Quantum Shock Waves in Collisions of Ultracold Atomic Clouds

Ultracold atomic gases represent an ideal toolbox to study quantum effects that are difficult to probe using other systems. Here, we use a time-dependent density matrix renormalization group approach to show that the collision of two interacting bosonic clouds in one dimension gives rise to shock waves with a concomitant local energy distribution typical of population inversion, i.e., an effective negative temperature. A classical hydrodynamic description compares well with the exact quantum dynamics only up to the gradient catastrophe time. Such a highly nonequilibrium local distribution, however, does not prevent the system from recovering its initial state after an oscillation period which is renormalized by the interaction. All these results can be tested experimentally.