In this talk, I will review our recent theoretical work on dynamic stimulation of various quantum states. The general idea of this line of research is that the equilibrium distribution function (Fermi-Dirac of Bose-Einstein for fermions or bosons respectively) is rarely optimal for the occurrence of a given quantum state. A generic mean-field equation always contains a distribution function of excitations and therefore its solution in non-equilibrium can be viewed as a functional of the distribution function that falls into two categories: it can either suppress an interesting quantum property or on the contrary enhance it compared to equilibrium. Stimulation of a quantum state means finding an external perturbation that gives rise to the latter. This general idea will be illustrated on two examples: First, I will show how non-equilibrium enhancement of Cooper pairing can be achieved in both solid-state and cold fermion systems by applying carefully chosen non-equilibrium perturbations. Second, dynamic stimulation of quantum coherence in periodically driven lattice bosons will be discussed. Finally, I will discuss how external time-dependent perturbations can be used to create and stabilize topological states and show how these "topological insulators in time" manifest themselves in quantized AC transport.
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