Indirect Methods to Control Population Distribution in a Large Spin System

We demonstrate how a large spin system $S=7/2$ with the ground and the first excited state separated by a seven photon transition exhibit non equilibrium thermodynamic properties and how the population distribution may be manipulated using coupling between energy levels. The first method involves non-adiabatic passage through an avoided level crossing controlled with an external DC magnetic field and the resulting Landau Zener transition. The second method is based on external cavity pumping to a higher energy state hybridised with another state that is two single photon transitions away from the ground state. The results are confirmed experimentally with Gd³⁺ impurity ion ensemble in a YVO₄ crystal cooled to 20 mK, which also acts as a microwave photonic whispering gallery mode resonator. Extremely long life times are observed due to large number of photons required for the transition between the ground and the first excited states.