Economic complexity of cities and its role for resilience.

The aim of the paper is to propose the construction of an index that captures the economic complexity of cities over the globe, as well as to explore whether it is a good predictor for a range of city-level economic outcomes. This index aspires to mitigate data scarcity for cities and to provide policy makers with the tools for monitoring the evolving role of cities in the global economy. Analytically, we implement the economic complexity methodology on data for the ownership, location and economic activities of the world's 3,000 largest firms and their subsidiaries to propose a new indicator that quantifies the network of the largest cities worldwide and the economic activities of their globalized firms. We first show that complex cities are the highly diversified cities that host non-ubiquitous economic activities of firms with global presence. Then, in a sample of EU cities, we show that complex cities tend to be more prosperous, have higher population, and are associated with more jobs, human capital, innovation, technology and transport infrastructure. Last, using OLS methodology and accounting for several other confounders, we show that a higher ECI, at the city level, enhances the resilience of cities to negative economic shocks, i.e., their ability to bounce back after a shock. Specifically, we find that the expected increase of the ratio of employment in 2012 over 2006 is 0.01 (mean: 0.992; standard deviation: 0.081) when the ECI increases by 1 unit (mean: 0.371; standard deviation: 1.094), i.e., a satisfactory pace of recovery, in terms of employment. The ability to diversify in the presence of a shock, the reallocation of factors of production to other sectors and the ability to extract rents associated with those diversified activities, uncovers the mechanics of the ECI index.

Hypersonic Bose-Einstein condensates in accelerator rings.

Some of the most sensitive and precise measurements-for example, of inertia1, gravity2 and rotation3-are based on matter-wave interferometry with free-falling atomic clouds. To achieve very high sensitivities, the interrogation time has to be very long, and consequently the experimental apparatus needs to be very tall (in some cases reaching ten or even one hundred metres) or the experiments must be performed in microgravity in space4-7. Cancelling gravitational acceleration (for example, in atomtronic circuits8,9 and matter-wave guides10) is expected to result in compact devices with extended interrogation times and therefore increased sensitivity. Here we demonstrate smooth and controllable matter-wave guides by transporting Bose-Einstein condensates (BECs) over macroscopic distances. We use a neutral-atom accelerator ring to bring BECs to very high speeds (16 times their sound velocity) and transport them in a magnetic matter-wave guide for 15 centimetres while fully preserving their internal coherence. The resulting high angular momentum of more than 40,000h per atom (where h is the reduced Planck constant) gives access to the higher Landau levels of quantum Hall states, and the hypersonic velocities achieved, combined with our ability to control potentials with picokelvin precision, will facilitate the study of superfluidity and give rise to tunnelling and a large range of transport regimes of ultracold atoms11-13. Coherent matter-wave guides are expected to enable interaction times of several seconds in highly compact devices and lead to portable guided-atom interferometers for applications such as inertial navigation and gravity mapping.

Quantum Logic with Cavity Photons From Single Atoms.

We demonstrate quantum logic using narrow linewidth photons that are produced with an a priori nonprobabilistic scheme from a single ^{87}Rb atom strongly coupled to a high-finesse cavity. We use a controlled-not gate integrated into a photonic chip to entangle these photons, and we observe nonclassical correlations between photon detection events separated by periods exceeding the travel time across the chip by 3 orders of magnitude. This enables quantum technology that will use the properties of both narrow-band single photon sources and integrated quantum photonics.

Quantum walks of correlated photon pairs in two-dimensional waveguide arrays.

We demonstrate quantum walks of correlated photons in a two-dimensional network of directly laser written waveguides coupled in a "swiss cross" arrangement. The correlated detection events show high-visibility quantum interference and unique composite behavior: strong correlation and independence of the quantum walkers, between and within the planes of the cross. Violations of a classically defined inequality, for photons injected in the same plane and in orthogonal planes, reveal nonclassical behavior in a nonplanar structure.

Two-photon quantum interference in integrated multi-mode interference devices.

Multi-mode interference (MMI) devices fabricated in silicon oxynitride (SiON) with a refractive index contrast of 2.4% provide a highly compact and stable platform for multi-photon non-classical interference. MMI devices can introduce which-path information for photons propagating in the multi-mode section which can result in degradation of this non-classical interference. We theoretically derive the visibility of quantum interference of two photons injected in a MMI device and predict near unity visibility for compact SiON devices. We complement the theoretical results by experimentally demonstrating visibilities of up to 97.7% in 2×2 MMI devices without the requirement of narrow-band photons.

Observing fermionic statistics with photons in arbitrary processes.

Quantum mechanics defines two classes of particles-bosons and fermions-whose exchange statistics fundamentally dictate quantum dynamics. Here we develop a scheme that uses entanglement to directly observe the correlated detection statistics of any number of fermions in any physical process. This approach relies on sending each of the entangled particles through identical copies of the process and by controlling a single phase parameter in the entangled state, the correlated detection statistics can be continuously tuned between bosonic and fermionic statistics. We implement this scheme via two entangled photons shared across the polarisation modes of a single photonic chip to directly mimic the fermion, boson and intermediate behaviour of two-particles undergoing a continuous time quantum walk. The ability to simulate fermions with photons is likely to have applications for verifying boson scattering and for observing particle correlations in analogue simulation using any physical platform that can prepare the entangled state prescribed here.

Quantum walks of correlated photons.

Quantum walks of correlated particles offer the possibility of studying large-scale quantum interference; simulating biological, chemical, and physical systems; and providing a route to universal quantum computation. We have demonstrated quantum walks of two identical photons in an array of 21 continuously evanescently coupled waveguides in a SiO(x)N(y) chip. We observed quantum correlations, violating a classical limit by 76 standard deviations, and found that the correlations depended critically on the input state of the quantum walk. These results present a powerful approach to achieving quantum walks with correlated particles to encode information in an exponentially larger state space.