Theory for self-bound states of dipolar Bose-Einstein condensates

Abstract

Ultracold gases of dipolar Dy have emerged as platforms where studying novel phases of matter, such as liquid droplets, poses many questions since standard theoretical methods fail to account for some of their observed properties. Here we investigate the self-bound states of dipolar Dy condensates by using general Gaussian-state ansatzes which go beyond conventional coherent-state ansatzes by including multimode squeezing. Our theory provides a transition between self-bound liquid and gas phases that agrees well with experimental observations and additionally reveals an experimentally unexplored transition in the self-bound gas region from a coherentdominated to a squeezed-dominated phase. Our theory also allows one to extract the real part of the three-body interaction strength of the Dy atoms from the particle number distribution of the condensates. This allows us to show that the self-bound states are stabilized by the short-range three-body repulsion. Our study sheds a different light onto the properties of self-bound droplets of Bose-Einstein condensates.

Self-bound droplets in quasi-two-dimensional dipolar condensates

“…To be self-contained, let us briefly review GST [33][34][35]37]. Assume that the ground state of our systems can be approximated by a pure Gaussian state |GS .…”

“…The order parameters for the ground state of the condensate can be obtained by minimizing the total energy with respect to φ, G, and F . After projecting the resulting equations onto the tangential space of the Gaussian manifold [33][34][35]37], we obtain the equations of motion in the imaginary time τ , i.e.,…”

“…To characterize the properties of the condensate, we introduce the normalized coherent mode function φc (ρ) = N −1/2 c φ(ρ), where N c = dρ|φ(ρ)| 2 is the occupation number of the coherent mode. Furthermore, the normal and anomalous Green functions can be diagonalized simultaneously by a set of orthonormal functions { φs,j } [33,40], i.e.,…”

“…Higher order corrections to the EGPE have also been developed [30][31][32]. In particular, we systematically studied the self-bound droplets of dipolar and binary condensates [33,34] using the Gaussian state theory (GST) [35,36], a generalization to the conventional coherent-state-based mean-field theory. In GST, quantum fluctuation is inherently included in the many-body wave function and is treated self-consistently.…”

“…In the presence of the three-body repulsion, we also studied the quantum phases of the self-bound droplets of both dipolar [33] and quasi-2D binary condensates [34]. We showed that, due to the competition between the 2B attraction and the 3B repulsion, the squeezed coherent state (SCS) and the coherent state (CS) phases also emerge as condensate density increases.…”