Droplets of Trapped Quantum Dipolar Bosons

Abstract

Strongly interacting systems of dipolar bosons in three dimensions confined by harmonic traps are analyzed using the exact Path Integral Ground State Monte Carlo method. By adding a repulsive two-body potential, we find a narrow window of interaction parameters leading to stable groundstate configurations of droplets in a crystalline arrangement. We find that this effect is entirely due to the interaction present in the Hamiltonian without resorting to additional stabilizing mechanisms or specific three-body forces. We analyze the number of droplets formed in terms of the Hamiltonian parameters, relate them to the corresponding s-wave scattering length, and discuss a simple scaling model for the density profiles. Our results are in qualitative agreement with recent experiments showing a quantum Rosensweig instability in trapped Dy atoms.Dipolar effects in quantum gases have been considered of major experimental and theoretical interest in the last decade since the initial studies of dilute clouds of Cr atoms, which present a relatively large magnetic dipolar moment. In the pioneering experiments of Ref.[1], the two-body scattering length of a cloud of 52 Cr atoms was drastically reduced by bringing it close to a Feshbach resonance. In this way, dipolar effects were enhanced and interesting new features, not observed before in other species like Rb or Cs, appeared. The long range and anisotropic character of the dipolar interaction has been largely explored since then, leading to interesting new phenomena such as d-wave superfluidity or d-wave collapse [2,3]. All these experiments have opened new perspectives on the field of dipolar quantum physics, and new systems with stronger dipolar interactions have since then been explored. The most promising ones, consisting initially in ultracold polar molecules of K and Rb or Cs and Rb, are unfortunately problematic due to the inherent difficulty to bring them down to the quantum degeneracy limit, although recent progress have been achieved with NaK [4] The anisotropy of the dipolar interaction plays a fundamental role on the behavior of the system, with different regimes and phases depending on the geometry and dimensionality. The particular form of the dipole-dipole potential makes the interaction be attractive or repulsive depending on the relative orientation of the dipoles, according to the expressionwhere C dd sets the strength of the interaction that is proportional to the square of the (magnetic or electric) dipolar moment, p j is the dipolar moment itself, and r is the relative position vector of the two interacting dipoles. The particular form of this interaction leads to surprising new features not present in other systems, like stripe phases in two-dimensional (2D) Bose systems [10]. Similar phases in Fermi systems have also been predicted [11,12], although these are more controversial [13]. One of the most interesting phenomenon recently reported in the field of dipolar quantum gases is the formation of self-bound droplets when a gas of trapped 164 Dy atoms...

Classical and quantum filaments in the ground state of trapped dipolar Bose gases

“…Indeed, the main physical effect that we set out to explore, namely the formation of a ordered arrays of filaments, appears observable in a rather wide range of physical conditions, considerably more extended than suggested in Ref. [24].…”

“…[24], namely ξ = 1.2 and γ = 4.0, i.e., the trap is squeezed in the z direction. This choice is aimed at rendering the geometry quantitatively close to that of most experiments.…”

“…Indeed, recent quantum Monte Carlo (QMC) studies have yielded evidence of both the stability of a trapped dipolar BEC against collapse [23], as well as the appearance of droplets [24], if a short range repulsion is added to the pair-wise dipolar interaction.…”

“…[24]; most significantly, whereas it is contended therein that the ground state of the system features ordered arrangements of filaments (in this regime, prolate droplets may be more appropriate a term) in a narrow range of values of the relevant interaction parameter (which, as stated above, is simply the characteristic diameter of the short distance repulsive core), we show here that, for a sufficient number of particles, the breakdown into filaments occurs whenever this parameter is small compared to the natural length of the dipolar interaction. Indeed, as mentioned above such a breakdown inevitably occurs in the classical limit (i.e., of vanishing hard core diameter).…”

“…We adopted the same microscopic model utilized in Ref. [24], including a hard core repulsive term and with parameters of the harmonic confining potential chosen to be close to those of typical experimental setups. We explore the different physics that emerges as the number of particles in the harmonic trap and the range of the short-distance repulsion are varied.…”