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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.
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We have studied the three-body recombination rates on both sides of the interspecies d-wave Feshbach resonance in the $^{85}$Rb,-$^{87}$Rb-$^{87}$Rb system using the $R$-matrix propagation method in the hyperspherical coordinate frame. Two different mechanisms of recombination rate enhancement for positive and negative $^{85}$Rb,-$^{87}$Rb d-wave scattering lengths are analyzed. On the positive scattering length side, the recombination rate enhancement occurs due to the existence of three-body shape resonance, while on the negative scattering length side, the coupling between the lowest entrance channel and the highest recombination channel is crucial to the appearance of the enhancement. In addition, our study shows that the intraspecies interaction plays a significant role in determining the emergence of recombination rate enhancements. Compared to the case in which the three pairwise interactions are all in d-wave resonance, when the $^{87}$Rb-$^{87}$Rb interaction is near the d-wave resonance, the values of the interspecies scattering length that produce the recombination enhancement shift. In particular, when the $^{87}$Rb-$^{87}$Rb interaction is away from the d-wave resonance, the enhancement disappears on the negative interspecies scattering length side.
We propose a novel mathematical approach for the calculation of near-zero energy states by solving potentials which are isospectral with the original one. For any potential, families of strictly isospectral potentials (with very different shape) having desirable and adjustable features are generated by supersymmetric isospectral formalism. The near-zero energy Efimov state in the original potential is effectively trapped in the deep well of the isospectral family and facilitates more accurate calculation of the Efimov state. Application to the first excited state in 4He trimer is presented.
Self-bound many-body systems are formed through a balance of attractive and repulsive forces and occur in many physical scenarios. Liquid droplets are an example of a self-bound system, formed by a balance of the mutual attractive and repulsive forces that derive from different components of the inter-particle potential. It has been suggested that self-bound ensembles of ultracold atoms should exist for atom number densities that are 10^8 times lower than in a helium droplet, which is formed from a dense quantum liquid. However, such ensembles have been elusive up to now because they require forces other than the usual zero-range contact interaction, which is either attractive or repulsive but never both. On the basis of the recent finding that an unstable bosonic dipolar gas can be stabilized by a repulsive many-body term, it was predicted that three-dimensional self-bound quantum droplets of magnetic atoms should exist. Here we report the observation of such droplets in a trap-free levitation field. We find that this dilute magnetic quantum liquid requires a minimum, critical number of atoms, below which the liquid evaporates into an expanding gas as a result of the quantum pressure of the individual constituents. Consequently, around this critical atom number we observe an interaction-driven phase transition between a gas and a self-bound liquid in the quantum degenerate regime with ultracold atoms. These droplets are the dilute counterpart of strongly correlated self-bound systems such as atomic nuclei and helium droplets.
Recently achieved two-component dipolar Bose-Einstein condensates open exciting possibilities for the study of mixtures of ultra-dilute quantum liquids. While non-dipolar self-bound mixtures are necessarily miscible with an approximately fixed ratio between the two densities, the density ratio for the dipolar case is free. As a result, self-bound dipolar mixtures present qualitatively novel and much richer physics, characterized by three possible ground-state phases: miscible, symmetric immiscible and asymmetric immiscible, which may in principle occur at any population imbalance. Self-bound immiscible droplets are possible due to mutual non-local inter-component attraction, which results in the formation of a droplet molecule. Moreover, our analysis of the impurity regime, shows that quantum fluctuations in the majority component crucially modify the miscibility of impurities. Our work opens intriguing perspectives for the exploration of spinor physics in ultra-dilute liquids, which should resemble to some extent that of 4He-3He droplets and impurity-doped helium droplets.
The devils staircase is a fractal structure that characterizes the ground state of one-dimensional classical lattice gases with long-range repulsive convex interactions. Its plateaus mark regions of stability for specific filling fractions which are controlled by a chemical potential. Typically such staircase has an explicit particle-hole symmetry, i.e., the staircase at more than half-filling can be trivially extracted from the one at less than half filling by exchanging the roles of holes and particles. Here we introduce a quantum spin chain with competing short-range attractive and long-range repulsive interactions, i.e. a non-convex potential. In the classical limit the ground state features generalized Wigner crystals that --- depending on the filling fraction --- are either composed of dimer particles or dimer holes which results in an emergent complete devils staircase without explicit particle-hole symmetry of the underlying microscopic model. In our system the particle-hole symmetry is lifted due to the fact that the staircase is controlled through a two-body interaction rather than a one-body chemical potential. The introduction of quantum fluctuations through a transverse field melts the staircase and ultimately makes the system enter a paramagnetic phase. For intermediate transverse field strengths, however, we identify a region, where the density-density correlations suggest the emergence of quasi long-range order. We discuss how this physics can be explored with Rydberg-dressed atoms held in a lattice.
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