An Arrested Implosion

Abstract

Quantum fluctuations are the origin of genuine quantum many-body effects, and can be neglected in classical mean-field phenomena. Here, we report on the observation of stable quantum droplets containing ∼800 atoms that are expected to collapse at the mean-field level due to the essentially attractive interaction. By systematic measurements on individual droplets we demonstrate quantitatively that quantum fluctuations mechanically stabilize them against the mean-field collapse. We observe in addition the interference of several droplets indicating that this stable many-body state is phase coherent. DOI: 10.1103/PhysRevLett.116.215301 Uncertainties and fluctuations around mean values are one of the key consequences of quantum mechanics. At the many-body level, they induce corrections to mean-field theory results, altering the many-body state, from a classical factorizable to an entangled state. Owing to their versatility, ultracold atom experiments offer numerous examples of interesting many-body states [1]. Among these systems, bosonic superfluids are well studied. They are described in the weakly interacting regime by a mean-field energy density proportional to the square of the particle density n 2 , with a negative prefactor in the attractive case. Since the seminal work of Lee, Huang, and Yang [2], it is known that interactions lead to a repulsive correction ∝ n 5=2 owing to quantum fluctuations. Therefore, an equilibrium between these two contributions can in principle stabilize an attractive Bose gas [3]. A similar stabilization mechanism using quantum fluctuations was proposed for an attractive Bose-Bose mixture in Ref. [4], which leads to the formation of droplets. In this reference liquidlike droplets are defined as the result of a competition between an attractive n 2 and a repulsive n 2þα term in the energy functional. Besides liquid helium droplets [5], such functionals are also used to describe atomic nuclei [6]. Here, we study a strongly dipolar Bose gas where the attractive mean-field interaction is due to the dipole-dipole interaction (DDI). This system is known to be unstable in the mean-field approximation [7]. We however show here that beyond mean-field effects lead to the stabilization of droplets. Our investigations are aimed at probing strongly dipolar Bose gases of 164 Dy, which are characterized by a dipolar length a dd ¼ μ 0 μ 2 m=12πℏ 2 ≃ 131a 0 , where a 0 is the Bohr radius with μ ¼ 9.93μ B Dy's magnetic dipole moment in units of the Bohr magneton μ B , ℏ the reduced Planck constant, and m the atomic mass. The additional short-range interaction of 164 Dy, characterized by the scattering length a has been the focus of several papers [8][9][10][11], and the background scattering length was measured to be a bg ¼ 92ð8Þa 0 , modulated by many Feshbach resonances. Thus, away from Feshbach resonances at the mean-field level the dipolar interaction dominates with ε dd;bg ¼ a dd =a bg ≃ 1.45. In a previous work [12], we have reported the observation of an instability of a dipolar Bose-Einste...