Quantum dynamics of damped and driven anharmonic oscillators

We study various techniques to characterize the quantum states of a strongly dissipative system, namely, the an-harmonic oscillator. One cannot directly access the quantum states themselves but only transitions between them. Various methods bring various advantages and inconvenients. We compare several observables under coherent and incoherent excitation. Incoherent excitation leads to huge broadening while coherent excitation quickly dresses the system at the energies required to access the excited states. Less perturbative methods such as four wave mixing appear to be superior but are, by construction, only usable for the lowest rungs.