Light-Matter interface detection of the full correlations distribution of quantum many-body systems

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The last fifty years have witnessed tremendous advances in science and technology with a huge impact on society and economy leading to a new information revolution in analogy with the industrial one. Although electronic devices have reached an incredible level of complexity, control and miniaturisation, information processing relies on the same classical principles enunciated by mathematicians in the 1930s (Turing, Church, von Neumann). In the 1980s, visionary ideas from theoretical physicists, including R. P. Feynman and D. Deutsch, and later from computer scientists such as P. Shor, combining concepts from quantum mechanics led to another revolution of information technology: the birth of quantum information theory. In the classical world, a bit, the smallest unit of information, can assume values 0 or 1 corresponding roughly to an electrical circuit being open or closed. In the quantum world, instead, one deals with quantum bits or qubits, embodied for example by an electron spin or a photon polarisation. These qubits can assume the two values 0 and 1 as in the classical case but they can also be prepared in a superposition of the two values simultaneously. This, apparently shocking, property has been verified in numerous experiments and is responsible for the amazing speed-up of certain tasks like integer numbers factorisation with quantum computers, i.e. devices that process qubits in analogy with traditional computers.So far quantum computers have only been realised with a small number of qubits-no more than ten-with trapped ions or neutral atoms, photons but also solid state devices. Large scale quantum computers are therefore expected to be realised only in a few decades.However special purposes quantum computers, called quantum simulators are currently being produced in laboratories working with atoms at temperatures one billionth above the absolute zero (ultracold). Such experiments aim at reproducing, with a controlled environment, the physics of hard to access quantum materials, for example a high-temperature superconductor, thus allowing scientists to probe its properties and test models and theories.A big open question for quantum simulators with ultracold atoms is how, once the sample is prepared in a quantum state, to detect its features. Several techniques are being used based on imaging through a high resolution optical microscope or on scattering of laser light off the sample. In this project we propose the use of a beam of polarised light to probe arrays of neutral atoms. As a consequence of the light-atoms interaction, the light polarisation rotates depending on the state of the atoms. Therefore the outgoing pulse of light, that can be measured, gives information about the state of the atoms.The advantage of this scheme is that one can perform the measurement without destroying the atomic samples as in other proposals. The outcomes of this project will shed light on the intimate structure of the quantum state of many qubits embodied by atoms trapped by electromagnetic fields. For this reason, it is expected to have a strong impact not only in quantum information theory, but also in atomic physics, in statistical mechanics and in the condensed matter physics. Qubits have another peculiarity compared to their classical counterpart: one can correlate the state of one qubit with that of another one in such a way that if one performs a measurement of the two qubits the outcomes always coincide. This phenomenon called entanglement is at the basis of quantum information applications like quantum teleportation. Another goal of this project is a proposal to entangle two of these ultracold atomic samples thus creating entanglement between two separated massive objects composed of hundreds of atoms. The scheme we propose can be implemented in the next generation of experiments with ultracold atoms.