Role of interbranch pumping on the quantum-statistical behavior of multi-mode magnons in ferromagnetic nanowires

Theoretical studies are reported for the quantum-statistical properties of microwave-driven multi-mode magnon systems as represented by ferromagnetic nanowires with a stripe geometry. Effects of both the exchange and the dipole-dipole interactions, as well as a Zeeman term for an external applied field, are included in the magnetic Hamiltonian. The model also contains the time-dependent nonlinear effects due to parallel pumping with an electromagnetic field. Using a coherent magnon state representation in terms of creation and annihilation operators, we investigate the effects of parallel pumping on the temporal evolution of various nonclassical properties of the system. A focus is on the interbranch mixing produced by the pumping field when there are three or more modes. In particular, the occupation magnon number and the multi-mode cross correlations between magnon modes are studied. Manipulation of the collapse and revival phenomena of the average magnon occupation number and the control of the cross correlation between the magnon modes are demonstrated through tuning of the parallel pumping field amplitude and appropriate choices for the coherent magnon states. The cross correlations are a direct consequence of the interbranch pumping effects and do not appear in the corresponding one- or two-mode magnon systems.