Phonon Stability and Sound Velocity of Bose Mixture Droplet

Han Pu, W. Zhang, Pierre Meystre

Qi Gu, Lan Yin

Quantum droplets have been realized in experiments on binary boson mixtures and dipolar Bose gases. In these systems, the mean-field energy of the Bose-Einstein condensation is attractive, and the repulsive Lee-Huang-Yang energy is crucial for stability. However, since the Lee-Huang-Yang term is not taken into account when constructing the Bogoliubov Hamiltonian, in the droplet regime one faces the problem of dynamically unstable phonon modes. In this work, we go beyond the Bogoliubov theory to study how the phonon mode is stabilized in the quantum droplet of a binary boson mixture. Similar to Beliaev's approach to a single-component Bose gas, we compute higher-order contributions to the self-energy of the boson propagator. We find that the interaction between spin and phonon excitations is the key for the phonon stability. We obtain the sound velocity which can be tested by measuring the superfluid critical velocity of the droplet in experiments. Beliaev damping of this quantum droplet is also discussed.

D. M. Semiz

Abdulla Rakhimov, Sanathon Tukhtasinova, Vyacheslav I. Yukalov

Abstract In 2015 Dmitry Petrov theoretically suggested that, in a binary mixture of bosons a quantum liquid droplet may arise due to the competition between attractive intercomponent and repulsive intracomponent forces. Although this prediction has been confirmed experimentally, the model by itself suffers from a serious conceptual problem: the low—lying excitation spectrum manifests a purely imaginary phonon velocity, c d 2 < 0 . In the present work, we develop a self consistent theory of two-component Bose systems with attractive interspecies interactions, which accurately takes into account pair correlations in terms of anomalous and mixed densities. We have shown that this procedure is able to resolve the problem of c d 2 < 0 . Limiting ourselves with a symmetric Bose mixture at zero temperature, we have found a region of stability in which a droplet can survive.

Khelifa Mohammed Elhadj, Laila Y. Al Sakkaf, Abdelâali Boudjemâa +1 more

Han Pu, Weiping Zhang, Martin Wilkens +1 more

We calculate the phonon excitation spectrum in a zero-temperature dilute boson-fermion gaseous mixture. We show how the sound velocity changes due to the boson-fermion interaction, and we determine the dynamical stability regime of a homogeneous mixture. We identify a resonant phonon-exchange interaction between the fermions as the physical mechanism leading to the instability.