SABRE and PHIP pumped RASER and the route to chaos

In a RASER (Radio-frequency Amplification by Stimulated Emission of Radiation), the fast relaxing electromagnetic modes of an LC resonator are enslaved by the slow nuclear spin motion, whose coherence decays with the transverse relaxation rate γ_m=1/T₂^∗. Such a system obeys the slaving principle, mathematically identical with the adiabatic elimination procedure, leading to multi-mode RASER equations. If the pumping rate of nuclear spin polarization Γ>>γ_m, a second adiabatic elimination process applies and the spectral properties of the RASER can be predicted. The resulting model is similar to the model of two non-linear coupled oscillators and predicts the observed RASER phenomena, including frequency combs and mode collapse. If the second adiabatic elimination is not applicable, mode collapse is completely absent and successive period doubling processes and chaos occur at very high population inversions. We compare these theoretical predictions with experimental results from a PHIP (Para-Hydrogen Induced Polarization) pumped ¹H RASER. Moreover, in SABRE (Signal Amplification By Reversible Exchange) pumped ¹H experiments, RASER revivals are observed long after the parahydrogen pumping source has been switched off. All these findings shed light onto the links between NMR spectroscopy, RASER physics, synergetics and chaos theory. Several new applications are envisioned in the fields of quantum sensor technology, structure investigation or magnetic resonance imaging (MRI).