Boltzmann–Loschmidt Dispute Reloaded: Quantum 150 Years Later

The Boltzmann–Loschmidt dispute of 1876 questioned the possibility of a statistical irreversible description by time-reversible classical equations of motion of atoms. Here we show analytically and numerically that the quantum chaos diffusion of cold atoms, or ions, in a harmonic trap and pulsed optical lattice can be inverted back in time with up to 100% efficiency. This is in sharp contrast to classical evolution, where exponentially small errors break time reversibility. We argue that the existing experimental skills allow highlighting the Boltzmann–Loschmidt dispute from a quantum perspective.