Using a mapping as a probe for heating suppression in periodically driven many-body quantum systems: a mean-field example with Bose gases

By using our recent results on the exact mappings between time evolutions of different quantum many-body systems [Phys. Rev. A 94, 043628 (2016)], we construct a mean-field model of many-body systems with rapid periodic driving. The single-particle potential and the inter-particle interaction strength are both time-dependent at once, in related ways. We map the evolutions of the model system onto evolutions with slowly varying parameters. Such a mapping between a Floquet evolution and a static or slow process allows us to investigate non-equilibrium many-body dynamics and examine how rapidly driven systems may avoid heating up, at least when mean-field theory is still valid. From that special but interesting case, we learn that rapid periodic driving may not yield to heating because the time evolution of the system has a kind of hidden adiabaticity, inasmuch as it can be mapped exactly onto that of an almost static system.