Beyond-mean-field crossover from one dimension to three dimensions in quantum droplets of binary mixtures

Abstract

The existence of quantum droplets in binary Bose-Einstein condensate mixtures rely on beyondmean field effects, competing with mean-field-effects. Interestingly, the beyond-mean field effects change from repulsive in three dimension (3D) to attractive in 1D leading to drastically different behaviors. We quantitatively model quantum droplets in the beyond-mean-field crossover from 1D to 3D in the relevant case of an elongated harmonic trap and give realistic numbers for experimental realizations. We identify and quantify two main limiting factors: three-body losses and tiny energy scales. The crossover region is appealing as it offers a trade-off between these two main limitations opening the possibility of observing stable flat-top density profiles, a yet unobserved, characteristic feature of quantum droplets. It would permit testing beyond-mean-field theories to an unprecedented precision.

Strongly dipolar gases in a one-dimensional lattice: Bloch oscillations and matter-wave localization

“…The dimensionality of the system is known to highly influence the size and even the sign of the beyond-meanfield contribution, in both Bose-Bose [76][77][78] and dipolar [56,79,80] gases. Here, we assess the validity of employing the full 3D LHY correction to our system.…”

Maintaining supersolidity in one and two dimensions

“…Inspired by recent work with nondipolar droplets [43], we assume the following ansatz for a dipolar droplet,…”

“…Note, when using this definition care should be taken for the special cases Q 5 (0) = 1 and Q 5 (1) = 3 √ 3/2. These integrals are evaluated upon substitution of the ansatz Ψ(x) = √ N φ(ρ)ψ(z) [43] [see main text Eq. ( 4)], with N the number of particles in the droplet.…”

Formation and quench of homonuclear and heteronuclear quantum droplets in one dimension

“…Their self evaporation due to lossy inelastic collisions [7,9] that prevent droplet observation at long timescales, has also been considered. This is a process that can be delayed using heteronuclear mixtures [10,17] or supressed using one-dimensional (1D) settings [18,19]. These recent developments clearly underscore the relevance of such structures in a wide range of theoretical and experimental studies and their interest in quantifying the interplay between mean-field and quantum effects.…”