Quantum filaments in dipolar Bose-Einstein condensates

Abstract

Collapse in dipolar Bose-Einstein condensates may be arrested by quantum fluctuations. Due to the anisotropy of the dipole-dipole interactions, the dipole-driven collapse induced by soft excitations is compensated by the repulsive Lee-Huang-Yang contribution resulting from quantum fluctuations of hard excitations, in a similar mechanism as that recently proposed for Bose-Bose mixtures. The arrested collapse results in self-bound filament-like droplets, providing an explanation to recent dysprosium experiments. Arrested instability and droplet formation are novel general features directly linked to the nature of the dipole-dipole interactions, and should hence play an important role in all future experiments with strongly dipolar gases. PACS numbers:Dipole-dipole interactions (DDI) lead to qualitatively new physics for dipolar gases compared to non-dipolar ones [1,2]. As a result, this physics constitute the focus of a large interest, including experiments on magnetic atoms [3][4][5][6], polar molecules [7][8][9][10], and Rydbergdressed atoms [11]. A characteristic feature of dipolar Bose-Einstein condensates (BECs) is their geometrydependent stability [12]. If the condensate is elongated along the dipole orientation, the DDI are attractive in average, and the BEC may become unstable, in a similar, but not identical, way as a BEC with negative s-wave scattering length, a < 0. Chromium experiments showed that, as for a < 0, the unstable BEC collapses, albeit with a peculiar d-wave post-collapse dynamics [13].This picture has been challenged by recent dysprosium experiments [14], in which destabilization, induced by a quench to a sufficiently low a, is not followed by collapse, but rather by the formation of stable droplets that are only destroyed in a large time scale by weak three-body losses (3BL). This surprising result, which resembles the Rosensweig instability in ferrofluids [15,16], points to an up to now unknown stabilization mechanism that plays a similar role as that of surface tension in classical ferrofluids. It has been recently suggested that large conservative three-body forces, with a strength several orders of magnitude larger than the 3BL, may account for the observation [17,18]. There is however no justification of why large three-body forces should be present, or whether there is a link between them and the DDI.This Letter explores an alternative mechanism, based on quantum fluctuations, which is suggested by very recent experiments [19]. As recently shown [20], LeeHuang-Yang (LHY) corrections may stabilize droplets in unstable Bose-Bose mixtures. This interesting effect results from the presence of soft and hard elementary excitations. Whereas soft modes may become unstable, quantum fluctuations of the hard modes may balance the instability, resulting in an equilibrium droplet. As shown below, due to the anisotropy of the DDI, a dipolar BEC also presents soft and hard modes, characterized in free space by momenta perpendicular or parallel to the dipole (a) (b) FIG. 1: (Color online)Crystal-lik...

An Arrested Implosion

“…This demonstrates unambiguously that quantum fluctuations constitute the stabilizing mechanism. The conclusion we drew here is reinforced by numerical simulations reported in [36] of which we have recently become aware. Finally, we observe that the droplets have internal phase coherence.…”

Ground-state properties and elementary excitations of quantum droplets in dipolar Bose-Einstein condensates

“…In these breakthrough experiments destabilization leads to the formation of stable droplets, that are only destroyed in a long time scale by three-body losses. Although first studies pointed to the possibility that large three-body conservative forces could stabilize the droplets [15,16], recent works have shown that the most plausible stabilization mechanism is due to quantum fluctuations [14,17,18], which play a similar role as that of surface tension in classical ferrofluids [19,20].…”

Excitations and stability of weakly interacting Bose gases with multibody interactions

“…(110) as a function of the dimensionless parametersŨ =Ũ 2 +Ũ 3 andC = ε ddŨ2 for α = π/2. We compute the specific values of these parameters for a condensate of 164 Dy also considering as the 3-body contact interaction the value given in [12] (notice however that by using other values of U 3 , as the ones given in [69], the effect of such terms is anyway rather small). From Fig.…”

“…Recent experiments with dipolar BECs showed that under certain conditions where instability is expected from a standard Bogoliubov approach, dense clusters with many atoms can occur [61][62][63][64][65], which are expected to be superfluid [66]. Two interpretations have been proposed to explain the stabilization of this phase, namely the presence of weak 3-body interactions [11,12] and beyond mean-field effects (Lee-Huang-Yang type corrections) [67][68][69]. Motivated by these recent developments, we analyse in further detail the stability of uniform superfluids in the presence of long-range dipolar interactions and 2-and 3-body contact potentials.…”