Collisions of Self-Bound Quantum Droplets

We report on the study of binary collisions between quantum droplets formed by an attractive mixture of ultracold atoms. We distinguish two main outcomes of the collision, i.e., merging and separation, depending on the velocity of the colliding pair. The critical velocity $v_c$ that discriminates between the two cases displays a different dependence on the atom number $N$ for small and large droplets. By comparing our experimental results with numerical simulations, we show that the nonmonotonic behavior of $v_c(N)$ is due to the crossover from a compressible to an incompressible regime, where the collisional dynamics is governed by different energy scales, i.e., the droplet binding energy and the surface tension. These results also provide the first evidence of the liquidlike nature of quantum droplets in the large $N$ limit, where their behavior closely resembles that of classical liquid droplets.

Figure 1

Production of two colliding droplets. (a) Schematic representation of the geometry of the optical potentials. (b) Experimental sequence used to provide a controlled velocity to the droplets.

Figure 2

Examples of two collision measurements resulting in merging (a) and separation (d) of the droplets. In (b) and (e) we report the corresponding evolution of the distance $d$ between the droplets and in (c) and (f) of the total atom number $N$. A linear fit of $d(t)$ before collision is used to measure $v_{\mathrm{rel}}$ and $t_{\mathrm{coll}}$. $N_{\mathrm{coll}}$ is then deduced from a linear interpolation between the two data points adjacent to $t_{\mathrm{coll}}$, as shown in (c) and (f). The data correspond to the average over four experiment repetitions. The error bars represent the statistical uncertainty and correspond to 1 standard deviation.

Figure 3

Outcomes of the collision measurements (b) and simulations (c) as a function of $\tilde{v}$ and ${\tilde{N}}_{\mathrm{coll}}$. In (a) we draw the droplet wave function for increasing values of $\tilde{N}$, which shows the crossover from compressible to incompressible droplets. In (c) the results of simulations in the ideal case without losses are represented as a color plot of the ratio $R$ introduced in the text, while the data points represent the results of the simulations with 3BL, distinguishing between merging (red diamonds) and separation (blue squares). The solid lines in (b) and (c) represent the expected trend ${\tilde{v}}_c\propto \sqrt{2|{\tilde{E}}_{\mathrm{drop}}|/\tilde{N}}$ at small $\tilde{N}$, while the dotted in line in (c) is ${\tilde{v}}_c\propto (\tilde{N}-{\tilde{N}}_0{)}^{-1/6}$, which is the predicted scaling at large $\tilde{N}$. The dashed lines in (b) and (c) correspond to the same ${\tilde{N}}^{-1/6}$ scaling, but in this case they are simply used as a guide to the eye. In (d) we report the timescale of the collision $\tilde{\tau }$ as a function of ${\tilde{N}}_{\mathrm{coll}}$ and, in the insets, two examples of the collisional dynamics observed in the simulations without 3BL, in the two opposite cases of small and large $\tilde{N}$. A detailed description of the estimation of the error bars in (b) is reported in Ref. [30].