Shocking Behavior in Condensates

Mark A. Hoefer, Mark J. Ablowitz, Ian R. Coddington +3 more

A Bose-Einstein condensate (BEC) is a quantum fluid that gives rise to interesting shock-wave nonlinear dynamics. Experiments depict a BEC that exhibits behavior similar to that of a shock wave in a compressible gas, e.g., traveling fronts with steep gradients. However, the governing Gross-Pitaevskii (GP) equation that describes the mean field of a BEC admits no dissipation, hence classical dissipative shock solutions do not explain the phenomena. Instead, wave dynamics with small dispersion is considered and it is shown that this provides a mechanism for the generation of a dispersive shock wave (DSW). Computations with the GP equation are compared to experiment with excellent agreement. A comparison between a canonical one-dimensional (1D) dissipative and dispersive shock problem shows significant differences in shock structure and shock-front speed. Numerical results associated with the three-dimensional experiment show that three- and two-dimensional approximations are in excellent agreement and 1D approximations are in good qualitative agreement. Using 1D DSW theory, it is argued that the experimentally observed blast waves may be viewed as dispersive shock waves.

Daniel S. Rokhsar

Eren Tosyalı

We investigate the Gross–Pitaevskii equation with the tilted bichromatical optical lattice potential for finding the dynamics of a Bose–Einstein condensate system under the Gaussian white noise. We construct the Poincare sections of system based on the relations between the system parameters and solution behaviors to understand how its shock wave like dynamic could be affected by the noise. Also the hierarchical cluster analysis method investigation of the system is presented.

Ryan Balili, David W. Snoke

Igor K. Kulikov, Michail A. Zak

A theoretical possibility of shock wave formation in a high-density Bose-Einstein condensate with strong repulsive interaction is reported. A mechanism of transformation of sound waves into shock waves is described. The speed of shock waves as well as relationships between jumps of velocity and density at the front of the surface of discontinuity are derived. The theory is illustrated by the analytical solution for shock wave propagation in a dense condensate cloud.

C. J. Pethick, H. Smith