Quantum droplets in one-dimensional Bose mixtures: A quantum Monte Carlo study

We use exact quantum Monte Carlo techniques to study the properties of quantum droplets in two-component bosonic mixtures with contact interactions in one spatial dimension. We systematically study the surface tension, the density profile and the breathing mode as a function of the number of particles in the droplet and of the ratio of coupling strengths between intraspecies repulsion and interspecies attraction. We find that deviations from the predictions of the generalized Gross-Pitaevskii equation are small in most cases of interest.

Figure 1

Energy per particle in units of ${\hslash }^2/\left(m{a}^2\right)$ as a function of the inverse particle number $1/N$ for increasing ratio $r$ between attraction and repulsion from the topmost to the lowermost. Solid dots are the results of our DMC simulations, and solid lines are linear fits to the DMC data in the limit of large $N$. Solid squares at $1/N=0$ correspond to the bulk energy calculated in Ref. [14]. Dashed lines show, instead, the GGP predictions. The slope of the linear fit, corresponding to the surface energy $E_S$, is shown in the inset together with the GGP result.

Figure 2

Density profiles for different ratios $r\text{:}r=0.95$ (top panel) and $r=0.6$ (bottom panel) for decreasing particle number $N$ from the topmost to the lowermost. Dashed lines correspond to the profiles obtained from the GGP equation in the same conditions. The dotted line is the equilibrium density computed for a uniform mixture at $r=0.6$ in Ref. [14].

Figure 3

Frequency of the breathing mode in units of $\hslash /\left(m{a}^2\right)$ for decreasing ratio $r$ from the topmost to the lowermost as a function of particle number $N$. Solid dots correspond to DMC results, and dashed lines correspond to GGP predictions.