Resolving the problem of complex sound velocity in binary Bose mixtures with attractive intercomponent interactions

TL;DR

This work tackles the instability of Petrov's two-component Bose-liquid droplets in the presence of attractive interspecies coupling, where a purely imaginary phonon velocity $c_d^2<0$ signals dynamical instability. It develops a self-consistent optimized perturbation theory (OPT) for a symmetric binary Bose gas, incorporating normal, anomalous, and cross densities via two chemical potentials to ensure a gapless, thermodynamically stable spectrum with two Goldstone modes, $c_d$ and $c_s$. The authors derive explicit self-consistent equations and identify a stability region in the $( ilde{oldsymbol{eta}}^2, ilde{oldsymbol{eta}})$-plane, obtaining a closed form for $ ilde{oldsymbol{eta}}_{ ext{crit}}$ and showing that including anomalous and mixed densities enlarges the stability domain. They further map out a phase diagram separating liquid droplets from dimerized gas phases through the total energy criterion $ar{{ m E}}_{tot}$, highlighting that the full fluctuation treatment reduces the droplet region relative to Petrov's model and aligns qualitatively with quantum Monte Carlo insights. The framework sets the stage for exploring polarized mixtures and more general regimes with strong correlations.

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.

Figures (6)

• Figure 1: (a): The phase diagram of symmetric binary Bose mixture on $(- \delta g /g,\gamma)$ plane; (b): The same as in (a) but the anomalous density $\sigma$ is neglected
• Figure 2: The fraction of condensed atoms (solid line), the anomalous (dashed line) and the mixed (dotted line) densities, for: (a) $\delta g/g=-0.15$ and (b) $\delta g/g=-0.7$.
• Figure 3: The dimensionless sound velocities $s_{p,m}=c_{p,m}ma_s$ vs $-\log_{10}(\gamma)$ for: (a) $\delta g/g =-0.01$; (b) $\delta g/g=-0.15$, and (c) $\delta g/g=-0.3$.
• Figure 4: The same as in Fig. 3 but in the model by Ota and Astrackharchik astra
• Figure 5: The dimensionless total energy of the system per particle for: (a) $\delta g/g =-0.01$, (b) $\delta g/g=-0.15$, and (c) $\delta g/g=-0.3$