Quantum droplets are small clusters of atoms self-bound by the balance of attractive and repulsive forces. Here we report on the observation of a novel type of droplets, solely stabilized by contact interactions in a mixture of two Bose-Einstein condensates. We demonstrate that they are several orders of magnitude more dilute than liquid helium by directly measuring their size and density via in situ imaging. Moreover, by comparison to a single-component condensate, we show that quantum many-body effects stabilize them against collapse. We observe that droplets require a minimum atom number to be stable. Below, quantum pressure drives a liquid-to-gas transition that we map out as a function of interaction strength. These ultra-dilute isotropic liquids remain weakly interacting and constitute an ideal platform to benchmark quantum many-body theories.Quantum fluids can be liquids -of fixed volume -or gases, depending on the attractive or repulsive character of the inter-particle interactions and their interplay with quantum pressure. Liquid helium is the prime example of quantum fluid. For small particle numbers it forms self-bound liquid droplets: nanometer-sized, dense and strongly interacting clusters of helium atoms. Understanding their properties, which directly reflect their quantum nature, is challenging and requires a good knowledge of the short-range details of the interatomic potential [1,2]. Very different quantum droplets, more than 2 orders of magnitude larger and 8 orders of magnitude more dilute, have recently been proposed in ultracold atomic gases [3]. Interestingly, these ultra-dilute systems enable a much simpler microscopic description, while remaining in the weakly interacting regime. They are thus amenable to well controlled theoretical studies.The formation of quantum droplets requires a balance between attractive forces, which hold them together, and repulsive ones that stabilize them against collapse. In helium droplets, the repulsion is dominated by the electronic Pauli exclusion principle, which arises from quantum statistics. In contrast, in ultracold atomic droplets the repulsion stems from quantum fluctuations, which are a genuine quantum many-body effect. These can be revealed in systems with competing interactions, where mean-field forces of different origins almost completely cancel out and result in a small residual attraction. There, beyond mean-field effects remain sizeable even in the weakly interacting regime. To first order they lead to the Lee-Huang-Yang repulsive energy [4], comparable in strength to the residual mean-field attraction. Recently, ultracold atomic droplets have been realized in magnetic quantum gases with competing attractive dipolar and repulsive contact interactions [5][6][7][8][9][10]. In this case, the anisotropic character of the magnetic dipole-dipole force leads to the formation of filament-like self-bound droplets with highly anisotropic properties [9,11,12]. Given the generality of the stabilization mechanism, droplets should in fact also exist in si...

Attractive Bose-Einstein condensates can host two types of macroscopic self-bound states: bright solitons and quantum droplets. Here, we investigate the connection between them with a Bose-Bose mixture confined in an optical waveguide. We show theoretically that, depending on atom number and interaction strength, solitons and droplets can be smoothly connected or remain distinct states coexisting only in a bistable region. We measure their spin composition, extract their density for a broad range of parameters, and map out the boundary of the region separating solitons from droplets.

We present a detailed study of the scattering properties of ultracold mixtures of bosonic potassium atoms. We locate 20 previously unobserved Feshbach resonances in isotopic 39 K-41 K mixtures. These are assigned to s-wave molecular channels by comparison to an asymptotic bound state model and coupled channels calculations. Additional Feshbach resonances are studied in spin mixtures of a single potassium isotope, both in 39 K and 41 K. In particular, we characterize the parameters of a selected 39 K Feshbach resonance by radio-frequency association of Feshbach molecules. Our results could be exploited to refine the model potentials for potassium scattering. Furthermore, these new Feshbach resonances enlarge the range of experiments possible with degenerate Bose-Bose mixtures.

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