Final Report Summary - LATTRICS (Efimov trimers of ultracold cesium in optical lattices) General ideas and objectivesUltracold atoms with flexible and well-controllable properties are being widely used to investigate many fundamental questions, from few- to many-body physics. In particular, the tunability of interactions via Feshbach resonances allows one to increase the scattering length a up to values that exceed the short-range details of the inter-particle potential. Such a long-range behaviour is a fundamental tool to 'simulate' situations present in different field of physics. This 'universality' links processes that are far in energy or length scale and allows finding very general solutions to different problems.Efimov trimers are the paradigm of universal few-body physics. Despite the observation of Efimov states in different species and also in hetero-nuclear atomic systems, many open questions remain on the border of universality. In this project, we addressed in particular the following questions:(i) Does universality survive when different Feshbach resonances are involved?(ii) Does universality survive for more than three particles?(iii) What happens to Efimov states in reduced dimensionality?Extending the tenability of the cesium scattering length The first observation of Efimov states in ultracold atoms has been possible for the unique connection between recombination losses from an atomic sample and the features of Efimov energy spectrum. The first part of the project was dedicated to the characterisation of the collisional properties of cesium in the high magnetic field region, up to 1000 G. Several broad Feshbach resonances in this range of magnetic field facilitate a precise and more accurate tuning of the scattering length, an essential prerequisite for the study of Efimov resonances in the case of strongly confined atoms. The determination of the conversion between scattering length and magnetic field requires a detail analysis of molecular potential and of the energy spectrum of the two-particles states. However, this was not available in this range of magnetic field for cesium before the measurements performed during this project. These measurements were extensive and manifold. They have included:1) determination of Feshbach resonance positions (more than 20 new Feshbach resonances have been detected, including the first reported i-wave resonances); 2) spectroscopy of the molecular spectrum (including unexpected avoided crossings); 3) measurement of the molecular magnetic moment; 4) creation of Bose-Einstein condensates at high field and detection of their collapse at negative scattering length (for precise determination of the zeroes of the scattering length).The numerical analysis of the cesium potential has been possible thanks to the external collabouration with theoreticians (P. S. Julienne, Boulder, United States of America (USA) and J. M. Hutson, Durham, United Kingdom (UK)).Universality of Efimov states and few-body cluster statesIn recent years, a large theoretical effort has been dedicated to understanding which quantity fixes the first step of the infinite series of Efimov states. Our most important result has been the experimental demonstration that, for observables in atomic samples, the Efimov physics is not depending on the Feshbach resonance involved in the tuning of the scattering length. Our work has triggered a new series of theoretical papers that have tried to explain why, in cold atoms, Efimov feature are directly related to the strength of the van der Waals interaction. Amazingly, we also observed that the same universal tools used for investigating the three-body states can be extended to four and five-body clusters (work in collabouration with C. Greene and J. von Stecher, Boulder, USA).The deep knowledge of the molecular spectrum allowed also us to create weakly bound dimers and measure their collisions properties with atoms. Because of the underling connection between trimer energy and atom-dimer collisions, these measurements are fundamental in order to define the energy landscape of three particle systems. In this case, we observed that universal properties are not conserved, suggesting that corrections to the universal framework are necessary. This will be of great importance in order to predict the trimer binding energy at different value of the scattering length.Efimov states in low-dimensionalityLow-dimensional physics is a wide field that has attracted a lot of interest in last years, in particular for the connections with open questions in solid-state physics (superconductivity, quantum wire, etc.). A system can be considered two-dimensional (2D) when one of the spatial degree of freedom is frozen. This lead to new phenomena strictly related to the 'flatness' of the dynamics. During the last part of the project, we observed for the first time that triatomic Efimov resonances shift towards smaller absolute values of the scattering length when atoms are confined in pancake-like structures. The accurate tuning of the scattering length close to high magnetic field Feshbach resonance allowed also observing the absence of shift for the universal four-body loss feature. These interesting observations in pancake structures are an amazing starting point towards an even richer scenario when the atomic degrees of freedom will be frozen in all the three spatial direction. The large parameter space gives a wide playground for many future investigations. These measurements are still ongoing and will require a longer time. We expect many intriguing results far beyond the current project period.