Level Attraction Due to Dissipative Magnon-Photon Coupling

We report dissipative magnon-photon coupling caused by the cavity Lenz effect, where the magnons in a magnet induce a rf current in the cavity, leading to a cavity backaction that impedes the magnetization dynamics. This effect is revealed in our experiment as level attraction with a coalescence of hybridized magnon-photon modes, which is distinctly different from level repulsion with mode anticrossing caused by coherent magnon-photon coupling. We develop a method to control the interpolation of coherent and dissipative magnon-photon coupling, and observe a matching condition where the two effects cancel. Our work sheds light on the so-far hidden side of magnon-photon coupling, opening a new avenue for controlling and utilizing light-matter interactions.

Figure 1

(a) The Lenz effect. The motion of a magnet falling down a conducting pipe is impeded by the induced magnetic field. (b) Magnon-photon coupling mechanisms including the cavity Lenz effect that impedes the magnetization dynamics. (c) Experimental setup, with a VNA measuring the microwave transmission through a waveguide loaded with a YIG sphere. The simulated $h$ field amplitude for the ${\mathrm{TE}}_{11}$ mode at the middle plane of the empty waveguide. $A$ and $B$ denote the $h$ antinode and node positions for loading YIG sphere. (d),(e) The hybridized mode frequency (${\mathrm{\Delta }}_{\omega }\equiv \omega -{\omega }_c$) and line width ($\mathrm{\Delta }\omega$) are plotted as a function of the field detuning [${\mathrm{\Delta }}_H\equiv {\omega }_r(H)-{\omega }_c$], for level repulsion and attraction predicted by solving Eq. (1) at $K_L=0$ and $K_A=0$, respectively. Sample parameters are given in the Letter.

Figure 2

Experimental transmission spectra mappings as a function of ${\mathrm{\Delta }}_{\omega }$ and ${\mathrm{\Delta }}_H$ for (a) level repulsion and (b) level attraction. The YIG sphere has been placed at positions $A$ and $B$ to observe level repulsion and attraction, respectively. Individual transmission spectra at different field detunings are shown for (c) level repulsion and (d) level attraction. (e) The phase behavior of level repulsion and (f) level attraction measured at ${\mathrm{\Delta }}_H=0$.

Figure 3

Transmission spectra at various angular positions $\theta$, demonstrating the change from level repulsion to level attraction. Thick black curves are experimental data and thin green curves are calculations. The corresponding ${\mathrm{\Delta }}_{\omega }-{\mathrm{\Delta }}_H$ transmission mappings are shown on the right.

Figure 4

Systematic control of the coupling strength and coupling phase in our setup. (a) The net coupling strength, $g$, measured at different YIG positions, $\theta$, as indicated by the insets. (b) The coupling phase, $\mathrm{\Phi }$, measured at different YIG position, $\theta$, reveals two distinct regions for level repulsion and attraction where $\mathrm{\Phi }=0$ and $\pi$, respectively.