Phase-Controlled Pathway Interferences and Switchable Fast-Slow Light in a Cavity-Magnon Polariton System

We study the phase-controlled transmission properties in a compound system consisting of a three-dimensional copper cavity and an yttrium-iron-garnet (YIG) sphere. By tuning the relative phase of the magnon pumping and cavity-probe tones, constructive and destructive interferences occur periodically, which strongly modify both the cavity-field transmission spectra and the group delay of light. Moreover, the tunable amplitude ratio between pump-probe tones allows us to further improve the signal absorption or amplification, accompanied by either significantly enhanced optical advance or delay. Both the phase and amplitude ratio can be used to realize in situ tunable and switchable fast-slow light. The tunable phase and amplitude ratio lead to the zero reflection of the transmitted light and an abrupt fast-slow light transition. Our results confirm that direct magnon pumping through the coupling loops provides a versatile route to achieve controllable signal transmission, storage, and communication, which can be further expanded to the quantum regime, realizing coherent-state processing or quantum-limited precise measurements.

Figure 1

Measurement setup and phase-induced interference mechanism diagrams. (a) The system consisting of a three-dimensional (3D) copper cavity and a YIG sphere, which is coherently pumped by the coupling loops shown as a black coil surrounding the YIG sphere. The red arrows and colors indicate the magnetic field directions and amplitudes of the ${\mathrm{TE}}_{101}$ mode distribution, respectively. The YIG sphere is placed at the area with maximum magnetic field distribution inside a 3D copper cavity box to obtain a strong cavity-magnon coupling. A small hole at the cavity sidewall is assembled with a standard SubMiniature version A connector (SMA connector), allowing us to do the reflection measurement $S_{11}$ of the probe field, i.e., such a SMA connector works as both the signal input and readout port. A beam of coherent microwave comes out from port 1 of the vector network analyzer (VNA) and splits into two beams, working as the magnon-pump tone and the cavity-probe tone. Here, we use an in-phase and quadrature mixer ($I$-$Q$ mixer) and an arbitrary waveform generator (AWG) to control and tune the phase difference $\phi$ and pump-probe amplitude ratio $\delta ={\epsilon }_m/{\epsilon }_c$ between the pump and probe tones. The interfering results are extracted by the circulator and finally transferred to port 2 of the VNA. (b) Diagram showing the relative phase between the magnon pump and cavity probe in the cavity-magnon coupled system. (c) The corresponding energy-level diagram. Two transition pathways to the higher energy level: $◯1$ probe-tone-induced direct excitation, and $◯2$ pump-tone excites magnons and then coherently transfers there to cavity photons. (d) Measurements of the reflection spectra $S_{11}$ versus the detuning ${\mathrm{\Delta }}_p={\omega }_c-{\omega }_p={\omega }_m-{\omega }_p$. The relative phase difference between pump and probe tones can be developed to realize an in situ switchable constructive and destructive interference, presented as MIABS with $\phi =0.35\pi ,\delta =1.2$ and MIT with $\phi =1.35\pi ,\delta =1.2$.

Figure 2

$S_{11}$ spectrum versus relative phase difference $\phi$. (a) Measured transmission spectrum $S_{11}$ versus phase $\phi$ and detuning ${\mathrm{\Delta }}_p$. The colors indicate the transmitted amplitudes in dB units. (b) Measured output spectrum $S_{11}$ with phases: $◯1$ $\phi =0.35\pi$, $◯2$ $\phi =0.85\pi$, $◯3$ $\phi =1.35\pi$, and $◯4$ $\phi =1.85\pi$. Here, the pump-probe amplitude ratio is fixed at $\delta =1.7$. Red-solid lines are the corresponding theoretical results.

Figure 3

Measured transmission spectrum $S_{11}$ versus pump-probe amplitude ratio $\delta$ with phase fixed at $\phi =0.35\pi$. (a) Measured output spectrum versus amplitude ratio $\delta$ and detuning ${\mathrm{\Delta }}_p$. The colors indicate transmitted power in dBs. (b) The extreme values of the $S_{11}$ transmission spectra of the output field versus the amplitude ratio parameter $\delta$. In the light-yellow (light-blue) regime, the extreme values represent the maximum (minimum) transmission amplitudes of the peaks (dips) around ${\mathrm{\Delta }}_p=0$. (c) Measured transmission spectrum $S_{11}$ with amplitude ratio: $◯1$ $\delta =0$, $◯2$ $\delta =0.3$, $◯3$ $\delta =3.0$, and $◯4$ $\delta =5.7$. Red-solid lines are the corresponding theoretical results.

Figure 4

Measured transmission spectrum $S_{11}$ versus pump-probe amplitude ratio $\delta ={\epsilon }_m/{\epsilon }_c$ with phase fixed at $\phi =1.35\pi$. (a) Measured output spectra $S_{11}$ versus amplitude ratio $\delta$ and frequency detuning ${\mathrm{\Delta }}_p$. The colors indicate the transmitted amplitude in dB units. (b) The extreme values of the $S_{11}$ transmission spectra of the output field versus the amplitude-ratio parameter $\delta$. The extreme values represent the maximum transmission amplitude of the peaks around ${\mathrm{\Delta }}_p=0$. (c) Measured transmission spectra $S_{11}$ with amplitude ratios: $◯1$ $\delta =0$, $◯2$ $\delta =0.9$, $◯3$ $\delta =1.2$, and $◯4$ $\delta =4.5$. The red-solid lines are the corresponding theoretical results.

Figure 5

Measured time delay versus pump-probe ratio $\delta$ for the phase $\phi =0.35\pi$ (a); and $\phi =1.35\pi$ (b). Light-yellow area indicates the group-delay regime, and the light-blue area indicates the group-advance regime. (c) Measured unwrapped phase versus frequency detuning ${\mathrm{\Delta }}_p$ with $\delta =2.7$ [point $◯1$ in (a)] and $\delta =3.3$ [point $◯2$ in (a)] for $\phi =0.35\pi$.