Chaotic probability density in two periodically driven and weakly coupled Bose-Einstein condensates

Using the idea of the macroscopic quantum wave function and the definition of the classical chaos, we analytically reveal that the probability density of two periodically driven and weakly coupled Bose-Einstein condensates is deterministic but not predictable. Numerical calculation for the time evolutions of the chaotic probability density demonstrates the analytical result and exhibits the nonphysical implosions and ultimate unboundedness. A method for controlling the implosions and unboundedness is proposed through adjustment of the initial conditions that leads the probability density to periodically oscillate.