Self-bound droplets of a dilute magnetic quantum liquid

Abstract

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 1, 2 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 3 , it was predicted that three-dimensional self-bound quantum droplets of magnetic atoms should exist 4, 5 . 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 6 and helium droplets 7 .Liquid droplets of water or helium are formed by the mutual attractive and repulsive forces that are created by the different parts of the inter-particle potential (and are due to covalent or van der Waals attraction and to the electronic Pauli exclusion principle, respectively). Helium droplets in particular have been a focus of research, owing to their interesting quantum nature 8,9 . Droplets can serve as closed, isolated quantum systems with which to probe, for example, superfluidity of mesoscopic ensembles 10 . In the context of ultracold atoms, the observation of an ensemble of stable droplets 11 in a dilute magnetic quantum gas opened up the possibility of a three-dimensional self-bound state 4, 5 . A trapped quantum droplet of magnetic atoms has recently also been observed using erbium atoms 12 . Here we demonstrate the observation of dilute, self-bound liquid droplets in a sample of ultracold bosonic dysprosium atoms, which have a strong longrange magnetic dipolar interaction and a tunable repulsive short-range contact interaction. The interplay between these two interactions can be tuned such that the overall mean field is weakly attractive, but so that the interactions also create quantum depletion and a corresponding many-body repulsion. This repulsion exactly counteracts the attraction when the density of the droplet reaches the stabilization density. We use the word 'liquid' here to describe a state of matter that is defined by the presence of self-bound dro...

Dissociation of One-Dimensional Matter-Wave Breathers due to Quantum Many-Body Effects

“…The observability of microscopic quantum effects involving a substantial fraction of the particles in a coherent macroscopic setting generally requires going beyond MF, for example, at low density in one dimension (1D) [1,2] or high density in three dimensions (3D). In 3D systems, the high-density Lee-Huang-Yang corrections, which are induced by quantum correlations, were realized experimentally using the Feshbach resonance [3] and in the spectacular form of "quantum droplets" in dipolar [4][5][6] and isotropic [7] bosonic gases, i.e., as self-trapped states stabilized against the collapse by the beyond-MF selfrepulsion. This stabilization was predicted in Refs.…”

How Bose–Einstein condensates keep revealing weird physics

“…Scientists have made other surprising observations, like magnetic liquid droplets that fall like solid rocks, or neutral particles that act like they carry a charge (4,5). Under certain conditions, BECs can be controlled to form swirling vortices, or explode like This velocity-distribution data for a gas of rubidium atoms confirmed the discovery of the Bose-Einstein condensate in 1995.…”

Excitations and stability of weakly interacting Bose gases with multibody interactions

“…To analyse the previous expression forĤ I , we denote by p a general function of theâ's operators entering in (64). In general the terms V p12 V 2 p12−pÂp and V p12 V 2 p12+pÂp are different.…”

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