We formulate a scattering theory to study magnetic films in microwave cavities beyond the independent-spin and rotating-wave approximations of the Tavis-Cummings model. We demonstrate that strong coupling can be realized not only for the ferromagnetic resonance mode, but also for spin-wave resonances; the coupling strengths are mode dependent and decrease with increasing mode index. The strong-coupling regime can also be accessed electrically by spin pumping into a metal contact.

Achieving magnetometers with ultrahigh sensitivity at room temperature is an outstanding problem in physical sciences and engineering. Recently developed non-Hermitian cavity spintronics offers new possibilities. In this work we predict an exceptional magnetic sensitivity of cavity magnon polaritons with the peculiar parity-time ($\mathcal{P}\mathcal{T}$) symmetry. Based on the input-output formalism, we demonstrate a “Z”-shape spectrum including two side-band modes and a dark-state branch with an ultranarrow linewidth in the exact $\mathcal{P}\mathcal{T}$ phase. The spectrum evolves to a step function when the polariton touches the third-order exceptional point, accompanied by an ultrahigh sensitivity with respect to the detuning. The estimated magnetic sensitivity can approach ${10}^{-15}\mathrm{T}{\mathrm{Hz}}^{-1/2}$ in the strong coupling region, which is two orders of magnitude higher than that of the state-of-the-art magnetoelectric sensor. We derive the condition for the noiseless sensing performance. Purcell-like effect is observed when the $\mathcal{P}\mathcal{T}$ symmetry is broken. A possible experimental scheme to realize our proposal is also discussed.

We apply Mie scattering theory to study the interaction of magnetic spheres with microwaves in cavities beyond the magnetostatic and rotating wave approximations. We demonstrate that both strong and ultrastrong coupling can be realized for stand alone magnetic spheres made from yttrium iron garnet (YIG), acting as an efficient microwave antenna. The eigenmodes of YIG spheres with radii of the order mm display distinct higher angular momentum character that has been observed in experiments.

We consider an experimentally feasible setup to demonstrate the existence and coherent dynamics of a Majorana fermion. The setup consists of a quantum dot and a tunnel-coupled semiconductor nanowire which is anticipated to support Majorana excitations under some conditions. For transport under finite bias voltage, we find that a subtraction of the source and drain currents can expose the essential features of the Majorana fermion, including the zero-mode nature by gate-voltage modulating the dot level. Moreover, the Majorana coherent oscillation dynamics between the nanowire and the quantum dot is revealed in the shot noise, via a spectral dip together with a pronounced zero-frequency noise enhancement effect. Important parameters, e.g., the Majorana's mutual interaction and its coupling to the quantum dot, can be extracted by using the derived analytic results.