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Understanding the effect of interactions in the phase evolution of expanding atomic Bose Einstein condensates is fundamental to describe the basic phenomenon of matter wave interference. Many theoretical and experimental works tackled this problem, always with the implicit assumption that the mutual interaction between two expanding condensates rigidly modifies the phase evolution through an effective force. In this paper, we present a combined experimental and theoretical investigation of the interference profile of expanding $^{87}$Rb condensates, with a specific focus on the effect of interactions. We come to the different conclusion that the mutual interaction produces local modifications of the condensate phase only in the region where the wavepackets overlap., Comment: 10 pages, 14 figures; published version

Ultrasound-vaporizable microdroplets can be exploited for targeted drug delivery. However, it requires customized microfluidic techniques able to produce monodisperse, capillary-sized and biocompatible multiple emulsions. Recent development of microfluidic devices led to the optimization of microdroplet production with high yields, low polydispersity and well-defined diameters. So far, only few were shown to be efficient for simple droplets or multiple emulsions production below 5 microns in diameter, which is required to prevent microembolism after intravenous injection. Here, we present a versatile microchip for both simple and multiple emulsion production. This parallelized system based on microchannel emulsification was designed to produce perfluorocarbon in water or water within perfluorocarbon in water emulsions with capillary sizes (<5 $\mu$m) and polydispersity index down to 5 % for in vivo applications such as spatiotemporally-triggered drug delivery using Ultrasound. We show that droplet production at this scale is mainly controlled by interfacial tension forces, how capillary and viscosity ratios influence droplet characteristics and how different production regimes may take place. The better understanding of droplet formation and its relation to applied pressures is supported by observations with a high-speed camera. Compared to previous microchips, this device opens perspectives to produce injectable and biocompatible droplets with a reasonable yield in order to realize preclinical studies in mice.

We consider a homogeneous heteronuclear Bose mixture with contact interactions at the mean-field collapse, i.e. with interspecies attraction equal to the mean geometrical intraspecies repulsion. We show that the Lee-Huang-Yang (LHY) energy functional is accurately approximated by an expression that has the same functional form as in the homonuclear case. The approximated energy functional is characterized by two exponents, which can be treated as fitting parameters. We demonstrate that the values of these parameters which preserve the invariance under permutation of the two atomic species are exactly those of the homonuclear case. Deviations from the exact expression of LHY energy functional are discussed quantitatively and a specific application is described., Comment: 7 pages, 3 figures

We report on the formation of heteronuclear quantum droplets in an attractive bosonic mixture of 41K and 87Rb. We observe long-lived self-bound states, both in free space and in an optical waveguide. In the latter case, the dynamics under the effect of a species-dependent force confirms their bound nature. By tuning the interactions from the weakly to the strongly attractive regime, we study the transition from expanding to localized states, in both geometries. We compare the experimental results with beyond mean-field theory and we find a good agreement in the full range of explored interactions. Our findings open up the production of long-lived droplets with important implications for further research., Comment: 9 pages, 7 figures

We investigate the superfluid-insulator transition of one-dimensional interacting Bosons in both deep and shallow periodic potentials. We compare a theoretical analysis based on Monte-Carlo simulations in continuum space and Luttinger liquid approach with experiments on ultracold atoms with tunable interactions and optical lattice depth. Experiments and theory are in excellent agreement. It provides a quantitative determination of the critical parameter for the Mott transition and defines the regime of validity of widely used approximate models, namely the Bose-Hubbard and sine-Gordon models, Comment: Technical problem in references fixed. Text and figures identical to version 1

Disorder, noise and interaction play a crucial role in the transport properties of real systems, but they are typically hard to control and study both theoretically and experimentally, especially in the quantum case. Here we explore a paradigmatic problem, the diffusion of a wavepacket, by employing ultra-cold atoms in a disordered lattice with controlled noise and tunable interaction. The presence of disorder leads to Anderson localization, while both interaction and noise tend to suppress localization and restore transport, although with completely different mechanisms. When only noise or interaction are present we observe a diffusion dynamics that can be explained by existing microscopic models. When noise and interaction are combined, we observe instead a complex anomalous diffusion. By combining experimental measurements with numerical simulations, we show that such anomalous behavior can be modeled with a generalized diffusion equation, in which the noise- and interaction-induced diffusions enter in an additive manner. Our study reveals also a more complex interplay between the two diffusion mechanisms in regimes of strong interaction or narrowband noise., Comment: 11 pages, 10 figures

Clarifying the interplay of interactions and disorder is fundamental to the understanding of many quantum systems, including superfluid helium in porous media, granular and thin-film superconductors, and light propagating in disordered media. One central aspect for bosonic systems is the competition between disorder, which tends to localize particles, and weak repulsive interactions, which instead have a delocalizing effect. Since the required degree of independent control of the disorder and of the interactions is not easily achievable in most available physical systems, a systematic experimental investigation of this competition has so far not been possible. Here we employ an ultracold atomic Bose-Einstein condensate with tunable repulsive interactions in a quasi-periodic lattice potential to study this interplay in detail. We characterize the entire delocalization crossover through the study of the average local shape of the wavefunction, the spatial correlations, and the phase coherence. Three different regimes are identified and compared with theoretical expectations: an exponentially localized Anderson glass, the formation of locally coherent fragments, as well as a coherent, extended state. Our results illuminate the role of weak repulsive interactions on disordered bosonic systems and show that the system and the techniques we employ are promising for further investigations of disordered systems with interactions, also in the strongly correlated regime., Comment: 8 pages, 10 figures

In 1970 V. Efimov predicted a puzzling quantum-mechanical effect that is still of great interest today. He found that three particles subjected to a resonant pairwise interaction can join into an infinite number of loosely bound states even though each particle pair cannot bind. Interestingly, the properties of these aggregates, such as the peculiar geometric scaling of their energy spectrum, are universal, i.e. independent of the microscopic details of their components. Despite an extensive search in many different physical systems, including atoms, molecules and nuclei, the characteristic spectrum of Efimov trimer states still eludes observation. Here we report on the discovery of two bound trimer states of potassium atoms very close to the Efimov scenario, which we reveal by studying three-particle collisions in an ultracold gas. Our observation provides the first evidence of an Efimov spectrum and allows a direct test of its scaling behaviour, shedding new light onto the physics of few-body systems., Comment: 10 pages, 3 figures, 1 table

We study the role played by the magnetic dipole interaction in an atomic interferometer based on an alkali Bose-Einstein condensate with tunable scattering length. We tune the s-wave interaction to zero using a magnetic Feshbach resonance and measure the decoherence of the interferometer induced by the weak residual interaction between the magnetic dipoles of the atoms. We prove that with a proper choice of the scattering length it is possible to compensate for the dipolar interaction and extend the coherence time of the interferometer. We put in evidence the anisotropic character of the dipolar interaction by working with two different experimental configurations for which the minima of decoherence are achieved for a positive and a negative value of the scattering length, respectively. Our results are supported by a theoretical model we develop. This model indicates that the magnetic dipole interaction should not represent a serious source of decoherence in atom interferometers based on Bose-Einstein condensates., Comment: 4 pages, 3 figures

One of the most intriguing phenomena in physics is the localization of waves in disordered media. This phenomenon was originally predicted by Anderson, fifty years ago, in the context of transport of electrons in crystals. Anderson localization is actually a much more general phenomenon, and it has been observed in a large variety of systems, including light waves. However, it has never been observed directly for matter waves. Ultracold atoms open a new scenario for the study of disorder-induced localization, due to high degree of control of most of the system parameters, including interaction. Here we employ for the first time a noninteracting Bose-Einstein condensate to study Anderson localization. The experiment is performed with a onedimensional quasi-periodic lattice, a system which features a crossover between extended and exponentially localized states as in the case of purely random disorder in higher dimensions. Localization is clearly demonstrated by investigating transport properties, spatial and momentum distributions. We characterize the crossover, finding that the critical disorder strength scales with the tunnelling energy of the atoms in the lattice. Since the interaction in the condensate can be controlled at will, this system might be employed to solve open questions on the interplay of disorder and interaction and to explore exotic quantum phases., Comment: 5 pages

We investigate magnetic Feshbach resonances in two different ultracold K-Rb mixtures. Information on the K(39)-Rb(87) isotopic pair is combined with novel and pre-existing observations of resonance patterns for K(40)-Rb(87). Interisotope resonance spectroscopy improves significantly our near-threshold model for scattering and bound-state calculations. Our analysis determines the number of bound states in singlet/triplet potentials and establishes precisely near threshold parameters for all K-Rb pairs of interest for experiments with both atoms and molecules. In addition, the model verifies the validity of the Born-Oppenheimer approximation at the present level of accuracy., Comment: 9 pages, 7 figures

We discover several magnetic Feshbach resonances in collisions of ultracold K(39) atoms, by studying atom losses and molecule formation. Accurate determination of the magnetic-field resonance locations allows us to optimize a quantum collision model for potassium isotopes. We employ the model to predict the magnetic-field dependence of scattering lengths and of near-threshold molecular levels. Our findings will be useful to plan future experiments on ultracold potassium atoms and molecules., Comment: 7 pages, 6 figures

We produce a Bose-Einstein condensate of 39-K atoms. Condensation of this species with naturally small and negative scattering length is achieved by a combination of sympathetic cooling with 87-Rb and direct evaporation, exploiting the magnetic tuning of both inter- and intra-species interactions at Feshbach resonances. We explore tunability of the self-interactions by studying the expansion and the stability of the condensate. We find that a 39-K condensate is interesting for future experiments requiring a weakly interacting Bose gas., Comment: 5 pages

We control the interspecies interaction in a two-species atomic quantum mixture by tuning the magnetic field at a Feshbach resonance. The mixture is composed by fermionic 40K and bosonic 87Rb. We observe effects of the large attractive and repulsive interaction energy across the resonance, such as collapse or a reduced spatial overlap of the mixture, and we accurately locate the resonance position and width. Understanding and controlling instabilities in this mixture opens the way to a variety of applications, including formation of heteronuclear molecular quantum gases., Comment: 5 Pages