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Innovation is to organizations what evolution is to organisms: it is how organisations adapt to changes in the environment and improve. Governments, institutions and firms that innovate are more likely to prosper and stand the test of time; those that fail to do so fall behind their competitors and succumb to market and environmental change. Yet despite steady advances in our understanding of evolution, what drives innovation remains elusive. On the one hand, organizations invest heavily in systematic strategies to drive innovation. On the other, historical analysis and individual experience suggest that serendipity plays a significant role in the discovery process. To unify these two perspectives, we analyzed the mathematics of innovation as a search process for viable designs across a universe of building blocks. We then tested our insights using historical data from language, gastronomy and technology. By measuring the number of makeable designs as we acquire more components, we observed that the relative usefulness of different components is not fixed, but cross each other over time. When these crossovers are unanticipated, they appear to be the result of serendipity. But when we can predict crossovers ahead of time, they offer an opportunity to strategically increase the growth of our product space. Thus we find that the serendipitous and strategic visions of innovation can be viewed as different manifestations of the same thing: the changing importance of component building blocks over time., Comment: 7 pages, 6 figures

Non-equilibrium phase transitions exist in damped-driven open quantum systems, when the continuous tuning of an external parameter leads to a transition between two robust steady states. In second-order transitions this change is abrupt at a critical point, whereas in first-order transitions the two phases can co-exist in a critical hysteresis domain. Here we report the observation of a first-order dissipative quantum phase transition in a driven circuit quantum electrodynamics (QED) system. It takes place when the photon blockade of the driven cavity-atom system is broken by increasing the drive power. The observed experimental signature is a bimodal phase space distribution with varying weights controlled by the drive strength. Our measurements show an improved stabilization of the classical attractors up to the milli-second range when the size of the quantum system is increased from one to three artificial atoms. The formation of such robust pointer states could be used for new quantum measurement schemes or to investigate multi-photon quantum many-body phases., Comment: 7 pages, 4 figures

Linking classical microwave electrical circuits to the optical telecommunication band is at the core of modern communication. Future quantum information networks will require coherent microwave-to-optical conversion to link electronic quantum processors and memories via low-loss optical telecommunication networks. Efficient conversion can be achieved with electro-optical modulators operating at the single microwave photon level. In the standard electro-optic modulation scheme this is impossible because both, up- and downconverted, sidebands are necessarily present. Here we demonstrate true single sideband up- or downconversion in a triply resonant whispering gallery mode resonator by explicitly addressing modes with asymmetric free spectral range. Compared to previous experiments, we show a three orders of magnitude improvement of the electro-optical conversion efficiency reaching 0.1% photon number conversion for a 10GHz microwave tone at 0.42mW of optical pump power. The presented scheme is fully compatible with existing superconducting 3D circuit quantum electrodynamics technology and can be used for non-classical state conversion and communication. Our conversion bandwidth is larger than 1MHz and not fundamentally limited., Comment: 8 pages, 5 figures; comments welcome!

We present a platform based upon silicon nitride nanomembranes for integrating superconducting microwave circuits with planar acoustic and optical devices such as phononic and photonic crystals. Utilizing tensile stress and lithographic patterning of a silicon nitride nanomembrane we are able to reliably realize planar capacitors with vacuum gap sizes down to $s \approx 80$nm. In combination with spiral inductor coils of micron pitch, this yields microwave ($\approx 8$GHz) resonant circuits of high impedance ($Z_{0} \approx 3.4$k$\Omega$) suitable for efficient electromechanical coupling to nanoscale acoustic structures. We measure an electromechanical vacuum coupling rate of $g_{0}/2\pi = 41.5$~Hz to the low frequency ($4.48$MHz) global beam motion of a patterned phononic crystal nanobeam, and through parametric microwave driving reach a backaction cooled mechanical mode occupancy as low as $n_{m} = 0.58$., Comment: 21 pages, 9 figures

A neutral network is a subgraph of a Hamming graph, and its principal eigenvalue determines its robustness: the ability of a population evolving on it to withstand errors. Here we consider the most robust small neutral networks: the graphs that interpolate pointwise between hypercube graphs of consecutive dimension (the point, line, line and point in the square, square, square and point in the cube, and so on). We prove that the principal eigenvalue of the adjacency matrix of these graphs is bounded by the logarithm of the number of vertices, and we conjecture an analogous result for Hamming graphs of alphabet size greater than two.

We fabricate and characterize a microscale silicon electro-opto-mechanical system whose mechanical motion is coupled capacitively to an electrical circuit and optically via radiation pressure to a photonic crystal cavity. To achieve large electromechanical interaction strength, we implement an inverse shadow mask fabrication scheme which obtains capacitor gaps as small as 30 nm while maintaining a silicon surface quality necessary for minimizing optical loss. Using the sensitive optical read-out of the photonic crystal cavity, we characterize the linear and nonlinear capacitive coupling to the fundamental 63 MHz in-plane flexural motion of the structure, showing that the large electromechanical coupling in such devices may be suitable for realizing efficient microwave-to-optical signal conversion., Comment: 8 papers, 4 figures

We introduce a simple class of distribution networks which withstand damage by being repairable instead of redundant. We prove a lower bound for the expected cost of repair, and show that for networks on the square and triangular lattice, this bound is achievable and results in a network with exactly three levels of structural hierarchy. We extend our results to networks subject to repeated attacks, in which the repairs themselves must be repairable. We find that, in exchange for a modest increase in repair cost, such networks are able to withstand any number of attacks., Comment: 5 pages, 5 figures

The analysis of networks characterized by links with heterogeneous intensity or weight suffers from two long-standing problems of arbitrariness. On one hand, the definitions of topological properties introduced for binary graphs can be generalized in non-unique ways to weighted networks. On the other hand, even when a definition is given, there is no natural choice of the (optimal) scale of link intensities (e.g. the money unit in economic networks). Here we show that these two seemingly independent problems can be regarded as intimately related, and propose a common solution to both. Using a formalism that we recently proposed in order to map a weighted network to an ensemble of binary graphs, we introduce an information-theoretic approach leading to the least biased generalization of binary properties to weighted networks, and at the same time fixing the optimal scale of link intensities. We illustrate our method on various social and economic networks., Comment: Accepted for presentation at SocInfo 2013, Kyoto, 25-27 November 2013 (http://www.socinfo2013.org)

The geometric aspects of quantum mechanics are underlined most prominently by the concept of geometric phases, which are acquired whenever a quantum system evolves along a closed path in Hilbert space. The geometric phase is determined only by the shape of this path and is -- in its simplest form -- a real number. However, if the system contains degenerate energy levels, matrix-valued geometric phases, termed non-abelian holonomies, can emerge. They play an important role for the creation of synthetic gauge fields in cold atomic gases and the description of non-abelian anyon statistics. Moreover, it has been proposed to exploit non-abelian holonomic gates for robust quantum computation. In contrast to abelian geometric phases, non-abelian ones have been observed only in nuclear quadrupole resonance experiments with a large number of spins and without fully characterizing the geometric process and its non-commutative nature. Here, we realize non-abelian holonomic quantum operations on a single superconducting artificial three-level atom by applying a well controlled two-tone microwave drive. Using quantum process tomography, we determine fidelities of the resulting non-commuting gates exceeding 95 %. We show that a sequence of two paths in Hilbert space traversed in different order yields inequivalent transformations, which is an evidence for the non-abelian character of the implemented holonomic quantum gates. In combination with two-qubit operations, they form a universal set of gates for holonomic quantum computation., Comment: In press in Nature. Published online on April 17, 2013

We report the experimental observation, and a theoretical explanation, of collective suppression of linewidths for multiple superconducting qubits coupled to a good cavity. This demonstrates how strong qubit-cavity coupling can significantly modify the dephasing and dissipation processes that might be expected for individual qubits, and can potentially improve coherence times in many-body circuit QED.

Interference at a beam splitter reveals both classical and quantum properties of electromagnetic radiation. When two indistinguishable single photons impinge at the two inputs of a beam splitter they coalesce into a pair of photons appearing in either one of its two outputs. This effect is due to the bosonic nature of photons and was first experimentally observed by Hong, Ou, and Mandel (HOM) [1]. Here, we present the observation of the HOM effect with two independent single-photon sources in the microwave frequency domain. We probe the indistinguishability of single photons, created with a controllable delay, in time-resolved second-order cross- and auto-correlation function measurements. Using quadrature amplitude detection we are able to resolve different photon numbers and detect coherence in and between the output arms. This measurement scheme allows us to observe the HOM effect and, in addition, to fully characterize the two-mode entanglement of the spatially separated beam splitter output modes. Our experiments constitute a first step towards using two-photon interference at microwave frequencies for quantum communication and information processing, e.g. for distributing entanglement between nodes of a quantum network [2, 3] and for linear optics quantum computation [4, 5].

A localized qubit entangled with a propagating quantum field is well suited to study non-local aspects of quantum mechanics and may also provide a channel to communicate between spatially separated nodes in a quantum network. Here, we report the on demand generation and characterization of Bell-type entangled states between a superconducting qubit and propagating microwave fields composed of zero, one and two-photon Fock states. Using low noise linear amplification and efficient data acquisition we extract all relevant correlations between the qubit and the photon states and demonstrate entanglement with high fidelity., Comment: 5 pages, 3 figures

Nonlinearity and entanglement are two important properties by which physical systems can be identified as non-classical. We study the dynamics of the resonant interaction of up to N=3 two-level systems and a single mode of the electromagnetic field sharing a single excitation dynamically. We observe coherent vacuum Rabi oscillations and their nonlinear speed up by tracking the populations of all qubits and the resonator in time. We use quantum state tomography to show explicitly that the dynamics generates maximally entangled states of the W class in a time limited only by the collective interaction rate. We use an entanglement witness and the threetangle to characterize the state whose fidelity F=78% is limited in our experiments by crosstalk arising during the simultaneous qubit manipulations which is absent in a sequential approach with F=91%.

We study the relative importance of "top-speed" (long-term growth rate) and "acceleration" (how quickly the long-term growth rate can be reached) in the evolutionary race to increase population size. We observe that fitness alone does not capture growth rate: robustness, a property of neutral network shape, combines with fitness to include the effect of deleterious mutations, giving growth rate. Similarly, we show that growth rate alone does not capture population size: regularity, a different property of neutral network shape, combines with growth rate to include the effect of higher depletion rates early on, giving size. Whereas robustness is a function of the principal eigenvalue of the neutral network adjacency matrix, regularity is a function of the principal eigenvector. We show that robustness is not correlated with regularity, and observe in silico the selection for regularity by evolving RNA ribozymes. Despite having smaller growth rates, the more regular ribozymes have the biggest populations.

Steering a quantum harmonic oscillator state along cyclic trajectories leads to a path-dependent geometric phase. Here we describe an experiment observing this geometric phase in an electronic harmonic oscillator. We use a superconducting qubit as a non-linear probe of the phase, otherwise unobservable due to the linearity of the oscillator. Our results demonstrate that the geometric phase is, for a variety of cyclic trajectories, proportional to the area enclosed in the quadrature plane. At the transition to the non-adiabatic regime, we study corrections to the phase and dephasing of the qubit caused by qubit-resonator entanglement. The demonstrated controllability makes our system a versatile tool to study adiabatic and non-adiabatic geometric phases in open quantum systems and to investigate the potential of geometric gates for quantum information processing.

Creating a train of single photons and monitoring its propagation and interaction is challenging in most physical systems, as photons generally interact very weakly with other systems. However, when confining microwave frequency photons in a transmission line resonator, effective photon-photon interactions can be mediated by qubits embedded in the resonator. Here, we observe the phenomenon of photon blockade through second-order correlation function measurements. The experiments clearly demonstrate antibunching in a continuously pumped source of single microwave photons measured using microwave beam splitters, linear amplifiers, and quadrature amplitude detectors. We also investigate resonance fluorescence and Rayleigh scattering in Mollow-triplet-like spectra.

Continuous variable entanglement between two modes of a radiation field is usually studied at optical frequencies. As an important step towards the observation of entanglement between propagating microwave photons we demonstrate the experimental state reconstruction of two field modes in the microwave domain. In particular, we generate two-mode correlated states with a Josephson parametric amplifier and detect all four quadrature components simultaneously in a two-channel heterodyne setup using amplitude detectors. Analyzing two-dimensional phase space histograms for all possible pairs of quadratures allows us to determine the full covariance matrix and reconstruct the four-dimensional Wigner function. We demonstrate strong correlations between the quadrature amplitude noise in the two modes. Under ideal conditions two-mode squeezing below the standard quantum limit should be observable in future experiments., Comment: 4 pages, 4 figures

Microwave cavities with high quality factors enable coherent coupling of distant quantum systems. Virtual photons lead to a transverse exchange interaction between qubits, when they are non-resonant with the cavity but resonant with each other. We experimentally probe the inverse scaling of the inter-qubit coupling with the detuning from a cavity mode and its proportionality to the qubit-cavity interaction strength. We demonstrate that the enhanced coupling at higher frequencies is mediated by multiple higher-harmonic cavity modes. Moreover, in the case of resonant qubits, the symmetry properties of the system lead to an allowed two-photon transition to the doubly excited qubit state and the formation of a dark state., Comment: 9 pages, 6 figures

A number of superconducting qubits, such as the transmon or the phase qubit, have an energy level structure with small anharmonicity. This allows for convenient access of higher excited states with similar frequencies. However, special care has to be taken to avoid unwanted higher-level populations when using short control pulses. Here we demonstrate the preparation of arbitrary three-level superposition states using optimal control techniques in a transmon. Performing dispersive read-out we extract the populations of all three levels of the qutrit and study the coherence of its excited states. Finally we demonstrate full quantum state tomography of the prepared qutrit states and evaluate the fidelities of a set of states, finding on average 96%., Comment: 4 pages, 4 figures

The quantum properties of electromagnetic, mechanical or other harmonic oscillators can be revealed by investigating their strong coherent coupling to a single quantum two level system in an approach known as cavity quantum electrodynamics (QED). At temperatures much lower than the characteristic energy level spacing the observation of vacuum Rabi oscillations or mode splittings with one or a few quanta asserts the quantum nature of the oscillator. Here, we study how the classical response of a cavity QED system emerges from the quantum one when its thermal occupation -- or effective temperature -- is raised gradually over 5 orders of magnitude. In this way we explore in detail the continuous quantum-to-classical crossover and demonstrate how to extract effective cavity field temperatures from both spectroscopic and time-resolved vacuum Rabi measurements., Comment: revised version: improved analysis, 4 pages, 4 figures, hi-res version available at http://qudev.ethz.ch/content/science/PubsPapers.html

At optical frequencies the radiation produced by a source, such as a laser, a black body or a single photon source, is frequently characterized by analyzing the temporal correlations of emitted photons using single photon counters. At microwave frequencies, however, there are no efficient single photon counters yet. Instead, well developed linear amplifiers allow for efficient measurement of the amplitude of an electromagnetic field. Here, we demonstrate how the properties of a microwave single photon source can be characterized using correlation measurements of the emitted radiation with such detectors. We also demonstrate the cooling of a thermal field stored in a cavity, an effect which we detect using a cross-correlation measurement of the radiation emitted at the two ends of the cavity., Comment: 5 pages, 4 figures

We present a quantitative measure of physical complexity, based on the amount of information required to build a given physical structure through self-assembly. Our procedure can be adapted to any given geometry, and thus to any given type of physical system. We illustrate our approach using self-assembling polyominoes, and demonstrate the breadth of its potential applications by quantifying the physical complexity of molecules and protein complexes. This measure is particularly well suited for the detection of symmetry and modularity in the underlying structure, and allows for a quantitative definition of structural modularity. Furthermore we use our approach to show that symmetric and modular structures are favoured in biological self-assembly, for example of protein complexes. Lastly, we also introduce the notions of joint, mutual and conditional complexity, which provide a useful distance measure between physical structures., Comment: 9 pages, submitted for publication

We present the realization of a cavity quantum electrodynamics setup in which photons of strongly different lifetimes are engineered in different harmonic modes of the same cavity. We achieve this in a superconducting transmission line resonator with superconducting qubits coupled to the different modes. One cavity mode is strongly coupled to a detection line for qubit state readout, while a second long lifetime mode is used for photon storage and coherent quantum operations. We demonstrate sideband based measurement of photon coherence, generation of n photon Fock states and the scaling of the sideband Rabi frequency with the square root of n using a scheme that may be extended to realize sideband based two-qubit logic gates., Comment: 4 pages, 5 figures, version with high resolution figures available at http://qudev.ethz.ch/content/science/PubsPapers.html

The exceptionally strong coupling realizable between superconducting qubits and photons stored in an on-chip microwave resonator allows for the detailed study of matter-light interactions in the realm of circuit quantum electrodynamics (QED). Here we investigate the resonant interaction between a single transmon-type multilevel artificial atom and weak thermal and coherent fields. We explore up to three photon dressed states of the coupled system in a linear response heterodyne transmission measurement. The results are in good quantitative agreement with a generalized Jaynes-Cummings model. Our data indicates that the role of thermal fields in resonant cavity QED can be studied in detail using superconducting circuits., Comment: ArXiv version of manuscript to be published in the Physica Scripta topical issue on the Nobel Symposium 141: Qubits for Future Quantum Computers(2009), 13 pages, 6 figures, hi-res version at http://qudev.ethz.ch/content/science/PubsPapers.html

The quantum state of a superconducting qubit nonresonantly coupled to a transmission line resonator can be determined by measuring the quadrature amplitudes of an electromagnetic field transmitted through the resonator. We present experiments in which we analyze in detail the dynamics of the transmitted field as a function of the measurement frequency for both weak continuous and pulsed measurements. We find excellent agreement between our data and calculations based on a set of Bloch-type differential equations for the cavity field derived from the dispersive Jaynes-Cummings Hamiltonian including dissipation. We show that the measured system response can be used to construct a measurement operator from which the qubit population can be inferred accurately. Such a measurement operator can be used in tomographic methods to reconstruct single and multiqubit states in ensemble-averaged measurements., Comment: Revised version: corrected typos, 8 pages, 6 figures, version with high resolution figures available at http://qudev.ethz.ch/content/science/PubsPapers.html

The already very active field of cavity quantum electrodynamics (QED), traditionally studied in atomic systems, has recently gained additional momentum by the advent of experiments with semiconducting and superconducting systems. In these solid state implementations, novel quantum optics experiments are enabled by the possibility to engineer many of the characteristic parameters at will. In cavity QED, the observation of the vacuum Rabi mode splitting is a hallmark experiment aimed at probing the nature of matter-light interaction on the level of a single quantum. However, this effect can, at least in principle, be explained classically as the normal mode splitting of two coupled linear oscillators. It has been suggested that an observation of the scaling of the resonant atom-photon coupling strength in the Jaynes-Cummings energy ladder with the square root of photon number n is sufficient to prove that the system is quantum mechanical in nature. Here we report a direct spectroscopic observation of this characteristic quantum nonlinearity. Measuring the photonic degree of freedom of the coupled system, our measurements provide unambiguous, long sought for spectroscopic evidence for the quantum nature of the resonant atom-field interaction in cavity QED. We explore atom-photon superposition states involving up to two photons, using a spectroscopic pump and probe technique. The experiments have been performed in a circuit QED setup, in which ultra strong coupling is realized by the large dipole coupling strength and the long coherence time of a superconducting qubit embedded in a high quality on-chip microwave cavity., Comment: ArXiv version of manuscript published in Nature in July 2008, 5 pages, 5 figures, hi-res version at http://www.finkjohannes.com/SqrtNArxivPreprint.pdf

This document contains four papers on aeronautics education, research, and partnerships that partly supported through the Aeronautics Education, Research, and Industry Alliance (AERIAL). The paper "2002 AERIAL Monograph" (Brent D. Bowen, Jocelyn S. Nickerson, Mary M. Fink, et al.) presents an overview of research and development in the following areas that is being conducted by the National Aeronautics and Space Administration (NASA) Nebraska Space Grant Consortium: spaceports; aviation safety; the Nebraska Native American Outreach Program; and geospatial research. "Airborne Remote Sensing (ARS) for Agricultural Research and Commercialization Applications (White Paper)" (Ram Narayanan, Brent D. Bowen, Jocelyn S. Nickerson) discusses the integration of aerospace technology enterprise applications at the Nebraska Remote Sensing Facility with other NASA enterprises as a model of cross-enterprise transfer of science with specific commercial applications. "Validated Numerical Models for the Convective Extinction of Fuel Droplets (CEFD)" (George Gogos, Brent D. Bowen, Jocelyn S. Nickerson) reports on a transient numerical model that was developed to study the combustion of suspended and moving fuel droplets. "The Small Aircraft Transportation System (SATS): Research Collaborations with the NASA Langley Research Center" (Scott E. Tarry, Brent D. Bowen, Jocelyn S. Nickerson) describes efforts to develop innovative solutions to various air transportation problems. Two papers contain substantial bibliographies. (MN)