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We report on the formation of multiple quantum droplets in a heteronuclear $^{41}$K-$^{87}$Rb mixture released in an optical waveguide. By a sudden change of the interspecies interaction from the non-interacting to the strongly attractive regime, we initially form a single droplet in an excited compression-elongation mode. The latter axially expands up to a critical length and then splits into two or more smaller fragments, recognizable as quantum droplets. We find that the number of formed droplets increases with decreasing interspecies attraction and increasing atom number. We show, by combining theory and experiment, that this behavior is consistent with capillary instability, which causes the breakup of the stretching droplet due to the surface tension. Our results open new possibilities to explore the properties of quantum liquids and systems of multiple quantum droplets in two-component bosonic mixtures.

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

We present a novel optical cooling scheme that relies on hyperfine dark states to enhance loading and cooling atoms inside deep optical dipole traps. We demonstrate a seven-fold increase in the number of atoms loaded in the conservative potential with strongly shifted excited states. In addition, we use the energy selective dark-state to efficiently cool the atoms trapped inside the conservative potential rapidly and without losses. Our findings open the door to optically assisted cooling of trapped atoms and molecules which lack the closed cycling transitions normally needed to achieve low temperatures and the high initial densities required for evaporative cooling., Comment: 5 pages, 5 figures + supplemental material 2 pages

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 derive an expression for the phase shift of an atom interferometer in a gravitational field taking into account both the finite duration of the light pulses and the effect of a small perturbing potential added to a stronger uniform gravitational field, extending the well-known results for rectangular pulses and at most quadratic potentials. These refinements are necessary for a correct analysis of present day high resolution interferometers., Comment: 12 pages, 3 figures

Self-bound quantum droplets are a newly discovered phase in the context of ultracold atoms. In this work we report their experimental realization following the original proposal by Petrov [Phys. Rev. Lett. 115, 155302 (2015)], using an attractive bosonic mixture. In this system spherical droplets form due to the balance of competing attractive and repulsive forces, provided by the mean-field energy close to the collapse threshold and the first-order correction due to quantum fluctuations. Thanks to an optical levitating potential with negligible residual confinement we observe self-bound droplets in free space and we characterize the conditions for their formation as well as their equilibrium properties. This work sets the stage for future studies on quantum droplets, from the measurement of their peculiar excitation spectrum, to the exploration of their superfluid nature.

Quantum dynamics of impurities in a bath of bosons is a long-standing problem of solid-state, plasma, and atomic physics. Recent experimental and theoretical investigations with ultracold atoms focused on this problem, studying atomic impurities immersed in a atomic Bose-Einstein condensate (BEC) and for various relative coupling strengths tuned by the Fano-Feshbach resonance technique. Here we report extensive numerical simulations on a closely related problem: the collision between a bosonic impurity made of few $^{41}$K atoms and a BEC made of $^{87}$Rb atoms in a quasi one-dimensional configuration and under a weak harmonic axial confinement. For small values of the interspecies interaction strength (no matter the sign of it), we find that the impurity, which starts from outside the BEC, simply oscillates back and forth the BEC cloud, but the frequency of oscillation depends on the interaction strength. For intermediate couplings, after a few cycles of oscillation the impurity is captured by the BEC and strongly changes its amplitude of oscillation. In the strong interaction regime, if the interspecies interaction is attractive, a local maximum (bright soliton) in the density of BEC occurs where the impurity is trapped; instead, if the interspecies interaction is repulsive, the impurity is not able to enter in the BEC cloud and the reflection coefficient is close to one. On the other hand, if the initial displacement of the impurity is increased, the impurity is able to penetrate in the cloud leading to the appearance of a moving hole (dark soliton) in the BEC., Comment: 10 pages, 4 figures and 6 short movies

Motivated by recent experiments and theoretical investigations on binary mixtures, we investigate the miscible-immiscible transition at finite temperature by means of Quantum Monte Carlo. Based on the observation that the segregated phase is strongly affected by temperature, we propose to use the degree of demixing for thermometry of a binary bosonic mixture trapped in an optical lattice. We show that the proposed method is especially sensitive at low temperatures, of the order of the tunnelling amplitude, and therefore is particularly suitable in the regime where quantum magnetism is expected., Comment: 10 pages, 6 figures, Supplemental Material

Using a species-selective dipole potential, we create initially localized impurities and investigate their interactions with a majority species of bosonic atoms in a one-dimensional configuration during expansion. We find an interaction-dependent amplitude reduction of the oscillation of the impurities' size with no measurable frequency shift, and study it as a function of the interaction strength. We discuss possible theoretical interpretations of the data. We compare, in particular, with a polaronic mass shift model derived following Feynman variational approach., Comment: 7 pages, 6 figures

We experimentally investigate the mix-dimensional scattering occurring when the collisional partners live in different dimensions. We employ a binary mixture of ultracold atoms and exploit a species-selective 1D optical lattice to confine only one atomic species in 2D. By applying an external magnetic field in proximity of a Feshbach resonance, we adjust the free-space scattering length to observe a series of resonances in mixed dimensions. By monitoring 3-body inelastic losses, we measure the magnetic field values corresponding to the mix-dimensional scattering resonances and find a good agreement with the theoretical predictions based on simple energy considerations., Comment: 5 pages, 4 figures, to be published in PRL

We investigate experimentally the entropy transfer between two distinguishable atomic quantum gases at ultralow temperatures. Exploiting a species-selective trapping potential, we are able to control the entropy of one target gas in presence of a second auxiliary gas. With this method, we drive the target gas into the degenerate regime in conditions of controlled temperature by transferring entropy to the auxiliary gas. We envision that our method could be useful both to achieve the low entropies required to realize new quantum phases and to measure the temperature of atoms in deep optical lattices. We verified the thermalization of the two species in a 1D lattice., Comment: 5 pages, 4 figures

The route toward a Bose-Einstein condensate of dipolar molecules requires the ability to efficiently associate dimers of different chemical species and transfer them to the stable rovibrational ground state. Here, we report on recent spectroscopic measurements of two weakly bound molecular levels and newly observed narrow d-wave Feshbach resonances. The data are used to improve the collisional model for the Bose-Bose mixture 41K87Rb, among the most promising candidates to create a molecular dipolar BEC., Comment: 13 pages, 3 figures

The Efimov effect represents a cornerstone in few-body physics. Building on the recent experimental observation with ultracold atoms, we report the first experimental signature of Efimov physics in a heteronuclear system. A mixture of $^{41}$K and $^{87}$Rb atoms was cooled to few hundred nanoKelvins and stored in an optical dipole trap. Exploiting a broad interspecies Feshbach resonance, the losses due to three-body collisions were studied as a function of the interspecies scattering length. We observe an enhancement of the three-body collisions for three distinct values of the interspecies scattering lengths, both positive and negative. We attribute the two features at negative scattering length to the existence of two kind of Efimov trimers, namely KKRb and KRbRb., Comment: 4 pages, 4 figures

We report on the creation of heterospecies bosonic molecules, associated from an ultracold Bose-Bose mixture of 41K and 87Rb, by using a resonantly modulated magnetic field close to two Feshbach resonances. We measure the binding energy of the weakly bound molecular states versus the Feshbach field and compare our results to theoretical predictions. We observe the broadening and asymmetry of the association spectrum due to thermal distribution of the atoms, and a frequency shift occurring when the binding energy depends nonlinearly on the Feshbach field. A simple model is developed to quantitatively describe the association process. Our work marks an important step forward in the experimental route towards Bose-Einstein condensates of dipolar molecules., Comment: 5 pages, 4 figures

We produce Bose-Einstein condensates of two different species, $^{87}$Rb and $^{41}$K, in an optical dipole trap in proximity of interspecies Feshbach resonances. We discover and characterize two Feshbach resonances, located around 35 and 79 G, by observing the three-body losses and the elastic cross-section. The narrower resonance is exploited to create a double species condensate with tunable interactions. Our system opens the way to the exploration of double species Mott insulators and, more in general, of the quantum phase diagram of the two species Bose-Hubbard model., Comment: 4 pages, 4 figures

We produce a heteronuclear quantum degenerate mixture of two bosonic species, $^{87}$Rb and $^{41}$K, in a three-dimensional optical lattice. On raising the lattice barriers, we observe the disapperance of the inference pattern of the heavier $^{87}$Rb, shifting toward shallower lattice depths in the presence of a minor fraction of $^{41}$K. This effect is sizable and requires only a marginal overlap between the two species. We compare our results with similar findings reported for Fermi-Bose mixtures and discuss the interpretation scenarios proposed to date, arguing that the explanation may be linked to the increased effective mass due to the interspecies interactions., Comment: 5 pages, 4 figures

We report the experimental evidence of the sympathetic cooling of $^{39}$K with $^{87}$Rb down to 1 $\mu$K, obtained in a novel tight confining magnetic trap. This allowed us to perform the first direct measurement of the elastic cross section of $^{39}$K below 50 $\mu$K. The result obtained for the triplet scattering length, $a_T = -51(7)$ Bohr radii, agrees with previous results derived from photoassociation spectra and from Feshbach spectroscopy of $^{40}$K., Comment: 7 pages, 4 figures, submitted to Phys. Rev. A

We report on an experimental realization of a two-dimensional magneto-optical trap (2D-MOT) that allows the generation of cold atomic beams of 39K and 41K bosonic potassium isotopes. The high measured fluxes up to 1.0x10^11 atoms/s and low atomic velocities around 33 m/s are well suited for a fast and reliable 3D-MOT loading, a basilar feature for new generation experiments on Bose-Einstein condensation of dilute atomic samples. We also present a simple multilevel theoretical model for the calculation of the light-induced force acting on an atom moving in a MOT. The model gives a good agreement between predicted and measured flux and velocity values for our 2D-MOT., Comment: Updated references, 1 figure added, 10 pages, 9 figures

We give an overview on current experiments on Bose-Einstein condensation (BEC) in a one-dimensional (1D) optical lattice. We introduce measurements of ground state, tunnelling and dynamical properties as well as investigations of atom optical applications and thermodynamical properties. Measurements of the coherent atomic current in an array of Josephson junctions and the critical velocity for the breakdown of superfluid motion are discussed in detail., Comment: 16 pages, To appear in: 'Experimental Quantum Computing and Information', Proceedings of the Internation School of Physics 'Enrico Fermi', Varenna, Course CXLVIII (2001), edited by C. Monroe, P. Mataloni and F. DeMartini (IOS Press, Amsterdam)

We report on the direct observation of an oscillating atomic current in a one-dimensional array of Josephson junctions realized with an atomic Bose-Einstein condensate. The array is created by a laser standing-wave, with the condensates trapped in the valleys of the periodic potential and weakly coupled by the inter-well barriers. The coherence of multiple tunneling between adjacent wells is continuously probed by atomic interference. The square of the small-amplitude oscillation frequency is proportional to the microscopic tunneling rate of each condensate through the barriers, and provides a direct measurement of the Josephson critical current as a function of the intermediate barrier heights. Our superfluid array may allow investigation of phenomena so far inaccessible to superconducting Josephson junctions and lays a bridge between the condensate dynamics and the physics of discrete nonlinear media.

We study the phase transition of a gas of Rb atoms to quantum degeneracy in the combined potential of a harmonically confining magnetic trap and the periodic potential of an optical lattice. For high optical lattice potentials we observe a significant change in the temperature dependency of the population of the ground state of the system. The experimental results are explained by the subsequent formation of quasi 2D condensates in the single lattice sites., Comment: 7 pages (including 3 figures)

We investigate the properties of a coherent array containing about 200 Bose-Einstein condensates produced in a far detuned 1D optical lattice. The density profile of the gas, imaged after releasing the trap, provides information about the coherence of the ground-state wavefunction. The measured atomic distribution is characterized by interference peaks. The time evolution of the peaks, their relative population as well as the radial size of the expanding cloud are in good agreement with the predictions of theory. The 2D nature of the trapped condensates and the conditions required to observe the effects of coherence are also discussed., Comment: 4 pages, 3 figures

We have investigated the center-of-mass oscillations of a Rb87 Bose-Einstein condensate in an elongated magneto-static trap. We start from a trapped condensate and we transfer part of the atoms to another trapped level, by applying a radio-frequency pulse. The new condensate is produced far from its equilibrium position in the magnetic potential, and periodically collides with the parent condensate. We discuss how both the damping and the frequency shift of the oscillations are affected by the mutual interaction between the two condensates, in a wide range of trapping frequencies. The experimental data are compared with the prediction of a mean-field model., Comment: 5 RevTex pages, 7 eps figures

We have performed time-domain interferometry experiments with matter waves trapped in an harmonic potential above and below the Bose-Einstein phase transition. We interrogate the atoms according to the method of separated oscillating fields, with a sequence of two radio-frequency pulses, separated by a time delay T. We observe the oscillation of the population between two internal Zeeman states, as a function of the delay T. We find a strong depletion of the interference fringes for both the Bose condensates and the thermal clouds above condensation, even at very short times, when the clouds are still overlapping. Actually, we explain the observed loss of contrast in terms of phase patterns imprinted by the relative motion, as a consequence of the entanglement between the internal and external states of the trapped atoms., Comment: 4 pages, 3 figures

We create Bose-Einstein condensates of 87-rubidium in a static magnetic trap with a superimposed blue-detuned 1D optical lattice. By displacing the magnetic trap center we are able to control the condensate evolution. We observe a change in the frequency of the center-of-mass oscillation in the harmonic trapping potential, in analogy with an increase in effective mass. For fluid velocities greater than a local speed of sound, we observe the onset of dissipative processes up to full removal of the superfluid component. A parallel simulation study visualizes the dynamics of the BEC and accounts for the main features of the observed behavior., Comment: 4 pages, including figures

A trapped 87Rb Bose-Einstein condensate is initially put into a superposition of two internal states. Under the effect of gravity and by means of a second transition, we prepare two vertically displaced condensates in the same internal state. These constitute two coherent sources of matter waves with adjustable spatial separation. Fringe patterns, observed after free expansion, are associated with the interplay between internal and external degrees of freedom and substantially agree with those for a double slit experiment.

We study the dynamics of two interacting Bose-Einstein condensates, by numerically solving two coupled Gross-Pitaevskii equations at zero temperature. We consider the case of a sudden transfer of atoms between two trapped states with different magnetic moments: the two condensates are initially created with the same density profile, but are trapped into different magnetic potentials, whose minima are vertically displaced by a distance much larger than the initial size of both condensates. Then the two condensates begin to perform collective oscillations, undergoing a complex evolution, characterized by collisions between the two condensates. We investigate the effects of their mutual interaction on the center-of-mass oscillations and on the time evolution of the aspect ratios. Our theoretical analysis provides a useful insight into the recent experimental observations by Maddaloni et al., cond-mat/0003402., Comment: 8 pages, 7 figures, RevTex

Two 87Rb condensates (F=2, m_f=2 and m_f=1) are produced in highly displaced harmonic traps and the collective dynamical behaviour is investigated. The mutual interaction between the two condensates is evidenced in the center-of-mass oscillations as a frequency shift of 6.4(3)%. Calculations based on a mean-field theory well describe the observed effects of periodical collisions both on the center-of-mass motion and on the shape oscillations., Comment: 5 pages, 3 figures, revtex - revised version

We have investigated the rf output coupling of a 87Rb condensate from a Ioffe-Pritchard magnetic trap. Multiple condensates in different Zeeman states are produced, their population being varied by playing with the duration and the amplitude of the rf pulse. Both pulsed and continuous outputs (atom laser) have been observed., Comment: 12 pages, 6 figures