Optomechanically Induced Transparency on Exceptional Surfaces

TL;DR

This paper addresses how OMIT behaves on exceptional surfaces (ES) in a non-Hermitian cavity optomechanical system. It introduces two ES types: a first kind with $J=0$ and a second kind with $J\neq 0$, forming continuous EP manifolds in parameter space. By deriving the non-Hermitian eigenvalues and performing linearized probe-response calculations, the authors show that OMIT spectra and group delays remain robust along ES lines or surfaces, while leaving the ES leads to pronounced peak–valley conversions and modified fast-slow light. The work also discusses experimental feasibility with current WGM platforms, highlighting potential for ES-enhanced robust sensing and high-dimensional non-Hermitian spectroscopy.

Abstract

Exceptional points (EPs) are singularities in non-Hermitian systems, where the system transmission spectrum varies significantly at the phase transition point. Here, we propose a practical scheme to study the changes of the optomechanically induced transparency (OMIT) spectrum on the exceptional surface (ES), which is formed by designing the structure of the waveguide in a non-Hermitian cavity optomechanical system. By comparing the transmission spectra of the system at different normal points, EPs on the same or different ESs, and exceptional derived points, we find that the peak-valley conversion of the system transmission spectra is obtained at the phase transition point and the arbitrary manipulation of the system transmission spectrum can be realized by moving the system on the same or different ESs. Furthermore, the phenomena of conversion and enhancement of the fast-slow light in the system transmission spectra have also been discovered in our researches. Different from the isolated EP, our proposal can discuss the system properties at different EPs, can find a richer transmission spectrum, and can provide more convenient options for experimental implementation, which paves the way for studying the nature of non-Hermitian systems in a higher dimension.

Figures (5)

• Figure 1: (a) Schematic of the proposed system in experiments, where PM is the phase modulator. (b) Schematic of the non-Hermitian optomechanical system shown in the top, where the CW and CCW photon modes are coupled with the symmetric coupling strength $J$ induced by a nanoparticle and the asymmetric coupling $\lambda$ induced by the structural design. And the breathing phonon mode $b$ is coupled to the CW and CCW photon modes with the same optomechanical coupling coefficient $G$. Blow is the eigenvalues coalesce in our proposal. The dashed line represents the general condition when $J=0$. And the solid line corresponds the phase transition point with $J=t_0\sqrt{\gamma_1\gamma_2}$, which can form the ES in a higher dimensional parameter space.
• Figure 2: (a, b) The transmission spectra of probe light as a function of the optical detuning $\delta_p=\omega_p-\omega_0$. (c) The schematic diagram of the ES for $J=0$ spanned by $\gamma_1$ and $\gamma_2$, where $\rm{EP}_1$, $\rm{EP}_2$, and $\rm{EP}_3$ are three EPs on the same line with $\{\gamma_1,~\gamma_2\}=\{0.7~\rm{MHz},~1.26~\rm{MHz}\},~\{1~\rm{MHz},~1~\rm{MHz}\}$, and {1.38 MHz, 0.68 MHz}, respectively. The equation of the line is $\gamma_2=f(\gamma_1)=-0.86\gamma_1+1.86$. (d) The transmission spectra on the dashed blue line in Fig. \ref{['fig2']}(c).
• Figure 3: Group delay of the probe light $\tau_{p}$ as a function of the detuning $\omega_p-\omega_0$. (a) The group delay when the system is located at $\rm{EP}_2, \rm{EP}_3$ in Fig. \ref{['fig2']}(c). (b,c) The group delay comparison diagrams of EP and it corresponding NP with $J=0.3~\rm{MHz}$.
• Figure 4: (a) Two different ESs with $t_{0}=1$ and $0.9$ of the second kind of ES. Those red and blue points correspond to EPs on different ESs, respectively. And the black point is the normal NP. (b-d) show the comparison between EPs on the same or different ESs, respectively. (e,f) are the comparison between EPs and $\rm{NP}_1$. Please refer to Tab. \ref{['tab1']} for the parameters of all points.
• Figure 5: Group delay of the probe light $\tau_{g}$ as a function of the detuning $\omega_p-\omega_0$. (a, b, d, e) show the group delay of different NPs. (c) The group delay of $\rm{EP_2}$ which is located on the second kind of ES with $J\neq0$.