First Observation of Bright Solitons in Bulk Superfluid ${}^4\mathrm{He}$

The existence of bright solitons in bulk superfluid ${}^4\mathrm{He}$ is demonstrated by time-resolved shadowgraph imaging experiments and density functional theory (DFT) calculations. The initial liquid compression that leads to the creation of nonlinear waves is produced by rapidly expanding plasma from laser ablation. After the leading dissipative period, these waves transform into bright solitons, which exhibit three characteristic features: dispersionless propagation, negligible interaction in a two-wave collision, and direct dependence between soliton amplitude and the propagation velocity. The experimental observations are supported by DFT calculations, which show rapid evolution of the initially compressed liquid into bright solitons. At high amplitudes, solitons become unstable and break down into dispersive shock waves.

Figure 1

Metal target geometry (scale accuracy $\pm 10\mu \mathrm{m}$). The primary waves (red) originate from the expanding plasma created by laser ablation (red circle) whereas the planar waves (black) are created by rapid boiling on the target surface. The optical axis for imaging is perpendicular to the plane shown. A photograph of the target is shown on the right.

Figure 2

Snapshots of the waves emitted from the target at given times $t$ ($T=1.7\mathrm{K}$). To increase the contrast in the images for display purposes, the lens system was placed slightly out of focus. The top portion of the target depicted in Fig. 1 is not shown.

Figure 3

The top panel shows the time evolution of the average soliton velocity (accuracy better than $\pm 1\mathrm{m}/\mathrm{s}$ at long times) at 1.7 K with the long-time regime magnified in the inset (total travel distance indicated by an arrow). The three lines (blue, red, green) highlight the changes in the wave deceleration. The time axis refers to the delay between the ablation and backlight laser pulses. The bottom panel shows the normalized shadowgraph intensity difference in front of the wave vs behind it. The dashed line provides a guide to the eye for correlating the velocity and intensity difference data.

Figure 4

Time evolution of the primary (spherical) and secondary (planar from top) solitons before, during, and after the collision ($T=1.7\mathrm{K}$). The red circle indicates the origin for the primary wave emission and the top (blue) surface for the secondary wave. The delay between the ablation and backlight laser pulses is indicated by $t$.

Figure 5

Snapshots of superfluid ${}^4\mathrm{He}$ density along the direction of soliton propagation ($x$ axis) from TDDFT. The initial compression was created on the simulation box boundary with $n=30$ (see text). Because of the periodic boundary condition, the solitons propagate as shown in (a)–(d), collide in (e), and continue propagating almost unchanged in (f)–(h). When compared with experiments, the $x$ axis is oriented perpendicular to the ablation target.

Figure 6

Soliton propagation velocity ($v_s$) vs amplitude (${\rho }_s/{\rho }_0$) from TDDFT. The horizontal dotted line indicates the velocity of first sound in superfluid ${}^4\mathrm{He}$ at $T=0$.