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...

The competition of dipole-dipole and contact interactions leads to exciting new physics in dipolar gases, well-illustrated by the recent observation of quantum droplets and rotons in dipolar condensates. We show that the combination of the roton instability and quantum stabilization leads under proper conditions to a novel regime that presents supersolid properties, due to the coexistence of stripe modulation and phase coherence. In a combined experimental and theoretical analysis, we determine the parameter regime for the formation of coherent stripes, whose lifetime of a few tens of milliseconds is limited by the eventual destruction of the stripe pattern due to three-body losses. Our results open intriguing prospects for the development of long-lived dipolar supersolids. arXiv:1811.02613v2 [cond-mat.quant-gas]

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.

The existence of a paradoxical supersolid phase of matter, possessing the apparently incompatible properties of crystalline order and superfluidity, was predicted 50 years ago 1-3 . Solid helium was the natural candidate, but there supersolidity has not been observed yet, despite numerous attempts 4-7 . Ultracold quantum gases have recently shown the appearance of the periodic order typical of a crystal, due to various types of controllable interactions 8-12 . A crucial feature of a Ddimensional supersolid is the occurrence of up to D+1 gapless excitations reflecting the Goldstone modes associated with the spontaneous breaking of two continuous symmetries: the breaking of phase invariance, corresponding to the locking of the phase of the atomic wave functions at the origin of superfluid phenomena, and the breaking of translational invariance due to the lattice structure of the system. The occurrence of such modes has been the object of intense theoretical investigations 1,13-17 , but their experimental observation is still missing. Here we demonstrate the supersolid symmetry breaking through the appearance of two distinct compressional oscillation modes in a harmonically trapped dipolar Bose-Einstein condensate, reflecting the gapless Goldstone excitations of the homogeneous system. We observe that the two modes have different natures, with the higher frequency mode associated with an oscillation of the periodicity of the emergent lattice and the lower one characterizing the superfluid oscillations. Our work paves the way to explore the two quantum phase transitions between the superfluid, supersolid and solid-like configurations that can be accessed by tuning a single interaction parameter.