Engineering synthetic gauge fields through the coupling phases in cavity magnonics

TL;DR

The paper addresses how coupling phases in cavity magnonics induce synthetic $U(1)$ gauge fields in loop-coupled systems and demonstrates experimental control over these phases using two YIG spheres in re-entrant cavities. By modeling the magnon–photon interactions with phases $\varphi_{kl}$ and performing unitary reductions, the authors identify physical phases $\theta$ that govern the system's physics, predicting and confirming configurations with a single phase $\theta_1$ (cavity $\pi$) and two phases $\theta_1=\pi$, $\theta_2=0$ (cavity $\pi0$). The experiments show spectral features consistent with the predicted phases, including non-crossing polariton branches and magnonic dark modes, and reveal a $\sqrt{2}$ enhancement in two-magnon coupling under appropriate conditions. The results establish a route to engineering synthetic gauge fields in cavity magnonics, enabling tunable indirect coupling and dark-mode memories with potential for quantum transduction and non-reciprocal devices, and point to future tunability via cavity geometry or driven magnons.

Abstract

Cavity magnonics, which studies the interaction of light with magnetic systems in a cavity, is a promising platform for quantum transducers and quantum memories. At microwave frequencies, the coupling between a cavity photon and a magnon, the quasi-particle of a spin wave excitation, is a consequence of the Zeeman interaction between the cavity's magnetic field and the magnet's macroscopic spin. For each photon/magnon interaction, a coupling phase factor exists, but is often neglected in simple systems. However, in "loop-coupled" systems, where there are at least as many couplings as modes, the coupling phases become relevant for the physics and lead to synthetic gauge fields. We present experimental evidence of the existence of such coupling phases by considering two spheres made of Yttrium-Iron-Garnet and two different re-entrant cavities. We predict numerically the values of the coupling phases, and we find good agreement between theory and the experimental data. These results show that in cavity magnonics, one can engineer synthetic gauge fields, which can be useful for cavity-mediated coupling and engineering dark mode physics.

Figures (14)

• Figure 1: Simplification of the physics of a system composed of two magnon modes $m_1$ and $m_2$ (in blue) coupling equally and simultaneously to three cavity modes $c_1,c_2$ and $c_3$ (in red). (a) The system where all the coupling phases remain. (b) After unitarily transforming the cavity modes using \ref{['eq:rotation-ci']}, the physics is determined only by three phases $\phi_k = \varphi_{k2}-\varphi_{k1}$, accounting for the difference in coupling for each cavity mode $k \in \qty{1, 2, 3}$. (c) After rotating $m_2$ using \ref{['eq:rotation-m2']}, we are left with two physical phases $\theta_1 = \phi_1 - \phi_2$ and $\theta_2 = \phi_3 -\phi_2$.
• Figure 2: (a) The three-posts re-entrant cavity $\pi$ used in the experiment. The lid of the cavity is not shown. (b-c) Electric and magnetic field norm simulated using COMSOL Multiphysics® of the first eigenmode $c_1$ (frequency $\omega_{c,1}/2\pi=4.524$ GHz) of cavity $\pi$. (d-e) Electric and magnetic field distribution simulated using COMSOL of the second eigenmode $c_2$ (frequency $\omega_{c,2}/2\pi=6.378$ GHz) of cavity $\pi$. For each mode, the magnetic field is maximal between the posts, where the YIG spheres are placed, while the electric field is concentrated between the top of the posts and the lid of the cavity. The vectors are only shown for the magnetic field
• Figure 3: (a) Experimental transmission amplitude $\abs{S_{21}}$ of the cavity $\pi$, along with the theoretical spectrum in dashed lines. The fit parameters are $\omega_{c,1}/2\pi = 4.527$ GHz, $\omega_{c,2}/2\pi=6.19$ GHz , $g_1/2\pi=81$ MHz, $g_2/2\pi=120$ MHz, and $\theta_1=\pi$. Inset: zoom for $5.1 \leq \omega_m/2\pi \leq 5.62$ GHz, and $5.02 \leq \omega/2\pi \leq 5.7$ GHz, showing that the hybridised photon-magnon polariton frequencies $\omega_2/2\pi$ and $\omega_3/2\pi$ do not cross. The ticks indicate the $\omega_m/2\pi$ cuts plotted in (b). (b) Line cuts for different values of $\omega_m/2\pi$ of the transmission amplitude $\abs{S_{21}}$ with the spectrum in dashed lines. The width of $\omega_/2\pi$ and $\omega_3/2\pi$ show the uncertainty $\pm 2.5$ MHz in frequency. For each line cut, the average value of the transmission is used to define the horizontal line from which the colouring begins: this allows to distinguish between resonances and anti-resonances. All the transmission line cuts are separated by 45 dB. The legend for the spectrum is common to (a) and (b).
• Figure 4: Electric (a) and magnetic (b) field distribution simulated using COMSOL Multiphysics® of the second eigenmode $c_2$ of cavity $\pi 0$. The two eigenmodes of cavity $\pi$ still exist but have different frequencies. (c) The three-posts re-entrant cavity $\pi 0$. Contrary to cavity $\pi$, the three posts do not have the same radius, leading to the creation of an additional cavity mode shown in (a) and (b).
• Figure 5: (a) Experimental transmission amplitude ($\abs{S_{21}}$) of cavity $\pi 0$, with the theoretical spectrum in dashed lines. The two rectangles show the data range used in (b) and (c), with the ticks on the bottom indicating the $\omega_m/2\pi$ cuts. (b-c) Transmission amplitude cuts for different $\omega_m/2\pi$, with the spectrum in dashed lines. As in \ref{['fig:cavity-pi:measurement:cuts']}, the average value of the transmission is used to define the horizontal line from which the colouring begins. The fit parameters are indicated in \ref{['tab:cavity-pi0']} with the cavity resonances $\omega_{c,1}/2\pi = 6.594$ GHz, $\omega_{c,2}/2\pi=7.562$ GHz and $\omega_{c,3}/2\pi= 8.619$ GHz. The legend is common to all three subfigures and the curves are all offset by 50 dB.