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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 cold
fermion systems by applying carefully chosen using Bragg pulses. 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.
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