Quantum Shock Waves and Domain Walls in the Real-Time Dynamics of a Superfluid Unitary Fermi Gas

We show that in the collision of two superfluid fermionic atomic clouds one observes the formation of quantum shock waves as discontinuities in the number density and collective flow velocity. Domain walls, which are topological excitations of the superfluid order parameter, are also generated and exhibit abrupt phase changes by $\pi$ and slower motion than the shock waves. The domain walls are distinct from the gray soliton train or number density ripples formed in the wake of the shock waves and observed in the collisions of superfluid bosonic atomic clouds. Domain walls with opposite phase jumps appear to collide elastically.

Figure 1

The space-time evolution of the 1D density profiles along the trap axis as reported in Fig. 2 of Ref. 12. We have outlined part of the shock wave front with a white oval here and in Figs. 2, 4, 5, 6.

Figure 2

The space-time evolution of the number density profile $n(x,0,t)$ along the collision axis in the TDSLDA simulation of the collision of two UFG clouds. Here $k_F$ and ${\epsilon }_F=k_F^2/2$ ($\hslash =m=1$) are the initial values of the Fermi wave vector and energy at the center of clouds. The region where one elastic collision of two DWs occurs is outlined with a white circle here and in Figs. 4, 5, 6.

Figure 3

Three consecutive frames showing the absolute magnitude of the pairing field $|\Delta (x,y,t)|$ in the $xy$ plane at times $t{\epsilon }_F=30,350,690$; see also Figs. 2, 4. The $x$ and $y$ directions (not shown to scale here) have an aspect ratio of $\approx 30$. By the time of the second frame, the QSWs have emerged from the cloud. DWs appear as planar number density depletions with a width comparable to the diameter of a quantum vortex, and can be highly visible using standard techniques [24]. We have observed the formation of DWs so far only in traps with elongations larger than in the previous experiment [12]. In simulations of clouds with smaller aspect ratios we observe only QSWs with density profiles very similar to Ref. 12.

Figure 4

The magnitude of the pairing gap $|\Delta (x,0,t)|$ corresponding to Fig. 2. The DWs appear as significant depletions of the pairing field, and always appear in pairs with opposite phase jumps; see also Figs. 5, 6.

Figure 5

The phase of the pairing gap $\arg \Delta (x,0,t)/\pi$.

Figure 6

The $x$ component of the collective flow velocity field $v_x(x,0,t)$ along the axis of collision. At the front of the two shock waves, the velocity field undergoes a rapid change and the matter flows in opposite directions.