Final Report Summary - MAG-QUPT (Exploring magnetic quantum phase transitions with ultra-cold Fermi gases) The goal of the project “Exploring magnetic quantum phase transitions with ultra-cold Fermi gases” (MAG-QUPT) was to develop a new experimental platform for the controlled study of quantum phase transitions using ultra-cold atomic gases, with the long-term objective of applying it to the study of magnetic quantum phase transitions in fermionic lattice systems. During the four year of the project, we have designed, constructed and validated a new experimental apparatus well adapted to these goals. It gives access to quantum degenerate mixtures of potassium, and is designed to work with the three isotopes (two bosons, 39K and 41K, and one fermion, 40K). Exploiting a combination of gray molasses sub-Doppler cooling and a hybrid magnetic/optical trap, it routinely produces large Bose-Einstein condensates of 41K that can be used to sympathetically cool the other two potassium isotopes. This approach has allowed us to observe for the first time dual Bose-Einstein condensation of 39K and 41K, and to demonstrate an alternative approach for cooling 39K to quantum degeneracy. The main scientific result of the project (which was actually not foreseen in the original proposal) has been the observation of a novel phase of matter: an ultra-dilute quantum liquid droplet in a mixture of two Bose-Einstein condensates of 39K [C. R. Cabrera et al., Science 359, 301-304 (2018)]. This is a self-bound cluster of ultra-cold atoms formed by the balance of attractive mean-field interactions - that hold the atoms together- and repulsive beyond-mean field effects - that stabilize it to a finite size. Its properties are liquid-like: it has surface tension, ripplon-like surface excitations and a very small compressibility. However, it is eight orders of magnitude more dilute than standard liquids, and does not fall under the standard van der Waals paradigm used to describe them. Ultra-cold atomic droplets were predicted theoretically by D. S. Petrov in 2015, one year after the start of this project. Similar physics was observed shortly afterwards in dipolar gases. Our group has been the first to observe quantum liquid droplets in a mixture of Bose-Einstein condensates, where the description of the system involves only isotropic contact interactions. Exploiting in situ phase-contrast imaging, we have directly measured their size and density, and shown that they are stabilized against collapse by quantum fluctuations. Furthermore, we have observed that droplets require a minimum atom number to be stable, below which quantum pressure drives a liquid-to-gas transition. We have mapped out this first order quantum phase transition as a function of atom number and interaction strength, and compared our results to a simple beyond-mean field theory. Interestingly, quantum droplets are a weakly interacting system but their behaviour is completely determined by quantum fluctuations and correlations. They thus constitute an ideal platform to benchmark quantum many-body theories.In a second series of experiments, we have studied the difference existing between these liquid droplets and more conventional bright solitons. In analogy to non-linear optics, the former can be seen as one-dimensional matter-wave solitons stabilized by dispersion, whereas the latter correspond to high-dimensional solitons stabilized by a higher order non-linearity due to quantum fluctuations. We have shown theoretically that a Bose-Bose mixture confined in an optical waveguide supports both solitons and droplets and that, depending on the system parameters, these can be smoothly connected or remain distinct states coexisting only in a bi-stable region. We have measured experimentally their spin composition, determined their density for a broad range of atom numbers and interaction strengths, and mapped out the boundary of the bi-stable region that separates bright solitons from quantum droplets [P. Cheiney et al., Phys. Rev. Lett. 120, 135301 (2018)].Additional experiments performed on the apparatus (and corresponding to preparatory work required by the droplet experiments) include an extensive study of the scattering properties of potassium Bose-Bose mixtures. We have located 27 new Feshbach resonances, including 39K-41K mixtures and spin mixtures of 39K and 41K. We are currently exploiting these results to further constrain the model potentials available for potassium scattering. Finally, we have also performed several theoretical studies within the project. These constitute preparatory work for future experiments that could be performed on the setup:• Magnetic polarons formed by an impurity immersed in a mixture of Bose-Einstein condensates [Y. Ashida et al., Phys. Rev. B 97, 060302(R) (2018)].• Measurement of the Chern number in ladder systems pierced by an artificial magnetic field [S. Mugel et al., SciPost Phys. 3, 012 (2017)].• Proximity effects in cold atom artificial graphene [T. Grass et al., 2D Mater. 4, 015039 (2017)]. • Simulation of the Unruh effect in fermionic lattice systems [J. Rodríguez-Laguna et al., Phys. Rev. A 95, 013627 (2017)].In conclusion, the main scientific results of the project have been: (i) the development of an experimental apparatus for the study of quantum many-body physics with mixtures of potassium gases; (ii) the first observation of quantum liquid droplets, stabilized by quantum fluctuations in a mixture of Bose-Einstein condensates; (iii) the study of the liquid-to-gas quantum phase transition, and of the soliton-to-droplet transition in an optical waveguide. These experiments had a significant scientific impact on the quantum gas community because quantum liquid droplets constitute a rare example of weakly interacting system that cannot be described simply in terms of a mean-field theory, their behavior being instead dominated by quantum fluctuations. Droplets are thus ideal to benchmark beyond mean-field theoretical approaches. The self-bound character of quantum droplets in three dimensions is also of interest in the field of non-linear optics, where the observation of high dimensional optical solitons – the so-called “light bullets”, which are analogous to quantum droplets - has remained elusive. Finally, the existence of such unconventional, ultra-dilute liquid that cannot be described within the van der Waals paradigm has attracted the interest of a broad audience, and of the media.Besides its scientific objectives, the project has also allowed me to integrate into the Spanish research community. My junior group leader position at ICFO was reinforced in January 2017 by a Ramón y Cajal fellowship (a tenure-track position within the Spanish research system). Furthermore, this project helped me to obtain additional Spanish and European funding for my research, and establish my own independent research group. During these four years, I have supervised at ICFO three postdoctoral researchers (one Marie Curie fellow), four PhD students (two Marie Curie COFUND fellows), three Master theses, four projects of visiting Master students and six undergraduate research projects. Thus, the project has not only allowed the development of a new experimental research activity on quantum many-body physics with ultracold quantum gases (the first Spanish Bose-Einstein condensate in Spain was observed by our group), but also the training of young Spanish researchers on this topic. Contact: leticia.tarruell@icfo.eu Website: www.qge.icfo.es
