We propose to realize a novel quantum simulator made of magnetic atoms in periodic potentials, which will enable the investigation of quantum-many body problems associated with long-range dipole-dipole interactions. Our proposal is based on a series of key new developments. We will develop new tools to increase the strength of dipole-dipole interactions (shorter-period UV lattices, magneto-association of magnetic atoms into molecules with a stronger magnetic moment), and to control and measure their interaction at the nano-scale (using super-resolution techniques and narrow spectroscopic lines). We will develop new probes to certify the presence of quantum correlations, which are expected to be particularly strong in these many-body long-range interacting systems. We will either probe correlations in real space (microscope, double-well lattices), in momentum space (Doppler spectroscopy), or in the spin sector. These probes will be developed in a joint theory-experiment endeavor, to find the best ways to define and quantify entanglement. The breakthrough realization of quantum simulators based on lattice-trapped magnetic atoms will allow us to explore for the first time two families of problems. First, we will probe low energy quantum phases stabilized by dipolar interactions; and second, out-of-equilibrium dynamics and quantum thermalization dominated by long-range interactions. A number of exotic phases will be within experimental reach, such as the checkerboard or stripe phases, or peculiar phases of spin systems with long-range interactions. We will aim at protocols to certify the nature of the quantum correlations within these systems. Such correlations can be explored in four different complementary setups: 1) an Er lattice gas within a Dy bath (Innsbruck); strongly dipolar lattice gases made of either 2) Dy atoms in UV lattices (Stuttgart) or 3) Dy2 molecules in standard lattices (Pisa/Florence), and 4) Cr atoms realizing lattice spin models (Paris). This project fits the Quantum Simulation part of the call. Magnetic atoms are the only currently available long-range interacting system which is collisionally stable and which possesses a scalable (>>100) number of particles. However, up to now dipolar interactions remain too weak for a number of applications. We propose technical improvements which will drive these systems into the relevant regime where novel quantum phases and out-of-equilibrium phenomena are expected to emerge. If our goals are fulfilled, lattice gases made of magnetic atoms will become a new competitive platform for quantum simulation, having access to a number of fundamental phenomena, many of them unexplored so far (magnetism of localized or itinerant long-range interacting spin; charge ordering in extended Hubbard models; localization of disordered long-range interacting systems). Our consortium aims at developing new tools to diagnose the non-classical nature of the quantum many-body states produced in the experiment (entanglement, Bell correlations). If successful, our project will have a lasting impact on the field of quantum simulation in general, in connection with central topics in quantum condensed matter and quantum information science.

The QScale project focuses on the development of advanced quantum communication technologies, specifically of quantum repeater architectures, which represent a major and timely challenge for the field of quantum information science and technology. Quantum repeaters are indeed needed in order to overcome losses and errors in the transmission of quantum data. It allows the distribution of entanglement at arbitrary large distances, which is a universal resource for quantum information applications, including quantum cryptography and quantum teleportation. QScale holds the promise for bringing major advances in this field of research. To reach these objectives, the consortium is composed of five academic and one industrial partners. Each team has a leading experience in quantum optics, atomic physics and quantum information processing. The consortium is spanning a variety of physical systems and encoding techniques: cold and ultracold atoms (Laboratoire Kastler Brossel in Paris and Istituto Nazionale di Ottica in Firenze), solid-­‐state (Institute of Photonic Sciences in Barcelona), trapped ions (Universitat des Saarlandes in Saarbrucken), continuous-­‐ variables and discrete variables. It also has a strong theoretical component with the group of Applied Physics in Geneva, who was a leading force in the last years to clearly identify physical requirements for scalable repeaters and proposed innovative solutions. The first part of the project is devoted to photonic components, i.e. the development of photonic sources compatible with quantum memories, and of continuous-­‐variable quantum light pulses, including non-­‐ Gaussian fields for hybrid quantum repeater architectures. In the second part, efficient coupling between light and material systems will be implemented. It will allow the reversible mapping of quantum photonic information into and out of the memory device or the synchronized emission of single-­‐photons from remote systems. The third part of the project will integrate these outcomes. It will address effective storage of entanglement in the devices developed previously, assessing their ability to operate as nodes of quantum repeaters. It will also pave the way towards deterministic entanglement swapping. The various photonic carriers and material memory systems investigated above will be compared. Finally, procedures and architectures for quantum repeater systems based on the previous elements will be examined and investigated, including novel hybrid schemes and new deterministic operations. Their implementation with the devices developed in the project will be assessed. A great variety of results have already been demonstrated during the first 18 months of the project and 20 papers have been published in international journals. Here are some of these achievements: ICFO developed a solid-­state quantum memory based on a Praseodymium doped Y2SiO5 crystal. For the first time, the team demonstrated the quantum storage of polarization photonic qubits in such a system. In this experiment, the storage was performed in the excited state of the ions, leading to short and pre-­determined storage times. In order to achieve on demand read-out and longer storage times, the optical excitations need to be transferred to a long-lived ground state level, such that the photons are converted to collective spin excitations as a spin wave. ICFO took also this step recently and demonstrated the most efficient full atomic frequency comb scheme to date. LKB demonstrated for the first time the storage and readout of twisted photons in the single-­ photon regime, with a large ensemble of cold atoms. The demonstrated capability opens the possibility to the storage of qubits encoded as superpositions of orbital angular momentum states and to multi-­dimensional light-­matter interfacing. LKB demonstrated a very high-­fidelity source of single-photons based on an optical parametric oscillator. The reported fidelity is the highest to date. In collaboration with GAP, they also demonstrated a novel operational and trustworthy witness suited for single-photon entanglement, a central resource of quantum repeater architectures. This tool constitutes the groundwork for insuring that future networks will perform well. INO developed an adaptive method to realize the mode-selective detection of quantum light states. They put this approach to a first stringent experimental test by analyzing the spectrotemporal mode of ultrashort single photons with a novel combination of techniques from the fields of ultrafast coherent control and quantum optics. Besides demonstrating the capability to detect and characterize states in unknown and arbitrarily shaped modes, they also showed that this scheme can be an important tool for novel quantum information protocols based on the encoding of qubits and qudits onto the spatiotemporal degrees of freedom of light. UdS used a single trapped ion as a resonant, polarization-sensitive absorber to detect and characterize the entanglement of tunable narrowband photon pairs. Single-photon absorption is marked by a quantum jump in the ion and heralded by coincident detection of the partner photon. In a second time, they also established heralded interaction between two remotely trapped single ions through the exchange of single photons. In the sender ion, they released single photons with controlled temporal shape and transmit them to the distant receiver ion, 1 meter apart. These works constitute very significant steps towards the use of ions trapped in remote strings for quantum communication schemes.

Summary The "Atomic Quantum Clock" is a milestone of the European Quantum Technologies Timeline. Q-Clocks seeks to establish a new frontier in the quantum measurement of time by joining state-of-the-art optical lattice clocks and the quantized electromagnetic field provided by an optical cavity. The goal of the project is to apply advanced quantum techniques to state-of-the-art optical lattice clocks, demonstrating enhanced sensitivity while preserving long coherence times and the highest accuracy. A three-fold atom-cavity system approach will be employed: the dispersive quantum non-demolition (QND) system in the weak coupling regime, the QND system in the strong collective coupling regime, and the quantum enhancement of narrow-linewidth laser light generation towards a continuous active optical frequency standard. Cross-fertilization of such approaches will be granted by parallel theoretical investigations on the available and brand-new quantum protocols, providing cavity-assisted readout phase amplification, adaptive entanglement and squeezed state preparation protocols. Novel ideas on quantum state engineering of the clock states inside the optical lattice will be exploited to test possible quantum information and communication applications. By pushing the performance of optical atomic clocks toward the Heisenberg limit, Q-Clocks is expected to substantially enhance all utilizations of high precision atomic clocks, including tests of fundamental physics (test of the theory of relativity, physics beyond the standard model, variation of fundamental constants, search for dark matter) and applied physics (relativistic geophysics, chrono geodetic leveling, precision geodesy and time tagging in coherent high speed optical communication). Finally, active optical atomic clocks would have a potential to join large scale laser interferometers in gravitational waves detection. Relevance Q-Clocks will provide a major advance in the area of "Quantum metrology sensing and imaging", in particular by “the use of quantum properties”, such as multi-particle entanglement, quantum state engineering and quantum non-demolition measurement, “to enhance the precision and sensitivity of time and frequency standards”. In atomic clocks, like all atom sensors, the information is encoded in the quantum wave function of atoms: the quantum protocols developed and experimented in this project aim at “developing detection schemes that are optimised with respect to extracting relevant information from physical systems” in order to reduce the inherent quantum noise associated with this extraction. With Q-clocks we pursue an important technological development that will extend sensing to new targets and applications, including Earth mass flow (better weather forecast), underground composition (mineral survey), surveying the Earth’s interior (models for earthquakes), chrono geodetic leveling (better models of the geoid) and time tagging in coherent high speed optical communication, with important spin-offs such as generation of ultra-stable microwave sources with numerous applications in advanced electronics.

Recent progress in various areas of physics has demonstrated our ability to control quantum effects in customized systems and materials, thus paving the way for a promising future for quantum technologies. The emergence of such quantum devices, however, requires one to understand fundamental problems in non-equilibrium statistical physics, which can pave the way towards full control of quantum systems, thus reinforcing new applications and providing innovative perspectives. This project is dedicated to the study and the control of out-of-equilibrium properties of quantum many-body systems which are driven across phase transitions. Among several approaches, it will mainly focus on slow quenches and draw on the understanding delivered by the Kibble-Zurek (KZ) mechanism. This rather simple paradigm connects equilibrium with out-of-equilibrium properties and constitutes a benchmark for scaling hypothesis. It could pave the way towards tackling relevant open questions, which lie at the heart of our understanding of out-of-equilibrium dynamics and are key issues for operating in a robust way any quantum simulator. Starting from this motivation, we will test the limits of validity of the KZ dynamics by analyzing its predictions, thus clarifying its predictive power, and extend this paradigm to quantum critical systems with long-range interactions and to topological phase transitions. We will combine innovative theoretical ideas of condensed-matter physics, quantum optics, statistical physics and quantum information, with advanced experiments with ultracold atomic quantum gases. Quantum gases are a unique platform for providing model systems with the level of flexibility and control necessary for our ambitious goal. Their cleanness and their robustness to decoherence will greatly enhance the efficient interplay between theory and experiments, and provide a platform of studies whose outcomes are expected to have a strong scientific impact over a wide range of disciplines. On the short time scale we will exploit this knowledge to develop viable protocols for quantum simulators. In general, we expect that the results of this project will lay the ground for the development of the next generation of quantum devices and simulators.n of the proposed research, which would lay the ground for future device/simulator development in the mid-term. Our proposed work lies deeply within the “Quantum Technologies” theme. More specifically, by providing a deeper understanding and direct control of out-of-equilibrium phenomena in quantum many-body systems, we will make impactful contributions to the areas of “Quantum simulation” and “Quantum metrology, sensing and imaging”. Firstly, we will make significant advances to the initialization of a quantum system in a well-controlled initial state (ground state, without defects) and optimize the adiabatic control of its time evolution to an “interesting” target state, both of which are crucial features for adiabatic quantum computing. It is expected that the initial state and target state could be separated by a phase transition, which brings to the fore the question of the time evolution of a quantum system near a critical point. The response of a system when driven across critical points is further relevant for developing atomtronic devices and quantum sensors at the limit, that may find applications to the detection of extremely weak signals. This could include applications in diverse fields such as the detection of dark matter. Our consortium is composed of world-leading scientists with pioneering contributions in non-equilibrium dynamics of ultracold atomic systems and possesses a unique combination of the relevant expertise and tools for the successful completion of the proposed research. We expect that the results of this project will lay the ground for the development of the next generation of quantum devices and simulators.