Optomagnonics in Dispersive Media: Magnon-Photon Coupling Enhancement at the Epsilon-near-Zero Frequency

Reaching strong light-matter coupling in solid-state systems has long been pursued for the implementation of scalable quantum devices. Here, we put forward a system based on a magnetized epsilon-near-zero (ENZ) medium, and we show that strong coupling between magnetic excitations (magnons) and light can be achieved close to the ENZ frequency due to a drastic enhancement of the magneto-optical response. We adopt a phenomenological approach to quantize the electromagnetic field inside a dispersive magnetic medium in order to obtain the frequency-dependent coupling between magnons and photons. We predict that, in the epsilon-near-zero regime, the single-magnon single-photon coupling can be comparable to the magnon frequency for a small magnetic volume and perfect mode overlap. For state-of-the-art illustrative values, this would correspond to achieving the single-magnon strong coupling regime, where the coupling rate is larger than all the decay rates. Finally, we show that the nonlinear energy spectrum intrinsic to this coupling regime can be probed via the characteristic multiple magnon sidebands in the photon power spectrum.

Figure 1

(a) Setup: a monochromatic electromagnetic wave propagates in a magnetized dielectric. The wave vector is perpendicular to the magnetization (Voigt configuration), which exhibits small fluctuations around its saturation value; (b) Minimal microscopic model leading to the dispersion of the permittivity tensor: light drives electric-dipole transitions responsible for the Faraday effect and the material’s optical response; (c) Permittivity (12) and (d) Faraday rotation angle (4) as functions of the frequency for this model of dispersion. At the frequency ${\omega }_{\mathrm{ENZ}}$, $ϵ[{\omega }_{\mathrm{ENZ}}]=0$, and the Faraday rotation angle is enhanced. Illustrative parameters corresponding to a resonance of yttrium iron garnet with ionic transition frequency ${\omega }_0=2\pi \times 600\mathrm{THz}$.

Figure 2

(a) Wave vectors of the plane wave modes $k_{\pm }[\omega ]$ given by Eq. (8) as a function of the frequency close to ENZ point. Close to the ENZ point, only one of the modes propagates; (b) Corresponding optomagnonic coupling given by Eq. (11) as a function of the frequency close to the ENZ point. The inset depicts an enlargement around ${\omega }_{\mathrm{ENZ}}$, showing the coupling enhancement. Illustrative parameters for YIG as discussed in the text and in correspondence with Fig. 1. Frequency in units of the ionic transition frequency ${\omega }_0=2\pi \times 600\mathrm{THz}$, wave vectors in units of ${\omega }_0/c$, and coupling in units of the magnon frequency ${\omega }_m=2\pi \times 10\mathrm{GHz}$.

Figure 3

Power spectrum as a function of the mode frequency ${\omega }_c$ and as a function of the frequency $\omega$. We work in a frame rotating at the driving frequency. Several peaks equally spaced by $\sim {\omega }_m$ are present when the coupling is comparable to the optical decay rate and to the magnon’s frequency, and the resonance lines exhibit a characteristic shift close to the ENZ frequency due to the nonlinear energy spectrum. Parameters: ${\kappa }_1/{\omega }_m={10}^{-1}$, $\mathrm{\Omega }/{\omega }_m={10}^{-4}$, and $\gamma /{\omega }_m={10}^{-3}$. Detuning in units of the magnon mode frequency ${\omega }_m=2\pi \times 10\mathrm{GHz}$ and photon mode frequency in units of the ionic transition frequency ${\omega }_0=2\pi \times 600\mathrm{THz}$.