In one spatial dimension, quantum exchange statistics and interactions are inextricably intertwined. As a manifestation, the expansion dynamics of a Tonks-Girardeau gas is characterized by dynamical fermionization (DF), whereby the momentum distribution approaches that of a spin-polarized Fermi gas. Using a phase-space analysis and the unitary evolution of the one-body reduced density matrix, we show that DF can be tailored and reversed, using a generalization of delta-kick cooling (DKC) to interacting systems, establishing a simple protocol to rescale the initial momentum distribution. The protocol applies to both expansions and compressions and can be used for the microscopy of quantum correlations.

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• Nonequilibrium statistical mechanics
• Quantum fluids & solids
• Quantum quench
• Quantum statistical mechanics
• 1-dimensional systems
• Nonequilibrium systems
• Ultracold gases