Final Report Summary - AAPLQIC (Light-phonon quantum interface with atomic arrays in a cavity) Light-phonon quantum interface with atomic arrays in a cavity.The impressive progress in the control of the interaction between light and matter over the latest two decades has paved the way to quantum technologies, such as information processing and metrology based on quantum mechanical features, which have no analog in classical physics. This progress was mainly pushed by the advances in optical cooling and trapping, which nowadays allow to prepare ensembles of atoms close to the absolute zero temperature. This progress opens novel perspectives of control over of the atomic motion at the quantum mechanical level and to realize novel regimes of strongly correlated phases of matter. One peculiar example is provided by cold atoms strongly coupled with the field of an optical cavity: Here, multiple scattering of cavity photons mediates long-range interactions between the atoms and give rise to hybrid excitations, strongly mixing atomic motion and photons. This optomechanical system exhibits interesting perspectives for quantum metrological applications and is being experimentally investigated in several laboratories worldwide.The goal of the present project was to construct a theoretical framework for an experimental platform, constituted by atoms trapped by an optical lattice inside a high-finesse optical cavity. The atoms form a periodic array, and the vibrations about the lattice strongly mix with the photonic excitations of the cavity field. In this project we have theoretically explored the perspectives of manipulating the atoms collective motion by means of the photons the atoms scatter. The first objective was to setup a model, which allowed us to analyse the open-system dynamics of the atomic array when coupled with the electric field of a resonator. The basic features were determined, which allowed us to identify dynamics where the collective atomic motion is driven into a nonclassical state. Differing from typical protocols employed for quantum information, the nonclassical features of the state which is prepared results at the asymptotics of noisy dynamics and is reached through the interplay between the coherent pump, which inject photons into the cavity, and the noise processes, which lead to photon losses. This property makes it robust against parameter fluctuations and experimental uncertainties, which is crucial for quantum technological applications. We first developed a protocol for bringing the collective modes of the array to the vibrational ground state. This analysis was accompanied by the identification of the fundamental limits in the protocol efficiency, such as the maximum fidelity and the shortest time scales achievable [1]. We then extended this protocol for preparing states, that are relevant for quantum metrology and sensors, such as squeezed states of the collective motion. We checked its feasibility for current experimental setups, and found that it can efficiently drive ensembles of thousands of atoms into squeezed states of the collective motion [2].We then focused on developing experimental methods of verification of the squeezing achieved. This task demanded a thorough study of the photon scattering processes, which support the formation of the squeezed state, and of the signatures they leave in the field emitted by the resonator. Drawing on this analysis we designed what we called the “quantum read-out protocol”. This protocol ideally realizes the prefect transfer of the squeezing of the atomic motion into the squeezing of the field emitted by the cavity: Thanks to the well developed technology in measuring the squeezing of light, the scheme allows one to determine the degree of squeezing of the atomic motion with high precision [2]. We further analysed the nature of quantum correlations which are established by the light-mediated interactions, and found that squeezing of the atoms collective motion is accompanied by quantum entanglement between the individual atoms. These quantum correlations can be measured using the concept of cluster states, which was successfully employed to reveal the topology of entanglement. For this purpose, we started a collaboration with an experimental group at the University of Pierre and Marie Curie in Paris, where a new source of quantum light is being implemented: the quantum frequency comb. The light it generates consist of entangled photons, and theoretically the system shares several analogies with a system of many phonons such as the quantas of the motion of the trapped atom, therefore this analysis was instrumental for developing viable methods for detecting quantum correlations between the atoms of the array. This collaboration resulted into a sophisticate proposal of an atomic memory for the quantum frequency comb, which was recently published in [3] and was highlighted as Editor’s Suggestion by Physical Review. This result thus provides a new tool which can be adapted for the analysis of quantum correlations between the atoms in the cavity QED setup. The physical system we analysed is rich and constitutes a promising platform for quantum technological applications. Our work sets the basis for further studies and directions of research. Among them, we mention here exotic realizations of quantum simulators of magnetism in an interface where phonons, photons, and spins are strongly coupled. This can be realised when the mechanical forces of the cavity light depend on the internal state of the scattering atoms. It is presently a research line the fellow intends to pursue in the future. The knowledge here acquired contributes to deepening our understanding the fundamental properties of the mechanical effects of light on atoms at low temperatures and of the resources that can be employed for quantum technological applications.The project was realised at the University of Saarland in the Theorerical Quantum Physics group lead by Prof. G. Morigi (web: http://qphys.uni-saarland.de/).Contact details: Oxana MishinaE-mail: omishina@gmail.comWeb:www.researchgate.net/profile/O_Mishina/infoReferences[1] O. Mishina, New Journal of Physics 16 033021, (2014). [2] O. Mishina and G. Morigi, manuscript in preparation (2015).[3] Z. Zheng, O. Mishina, N. Treps, and C. Fabre, Phys. Rev. A (Rapid communication) 91, 031802 (2015).
