Formation of Dispersive Shock Waves by Merging and Splitting Bose-Einstein Condensates

The processes of merging and splitting dilute-gas Bose-Einstein condensates are studied in the nonadiabatic, high-density regime. Rich dynamics are found. Depending on the experimental parameters, uniform soliton trains containing more than ten solitons or the formation of a high-density bulge as well as dispersive shock waves are observed experimentally within merged BECs. Our numerical simulations indicate the formation of many vortex rings. In the case of splitting a BEC, the transition from sound-wave formation to dispersive shock-wave formation is studied by use of increasingly stronger splitting barriers. These experiments realize prototypical dispersive shock situations.

Figure 1

Left column: experimental antitrapped expansion images of a BEC collision at $t=$ (a) 2 ms, (b) 7 ms, (c) 12 ms, (d) 22 ms, and (e) 57 ms (including the 2 ms antitrapped expansion time). Middle column: numerical simulations at $t=$ (f) 2 ms, (g) 7 ms, (h) 12 ms, (i) 22 ms, and (j) 57 ms. The antitrapped expansion was not simulated; therefore, the vertical scale of (f)–(j) is about $\frac{3}{57}$ the vertical scale of (a)–(e), see also 20. Right column: (k)–(m) simulations showing zoomed-in density slices of the BEC by the plane $z=0$ after (k) 5 ms, (l) 6.25 ms, and (m) 7.5 ms. (n) Integrated cross section of (d). (o) Typical uniform soliton train observed for lower atom numbers (experimental image; parameters see text).

Figure 2

Dynamics induced by repulsive barrier. (a), (b) Turning a barrier off after forming a BEC in the presence of the barrier. (c), (d) Turning a barrier on after forming a BEC without the presence of the barrier. (e), (f) Pulsing the barrier on for 1.5 ms after the formation of a BEC without the presence of the barrier. (a), (c), (e) Weak barrier, laser power $360\mu \mathrm{W}$. (b), (d), (f) Strong barrier, laser power 1.99 mW. Evolution times before start of imaging procedure: (a), (b) 16 ms, (c), (d) 12 ms, (e), (f) 10 ms.

Figure 3

Speed of wave front propagation through a BEC. After a BEC is formed, a repulsive dipole laser is suddenly turned on. The plot shows the propagation speed of the resulting wave fronts vs the applied laser power. Error bars are taken from fits of distances vs time. The line shows the function $v(P)=a+b\sqrt{P}$ fitted to the data. Insets show two representative images obtained with an evolution time of 12.5 ms and a laser power, respectively, below and above the power at which the wave fronts start breaking into solitons.

Figure 4

Dynamics induced by suddenly turning off a local, attractive dipole potential in the center of a BEC. Dipole laser wavelength 830 nm, power $61\mu \mathrm{W}$. Evolution time between turnoff and start of expansion: (a) 0 ms, (b) 0.25 ms, (c) 1 ms, (d) 14 ms. (e), (f) Development of dispersive shock waves when a laser power of $183\mu \mathrm{W}$ is used. Evolution time (e) 1 ms, (f) 8 ms.