Nonequilibrium Dynamics of a Bose-Einstein Condensate Excited by a Red Laser Inside a Power-Law Trap with Hard Walls

We explore the nonequilibrium dynamics of a two-dimensional trapped Bose-Einstein condensate excited by a moving red-detuned laser potential. The trap is a combination of a general power-law potential cutoff by a hard wall box potential. The red laser potential is allowed to exit the box potential, leaving the system in a highly nonequilibrium state. This is crucial since the red laser potential squeezes the BEC trapped inside it against the hard wall-boundary at this instant, paving the way for the creation of a shock wave. Once the red laser potential has left the box potential, the Hamiltonian of the system becomes time-independent and the total energy stabilizes. Our systems are simulated by the time-dependent Gross-Ptiaevskii Equation which is numerically solved by the split-step Crank-Nicolson method in real time. It is found that the value at which the total energy stabilizes in the transient stage of the simulation is largely controlled by the initialization process. Before the red laser potential leaves the trap, when the Hamiltonian of the system is still time-dependent, oscillations in the total energy occur if the system is initialized adiabatically by application of a gradually growing and moving red laser potential. If this laser potential is not moving, yet fully present in the initialization process, these oscillations are not observed in the transient stage of the simulation. In addition, the system displays oscillations in the root-mean-square radius of the trapped cloud. The amplitudes of these radial oscillations continue even after the red laser potential leaves the box potential and are used to explore the deviation of the nonstationary states from the corresponding ground states. It is demonstrated that the geometry of the power law potential influences the amplitude of these radial oscillations, reducing them and bringing the systems closer to an equilibrium state. We then argue that by going to tighter trapping geometries, it is not possible to achieve a completely stable system which has been earlier excited by a red laser potential. Most importantly, an increase in the curvature of the power law trap results in chaotic oscillations of the cloud. This work should stimulate further experiments exploring the extent of the nonequilibrium states by a measurement of the amplitude of the root-mean-square radial oscillations of the trapped cloud.