Self-Bound Liquid Droplets in Optical Speckle Potentials

Matthias Schmitt, Matthias Wenzel, Fabian Böttcher +2 more

Karima Abbas, Abdelâali Boudjemâa

Abstract We present a comprehensive description of the equilibrium properties of self-bound liquid droplets in one-dimensional optical speckle potentials at both zero and finite temperatures. Using the Bogoliubov theory we calculate analytically the equation of state, fluctuations induced by disorder, and the equilibrium density. In particular, we show that the peculiar competition between the speckle disordered, the interactions and the Lee-Huang-Yang quantum fluctuations may strongly affect the stability and the formation of the self-bound droplet. We address also the static and dynamical properties of such a disordered droplet using the generalized disorder-dependent Gross-Pitaevskii equation. Notably, impacts of a weak speckle potential are treated numerically for both small droplets of an approximately Gaussian shape and large droplets with a flat-top plateau.

Tim Langen, Matthias Wenzel, M. Schmitt +4 more

Leon Mixa, Milan Radonjić, Axel Pelster +1 more

Quantum droplets are formed in quantum many-body systems when the competition of quantum corrections with the mean-field interaction yields a stable self-bound quantum liquid. We predict the emergence of a quantum droplet when a Bose-Einstein condensate is placed in a transverse-pumped optical cavity. The strong coupling between the atoms and a cavity mode induces long-range interactions in the atoms, and a roton mode for negative cavity detuning emerges. Using Bogoliubov theory, we show that the roton mode competes with the repulsive atomic s -wave scattering. Due to the favorable scaling of the quantum fluctuations with respect to the volume, a self-bound stable quantum liquid emerges.

Kristin Dettmers, Daniel M. Harris, Anand U. Oza +2 more

Karima Abbas, Abdelâali Boudjemâa

We study the properties of self-bound liquid droplets of three-dimensional Bose mixtures in a weak random potential with Gaussian correlation function at both zero and finite temperatures. Using the Bogoliubov theory, we derive useful formulas for the ground-state energy, the equilibrium density, the depletion, and the anomalous density of the droplet. The quantum fluctuation induced by the disorder known as the glassy fraction is also systematically computed. At finite temperature, we calculate the free energy, the thermal equilibrium density, and the critical temperature in terms of the disorder parameters. We show that when the strength and the correlation length of the disorder potential exceed a certain critical value, the droplet evaporates and is eventually entirely destroyed. We calculate the density profiles of this exotic state by means of numerical simulations of the corresponding generalized disorder Gross-Pitaevskii equation. Our predictions reveal that as the strength of the disorder gets larger, the atomic density varies rapidly in the plateau region. We point out in addition that the peculiar interplay of the disorder and the repulsive Lee-Huang-Yang corrections play a pivotal role in the collective modes of the self-bound droplet.