Quantum Chaos: an answer to the Boltzmann-Loschmidt controversy? An experimental approach

We revive the long standing Boltzmann-Loschmidt polemic which confronts irreversible Thermodynamics with reversible Mechanics. While this is solved within classical physics by the theory of Chaos, until now, there is no quantum de ̄nition of dynamical chaos. A nice possibility o®ered by NMR is to invert the direction of time (quantum Loschmidt daemon) in a many-body spin system. The e±ciency of this reversion MPE(tR) decays with the elapsed time tR before reversal, with a characteristic irreversibility time ¿Á. What controls this time? By changing the time scales of the system in several ways, we observe cases where ¿Á is determined by the reversible spin-spin interactions. A natural de ̄nition of quantum chaos in our experimental context is the instability of dynamical quantum correlations with respect to in ̄nitesimal perturbations in the Hamiltonian. Therefore, our whole set of experiments indicates that there is quantum chaos intrinsic to the many-body spin dynamics in the thermodynamic limit. It manifests as an instability towards perturbations (decoherence) with a ¿Á independent on how small the interaction with the environment is. We also argue that ¡ ln[MPE(tR)] represents a measure of the increasing entropy. This new evidence in support to Boltzmann's physical insight also serves as a landmark to direct the theoretical and experimental work in the new ̄eld of quantum chaos.