the angular distribution of the average intensity, focusing on pencil- and disc-shaped samples. The formalism is developed around an unravelling of the master equation in terms of source mode quantum jumps. A modified boson approximation is made to treat the many-atom case, where it is found that strong directional superradiance with shot-to-shot fluctuations occurs for a few hundred to a few thousand atoms.

We obtain the standard quadrature-phase positive operator-valued measure (POVM) for homodyne detection directly and rigorously from the POVM for photon counting without directly employing the mean field approximation for the local oscillator. In addition we obtain correction terms for the quadrature-phase POVM that are applicable for relatively weak local oscillator field strengths and typical signal states., 15 pages, notes about strong local oscillator condition and on imperfections added, abstract changed slightly

We propose an efficient scheme for sharing a continuous variable quantum secret using passive optical interferometry and squeezers: this efficiency is achieved by showing that a maximum of two squeezers is required to replicate the secret state, and we obtain the cheapest configuration in terms of total squeezing cost. Squeezing is a cost for the dealer of the secret as well as for the receivers, and we quantify limitations to the fidelity of the replicated secret state in terms of the squeezing employed by the dealer., Comment: 7 pages, 3 figures

We analyze the quantum walk in higher spatial dimensions and compare classical and quantum spreading as a function of time. Tensor products of Hadamard transformations and the discrete Fourier transform arise as natural extensions of the quantum coin toss in the one-dimensional walk simulation, and other illustrative transformations are also investigated. We find that entanglement between the dimensions serves to reduce the rate of spread of the quantum walk. The classical limit is obtained by introducing a random phase variable., Comment: 6 pages, 6 figures, published version

We characterize surface-plasmon polaritons at lossy planar interfaces between one dispersive and one nondispersive linear isotropic homogeneous media, i.e., materials or metamaterials. Specifically we solve Maxwell's equations to obtain strict bounds for the permittivity and permeability of these media such that satisfying these bounds implies surface-plasmon polaritons successfully propagate at the interface, and violation of the bounds impedes propagation, i.e., the field delocalizes from the surface into the bulk. Our characterization of surface-plasmon polaritons is valuable for checking viability of a proposed application, and, as an example, we employ our method to falsify a previous prediction that surface-plasmon propagation through a surface of a double-negative refractive index medium occurs for any permittivity and permeability; instead we show that propagation can occur only for certain medium parameters., 17 pages, 5 figures

We present an experimental study of a Δ system in a room temperature, dilute sample of 85Rb atoms. A Δ system in the D2 manifold of 85Rb is formed by connecting the two lower hyperfine energy levels of a Λ system by a microwave drive field at 3.0357 GHz. We show that when the Rabi frequency of a microwave drive field exceeds that of the optical probe field, a three-wave mixing nonlinear interaction is established. This nonlinear interaction changes the enhanced transmission of the optical probe to a deep absorption for a relative phase difference of π between all the three fields. We establish through our experiment and our numerical simulation, the phase-sensitive and nonlinear nature of the Δ system's response to the applied microwave and optical fields. Using this feature, we demonstrate a high-contrast microwave phase controlled switch for the optical probe field. In comparison with intensity and phase switching demonstrated with all-optical fields so far, our experiment opens up the possibility of obtaining the highest contrast optical switching with room temperature atoms.

We show that a nonlinear Hamiltonian evolution can transform an SU(3) coherent state into a superposition of distinct SU(3) coherent states, with a superposition of two SU(2) coherent states presented as a special case. A phase space representation is depicted by projecting the multi-dimensional $Q$-symbol for the state to a spherical subdomain of the coset space. We discuss realizations of this nonlinear evolution in the contexts of nonlinear optics and Bose--Einstein condensates.

Entangled SU(2) and SU(1,1) coherent states are developed as superpositions of multiparticle SU(2) and SU(1,1) coherent states. In certain cases, these are coherent states with respect to generalized su(2) and su(1,1) generators, and multiparticle parity states arise as a special case. As a special example of entangled SU(2) coherent states, entangled binomial states are introduced and these entangled binomial states enable the contraction from entangled SU(2) coherent states to entangled harmonic oscillator coherent states. Entangled SU(2) coherent states are discussed in the context of pairs of qubits. We also introduce the entangled negative binomial states and entangled squeezed states as examples of entangled SU(1,1) coherent states. A method for generating the entangled SU(2) and SU(1,1) coherent states is discussed and degrees of entanglement calculated. Two types of SU(1,1) coherent states are discussed in each case: Perelomov coherent states and Barut-Girardello coherent states.

We introduce vector phase states for multipath quantum interferometry and construct the vector phase positive operator-valued measure. We calculate SU(3) phase distributions for three-path quantum interferometry and discuss measurement limits.

We extend the analysis of photon coincidence spectroscopy beyond bichromatic excitation and two-photon coincidence detection to include multichromatic excitation and multiphoton coincidence detection. Trichromatic excitation and three-photon coincidence spectroscopy are studied in detail, and we identify an observable signature of a triple resonance in an atom-cavity system., 6 page, REVTeXs, 6 Postscript figures. The abstract appeared in the Proceedings of ACOLS98

We show that the quantum state of the electromagnetic field can be determined by performing electron interferometry and exploiting the ac analogue of the Aharonov-Bohm effect. The interferometric phase shift is proportional to the magnetic-flux operator, and measurements of output electron intensity for various interferometer geometries yields the Weyl function, which is the Fourier transform of the Wigner function. In contradistinction to optical methods for state determination, this scheme relies on electron interferometry and could enable probing of intracavity field states. Second-order correlations in this context are also discussed.

Wave-like and particle-like features are identified for entangled coherent states, analogous to those identified for single-photon states. A generalized interferometer is introduced for testing complementarity with entangled coherent states.

Cat states are coherent quantum superpositions of macroscopically distinct states and are useful for understanding the boundary between the classical and the quantum world. Due to their macroscopic nature, cat states are difficult to prepare in physical systems. We propose a method to create cat states in one-dimensional quantum walks using delocalized initial states of the walker. Since the quantum walks can be performed on any quantum system, our proposal enables a platform-independent realization of the cat states. We further show that the linear dispersion relation of the effective quantum walk Hamiltonian, which governs the dynamics of the delocalized states, is responsible for the formation of the cat states. We analyze the robustness of these states against environmental interactions and present methods to control and manipulate the cat states in the photonic implementation of quantum walks.

The theory of relativity requires that no information travel faster than light, whereas the unitarity of quantum mechanics ensures that quantum information cannot be cloned. These conditions provide the basic constraints that appear in information replication tasks, which formalize aspects of the behavior of information in relativistic quantum mechanics. In this article, we provide continuous variable (CV) strategies for spacetime quantum information replication that are directly amenable to optical or mechanical implementation. We use a new class of homologically-constructed CV quantum error correcting codes to provide efficient solutions for the general case of information replication. As compared to schemes encoding qubits, our CV solution requires half as many shares per encoded system. We also provide an optimized five-mode strategy for replicating quantum information in a particular configuration of four spacetime regions designed not to be reducible to previously performed experiments. For this optimized strategy, we provide detailed encoding and decoding procedures using standard optical apparatus and calculate the recovery fidelity when finite squeezing is used. As such we provide a scheme for experimentally realizing quantum information replication using quantum optics., Comment: 38 pages, 16 figures. Version 2: added major appendix, simplified discussion throughout (especially continuous variable codes), simplified decoding circuits. Version 3: Published version: added Figure 10, other minor changes. Version 4: updated acknowledgments and funding sources

Barry Sanders says that successful collaboration with researchers in China can be fostered by being sensitive to cultural norms.

We determine the linear optical susceptibility of a radiation pulse propagating through a mixture of a gas of atoms or molecules and a plasma. For a specific range of radiation and plasma frequencies, resonant generation of volume plasmons significantly amplifies the radiation intensity. The conditions for resonant amplification are derived from the dispersion relations in the mixture, and the amplification is demonstrated in a numerical simulation of pulse propagation., 17 pages, 9 figures

We show that the stability theorem of the depolarizing channel holds for the output quantum $p$-R\'enyi entropy for $p \ge 2$ or $p=1$, which is an extension of the well known case $p=2$. As an application, we present a protocol in which Bob determines whether Alice prepares a pure quantum state close to a product state. In the protocol, Alice transmits to Bob multiple copies of a pure state through a depolarizing channel, and Bob estimates its output quantum $p$-R\'enyi entropy. By using our stability theorem, we show that Bob can determine whether her preparation is appropriate., Comment: 9 pages, no figure

An atomic beam which is incident on a laser beam can be reflected or transmitted depending on the choice of atomic and laser beam parameters. The authors show that quantum reflection and tunnelling by atoms through a laser beam is possible in principle and develop a novel scheme for an atomic beamsplitter which is based on quantum reflection and tunnelling. They compare this scheme to other proposals for atomic beamsplitters.

The authors present analytical and numerical results for resonance fluorescence produced by a two-level atom damped by a broad-band squeezed vacuum. Previous theoretical analyses of this model have assumed that the laser frequency and the carrier frequency of the squeezed vacuum are equal. The authors introduce a non-zero detuning between the laser frequency and the carrier frequency while maintaining resonance between the laser frequency and atomic resonance. In the absence of the driving field there is a squeezing threshold: above threshold the decay rate of the atomic polarization can be reduced, and below threshold a squeezing-induced two peak spectrum and frequency shift, which is analogous to the Bloch-Siegert shift, are predicted. In the presence of the driving field, the spectrum is asymmetric for Rabi frequencies smaller or comparable to the detuning of the squeezed vacuum. A symmetric spectrum is obtained for large Rabi frequencies. An interpretation is predicted by means of a dressed-state analysis. The authors find that for not too large Rabi frequencies a remarkably large population inversion can be induced in the dressed states, even at exact resonance of the driving field, provided that the laser frequency and carrier frequency are detuned. Moreover, for detection times larger than the inverse detuning, the spectrum is insensitive to the phase between the driving field and the squeezed vacuum, in marked contrast to the case of no detuning.

The authors investigate the dipole-dipole interaction role in the resonance fluorescence of two identical two-level atoms, which are confined to a region much smaller than the resonant wavelength and which are damped by a squeezed vacuum. The spectrum consists of seven or five lines, depending on the relative phase between the driving field and the squeezed vacuum, whereas the spectrum without the dipole-dipole interaction displays three lines. The widths of these lines depend on the parameters of the squeezed vacuum and can be subnatural or supernatural depending on the phase. The central line and additional sidebands at double the Rabi frequency can have intensities larger than in the normal vacuum but the intensities of lines at one Rabi frequency are always less than in the normal vacuum.

It is safe to say that, when the concept of the photon was first introduced, the generation of single photons was not being considered. Until the emergence of the ideas and methods of quantum optics, the `single-photon regime' was attained by strongly attenuating a laser beam to ensure that the probability of having more than one photon became negligible. However, such attenuated beams differ from `true' single photons in at least two respects: first, the vacuum probability is much higher than the probability of detecting a photon, so one gets predominantly a `no-photon' regime with occasional detection of a photon; second, the probability of getting two photons is never zero, but essentially follows a Poisson law. Although the weak beam has been useful in quantum optics, the advent of quantum information science has placed stringent demands on optical sources, namely that sources produce single photons either on demand or heralded. In particular secure quantum cryptography and linear optical quantum computing depend on the availability of such single-photon sources. The combination of strict requirements for single photons, plus new technologies, is driving an exciting research effort into single-photon generation. This Focus Issue recognizes that single-photon sources are rapidly developing and presents research articles covering the spectrum of activity in the field. Significant advances are reported for single-photon and photon-pair sources constructed from quantum dots in pillar microcavities, parametric down converters, falling neutral atoms and trapped ions in cavities, defects in diamond nanocrystals and a single molecule in a solid. In addition to producing single-photon pulses, one article reports on the latest developments regarding the production of photon number states in a microwave cavity. Another article discusses the application of a nitrogen-vacancy-based single-photon source to an experimental demonstration of quantum key distribution in open air. Photodetection performs a critical role in assessing single-photon sources as well as heralding the arrival of a single photon based on detecting a correlated partner, and this issue presents the latest results on single-photon counting with a superconducting niobium nitride hot-electron bolometer. Another article provides a detailed study of how to characterize single-photon sources via intensity noise analyses. Photodetection is also important for post-selection-based processing for non-deterministic quantum information tasks, and this issue presents an analysis of photodetection and post-selection used in another way: enhancing the efficiency of single-photon sources by interferometry, photodetection and post-selection. New Journal of Physics appreciates the rapid pace of development in the area of single photons on demand. This Focus Issue presents the latest developments and also points to a bright future with better photon sources. Focus on Single Photons on Demand Contents Photon statistics characterization of a single-photon source R Alleaume, F Treussart, J-M Courty and J-F Roch Photon statistics of a non-stationary periodically driven single-photon source M Hennrich, T Legero, A Kuhn and G Rempe On the measurement of two-photon single-mode coupling efficiency in parametric down-conversion photon sources S Castelletto, I P Degiovanni, A Migdall and M Ware Single-photon sources based on single molecules in solids W E Moerner Single-photon generation with InAs quantum dots Charles Santori, David Fattal, Jelena Vuckovic, Glenn S Solomon and Yoshihisa Yamamoto Visible single-photon generation from semiconductor quantum dots Thomas Aichele, Valery Zwiller and Oliver Benson Enhanced correlated photon pair emission from a pillar microcavity M Benyoucef, S M Ulrich, P Michler, J Wiersig, F Jahnke and A Forchel Experimental open-air quantum key distribution with a single-photon source R Alleaume, F Treussart, G Messin, Y Dumeige, J-F Roch, A Beveratos, R Brouri-Tualle, J-P Poizat and P Grangier Post-processing with linear optics for improving the quality of single-photon sources Dominic W Berry, Stefan Scheel, Casey R Myers, Barry C Sanders, Peter L Knight and Raymond Laflamme A single-photon source based on a single Ca+ ion Christian Maurer, Christoph Becher, Carlos Russo, Jurgen Eschner and Rainer Blatt A calcium ion in a cavity as a controlled single-photon source M Keller, B Lange, K Hayasaka, W Lange and H Walther Quantum optics with single quantum dot devices Valery Zwiller, Thomas Aichele and Oliver Benson The creation and detection of arbitrary photon number states using cavity QED Benjamin T H Varcoe, Simon Brattke and Herbert Walther Stable single-photon source in the near infrared T Gaebel, I Popa, A Gruber, M Domhan, F Jelezko and J Wrachtrup Colloidal CdSe/ZnS quantum dots as single-photon sources X Brokmann, G Messin, P Desbiolles, E Giacobino, M Dahan and J P Hermier Towards a periodic deterministic source of arbitrary single-photon states Evan Jeffrey, Nicholas A Peters and Paul G Kwiat Fabrication of a superconducting niobium nitride hot electron bolometer for single-photon counting R Romestain, B Delaet, P Renaud-Goud, I Wang, C Jorel, J-C Villegier and J-Ph Poizat High-quality asynchronous heralded single-photon source at telecom wavelength Sylvain Fasel, Olivier Alibart, Sebastien Tanzilli, Pascal Baldi, Alexios Beveratos, Nicolas Gisin and Hugo Zbinden Philippe Grangier, Institut d'Optique Theorique et Appliquee, Orsay, France Barry Sanders, University of Calgary, Canada Jelena Vuckovic, Stanford University, CA, USA

The Trotter-Suzuki decomposition is an important tool for the simulation and control of physical systems. We provide evidence for the stability of the Trotter-Suzuki decomposition. We model the error in the decomposition and determine sufficiency conditions that guarantee the stability of this decomposition under this model. We relate these sufficiency conditions to precision limitations of computing and control in both classical and quantum cases. Furthermore we show that bounded-error Trotter-Suzuki decomposition can be achieved by a suitable choice of machine precision., Comment: 18 pages, 1 figure

We review entangled coherent state research since its first implicit use in 1967 to the present. Entangled coherent states are important to quantum superselection principles, quantum information processing, quantum optics, and mathematical physics. Despite their inherent fragility they have produced in a conditional propagating-wave quantum optics realization. Fundamentally the states are intriguing because they are entanglements of the coherent states, which are in a sense the most classical of all states of a dynamical system., Comprehensive review of entangled coherent states. Comments welcome, especially advice on missing references or perhaps misrepresentations of existing references, which will be accommodated in version 2

We introduce a class of bipartite entanglement measures based on Renyi-α entropy, namely Renyi-α entanglement with an analytic formula in two-qubit systems for α ≥ 1. We also show that multi-qubit entanglement has a monogamy inequality in terms of Renyi-α entanglement for all α ≥ 2.

Two closely spaced dangling bonds positioned on a silicon surface and sharing an excess electron are revealed to be a strong candidate for a charge qubit. Based on our study of the coherent dynamics of this qubit, its extremely high tunneling rate ~ 10^14 1/s greatly exceeds the expected decoherence rates for a silicon-based system, thereby overcoming a critical obstacle of charge qubit quantum computing. We investigate possible configurations of dangling bond qubits for quantum computing devices. A first-order analysis of coherent dynamics of dangling bonds shows promise in this respect., 17 pages, 3 EPS figures, 1 table

We establish a framework for oracle identification problems in the continuous variable setting, where the stated problem necessarily is the same as in the discrete variable case, and continuous variables are manifested through a continuous representation in an infinite-dimensional Hilbert space. We apply this formalism to the Deutsch-Jozsa problem and show that, due to an uncertainty relation between the continuous representation and its Fourier-transform dual representation, the corresponding Deutsch-Jozsa algorithm is probabilistic hence forbids an exponential speed-up, contrary to a previous claim in the literature.

Light is composed of photons, but only recently has it become relatively common, albeit still challenging, to manipulate single or few photons. This special issue presents state-of-the-art theory and experiment concerning the production of few-photon states of light, processing the states, and performing highly sensitive low-noise detection at the single-photon level. In many cases, the connection between photon manipulation and quantum information science is apparent. Few-photon sources have applications for quantum cryptography and optical quantum computing. Photon processing can involve producing entangled states of light as resources for quantum information processing, performing optical gates for example by interferometry, and realizing quantum memory to store information and synchronize gate operations. Ultimately the photons are carriers of information, and this information is acquired by detectors, which have to be reliable, highly sensitive, fast and operate with low noise. Many of these photon generation, processing and detection issues are exemplified in the papers presented here. This special issue thus serves as a compendium of recent results in the area of few-photon optics, covering the development of new sources, the characterization and improvement of detection schemes, and the analysis and proposal of processing protocols. We trust that this issue will serve as a valuable resource for the community for years to come.

Quantum computation is a fast-growing, multi-disciplinary research field. The purpose of a quantum computer is to execute quantum algorithms that efficiently solve computational problems intractable within the existing paradigm of 'classical' computing built on bits and Boolean gates. While collaboration between computer scientists, physicists, chemists, engineers, mathematicians and others is essential to the project's success, traditional disciplinary boundaries can hinder progress and make communicating the aims of quantum computing and future technologies difficult. We have developed a four minute animation as a tool for representing, understanding and communicating a silicon-based solid-state quantum computer to a variety of audiences, either as a stand-alone animation to be used by expert presenters or embedded into a longer movie as short animated sequences. The paper includes a generally applicable recipe for successful scientific animation production.

Advances in physics are intimately connected with developments in a new technology, the telescope, precision clocks, even the computer all have heralded a shift in thinking. These landmark developments open new opportunities accelerating research and in turn new scientific directions. These technological drivers often correspond to new instruments, but equally might just as well flag a new mathematical tool, an algorithm or even means to visualize physics in a new way. Early on in this twenty-first century, scientific communities are just starting to explore the potential of digital visualization. Whether visualization is used to represent and communicate complex concepts, or to understand and interpret experimental data, or to visualize solutions to complex dynamical equations, the basic tools of visualization are shared in each of these applications and implementations. High-performance computing exemplifies the integration of visualization with leading research. Visualization is an indispensable tool for analyzing and interpreting complex three-dimensional dynamics as well as to diagnose numerical problems in intricate parallel calculation algorithms. The effectiveness of visualization arises by exploiting the unmatched capability of the human eye and visual cortex to process the large information content of images. In a brief glance, we recognize patterns or identify subtle features even in noisy data, something that is difficult or impossible to achieve with more traditional forms of data analysis. Importantly, visualizations guide the intuition of researchers and help to comprehend physical phenomena that lie far outside of direct experience. In fact, visualizations literally allow us to see what would otherwise remain completely invisible. For example, artificial imagery created to visualize the distribution of dark matter in the Universe has been instrumental to develop the notion of a cosmic web, and for helping to establish the current standard model of cosmology wherein this (in principle invisible) dark matter dominates the cosmic matter content. The advantages of visualization found for simulated data also hold for real world data as well. With the application of computerized acquisition many scientific disciplines are witnessing exponential growth rates of the volume of accumulated raw data, which often makes it daunting to condense the information into a manageable form, a challenge that can be addressed by modern visualization techniques. Such visualizations are also often an enticing way to communicate scientific results to the general public. This need for visualization is especially true in basic science, with its reliance on a benevolent and interested general public that drives the need for high-quality visualizations. Despite the widespread use of visualization, this technology has suffered from a lack of the unifying influence of shared common experiences. As with any emerging technology practitioners have often independently found solutions to similar problems. It is the aim of this focus issue to celebrate the importance of visualization, report on its growing use by the broad community of physicists, including biophysics, chemical physics, geophysics, astrophysics, and medical physics, and provide an opportunity for the diverse community of scientists using visualization to share work in one issue of a journal that itself is in the vanguard of supporting visualization and multimedia. A remarkable breadth and diversity of visualization in physics is to be found in this issue spanning fundamental aspects of relativity theory to computational fluid dynamics. The topics span length scales that are as small as quantum phenomena to the entire observable Universe. We have been impressed by the quality of the submissions and hope that this snap-shot will introduce, inform, motivate and maybe even help to unify visualization in physics. Readers are also directed to the December issue of Physics World which includes the following features highlighting work in this collection and other novel uses of visualization techniques: 'A feast of visualization' Physics World December 2008 pp 20–23 'Seeing the quantum world' by Barry Sanders Physics World December 2008 pp 24–27 'A picture of the cosmos' by Mark SubbaRao and Miguel Aragon-Calvo Physics World December 2008 pp 29–32 'Thinking outside the cube' by Cesar A Hidalgo Physics World December 2008 pp 34–37 Focus on Visualization in Physics Contents Visualization of spiral and scroll waves in simulated and experimental cardiac tissue E M Cherry and F H Fenton Visualization of large scale structure from the Sloan Digital Sky Survey M U SubbaRao, M A Aragon-Calvo, H W Chen, J M Quashnock, A S Szalay and D G York How computers can help us in creating an intuitive access to relativity Hanns Ruder, Daniel Weiskopf, Hans-Peter Nollert and Thomas Muller Lagrangian particle tracking in three dimensions via single-camera in-line digital holography Jiang Lu, Jacob P Fugal, Hansen Nordsiek, Ewe Wei Saw, Raymond A Shaw and Weidong Yang Quantifying spatial heterogeneity from images Andrew E Pomerantz and Yi-Qiao Song Disaggregation and scientific visualization of earthscapes considering trends and spatial dependence structures S Grunwald Strength through structure: visualization and local assessment of the trabecular bone structure C Rath, R Monetti, J Bauer, I Sidorenko, D Muller, M Matsuura, E-M Lochmuller, P Zysset and F Eckstein Thermonuclear supernovae: a multi-scale astrophysical problem challenging numerical simulations and visualization F K Ropke and R Bruckschen Visualization needs and techniques for astrophysical simulations W Kapferer and T Riser Flow visualization and field line advection in computational fluid dynamics: application to magnetic fields and turbulent flows Pablo Mininni, Ed Lee, Alan Norton and John Clyne Splotch: visualizing cosmological simulations K Dolag, M Reinecke, C Gheller and S Imboden Visualizing a silicon quantum computer Barry C Sanders, Lloyd C L Hollenberg, Darran Edmundson and Andrew Edmundson Colliding galaxies, rotating neutron stars and merging black holes—visualizing high dimensional datasets on arbitrary meshes Werner Benger A low complexity visualization tool that helps to perform complex systems analysis M G Beiro, J I Alvarez-Hamelin and J R Busch Visualizing astrophysical N-body systems John Dubinski

We generalize the W class of states from $n$ qubits to $n$ qudits and prove that their entanglement is fully characterized by their partial entanglements even for the case of the mixture that consists of a W-class state and a product state $\ket{0}^{\otimes n}$., 12 pages, 1 figure

We propose a variation of the quantum walk on a circle in phase space by conjoining the Hadamard coin flip with simultaneous displacement of the walker's location in phase space and show that this generalization is a proper quantum walk albeit over multiple concentric circles in phase instead of just over one circle. We motivate the conjoining of Hadamard and displacement operations by showing that the Jaynes-Cummings model for coin+walker approximately yields this description in the dispersive limit. The quantum walk signature is evident in the phase distribution of the walker provided that appropriate pulse durations are applied for each coin flip.

We develop a comprehensive, elegant theory to explain terahertz (THz) emission from a superlattice over a wide range of applied electric field,which shows excellent agreement between theory andexperiment for a GaAs/Al{0.3}Ga{0.7As superlattice. Specifically we show that increasing electric field increases THz emission for low fields, then reduces emission for medium fields due to field-induced wave function localization, and then increases emission in the high field due to delocalization and Zener tunneling between minibands. Our theory shows that Zener tunneling resonances yield high THz emission intensities and points to superlattice design improvements., 10 pages, 3 figures