Bidirectional optical non-reciprocity in a multi-mode cavity optomechanical system

TL;DR

This work addresses on-chip optical nonreciprocity without magnetic fields by analyzing a three-mode cavity optomechanical system coupled to two nano-mechanical resonators in a two-port setup. Using linearized quantum Langevin dynamics and input-output theory, it demonstrates that near-resonant effective detunings $Δ_i$ induce perfect nonreciprocal transmission through interference in a closed optical–mechanical loop, with transmission controlled by optomechanical couplings, cavity losses, and input phases. The study shows that NR can be switched from reciprocal to non-reciprocal and vice versa by tuning $O_{m3}$, $κ_i$, and the relative phases $φ_{ ext{rel}}$, offering robust directional routing around resonance. The findings suggest practical implementations for all-optical diodes, transistors, and switches in integrated photonics and quantum information processing.

Abstract

Optical non-reciprocity, a phenomenon that allows unidirectional flow of optical field is pivoted on the time reversal symmetry breaking. The symmetry breaking happens in the cavity optomechanical system (COS) due to non uniform radiation pressure as a result of light-matter interaction, and is crucial in building non-reciprocal optical devices. In our proposed COS, we study the non-reciprocal transport of optical signals across two ports via three optical modes optomechanically coupled to the mechanical excitations of two nano-mechanical resonators (NMRs) under the influence of strong classical drive fields and weak probe fields. By tuning different system parameters, we discover the conversion of reciprocal to non-reciprocal signal transmission. We reveal perfect nonreciprocal transmission of output fields when the effective cavity detuning parameters are near resonant to the NMRs' frequencies. The unidirectional non-reciprocal signal transport is robust to the optomechanical coupling parameters at resonance conditions. Moreover, the cavities' photon loss rates play an inevitable role in the unidirectional flow of signal across the two ports. Bidirectional transmission can be fully controlled by the phase changes associated with the incoming probe and drive fields via two ports. Our scheme may provide a foundation for the compact non-reciprocal communication and quantum information processing, thus enabling new devices that route photons in unconventional ways such as all-optical diodes, optical transistors and optical switches.

Figures (6)

• Figure 1: Schematic of a two ports multi-mode optomechanical cavity setup excited by external classical fields. The setup includes two fixed partially transparent mirrors (M$_{1}$ and M$_{2}$) and two movable perfectly reflecting nano-mechanical resonators (NMR$_{1}$ and NMR$_{2}$) with small displacements $q_1$ and $q_2$ from their respective equilibrium positions. A partial BS is placed at the center inside the mirrors configuration which form three uneven cavity modes. These cavity modes, that is, $a_1$, $a_2$ and $a_3$, and two mechanical (phononic) modes ($b_1$ and $b_2$) in this system are interconnected via optomechanical couplings, while a standing wave between M$_{1}$ and M$_{2}$ being represented by a straight horizontal arrow is formed. Four classical fields, i.e., strong drive fields with strengths $\Omega_{d1}$ and $\Omega_{d2}$ (same frequency $\omega_{d}$), and weak probe fields having strengths $\Omega_{p1}$ and $\Omega_{p2}$ (same frequency $\omega_{p}$) interact with the cavity system from the respective sides via M$_{1}$ and M$_{2}$, while the output fields ($\varepsilon_{\rm{out,1}}$ and $\varepsilon_{\rm{out,2}}$) can be drawn out via left and right ports, respectively.
• Figure 2: Transmission intensities T$_{2\rightarrow 1}$ (red dash-dot curves) and T$_{1 \rightarrow 2}$ (black solid curves) as a function of the probe-drive field detuning $\Delta_{p}$ under different values of the effective cavity detunings: (a) the same values of effective cavity detunings $\Delta_1=\Delta_2=\Delta_3= \omega_{m1}$, (b) the inset for a short frequency range showing the smaller dip and peak of intensity profile near the origin of (a), (c) $\Delta_1=1.1 \omega_{m1}$, $\Delta_2=0.9 \omega_{m1}$, $\Delta_3= \omega_{m1}$, and (d) $\Delta_1=0.9 \omega_{m1}$, $\Delta_2=1.1 \omega_{m1}$, $\Delta_3= \omega_{m1}$. The general parameters are given as $\omega_{m1}/2\pi=\omega_{m2}/2\pi= 12.6$ GHz, $\kappa_{1}/2\pi=\kappa_{2}/2\pi=\kappa_{3}/2 \pi=73$ MHz, $\gamma_{1}/2\pi=\gamma_{2}/2 \pi=88$ kHz, $\Delta_{a1}/2\pi=79.96$ GHz, $\Delta_{a2}/2\pi=78.38$ GHz, $\Delta_{a3}/2\pi=84.71$ GHz, $O_{m1}/2\pi=O_{m2}/2\pi=O_{m31}/2 \pi= O_{m32}/2 \pi=1.5$ MHz, $\textit{L}_{i}=\textit{L}_{3i}=5.19$ mm ($i=1,2$), $m_{\text{eff},j}=20~\upmu$g ($j=1,2$), $\Phi_{d1}=\Phi_{d2}=\Phi_{p1}=\Phi_{p2}=0$, $\Omega_{d1}=\Omega_{d2}=2 \omega_{m1}$, and $\Omega_{p1}=\Omega_{p2}=0.2 \omega_{m1}$.
• Figure 3: (Color online) (a) (b) Transmission intensities T$_{2\rightarrow 1}$ (red dash-dot curves) and T$_{1 \rightarrow 2}$ (black solid curves) as a function of the probe-drive field detuning $\Delta_{p}$ under different values of optomechanical coupling strengths $O_{m1}$, $O_{m2}$, $O_{m31}$ and $O_{m32}$: (a) $O_{m1}/2\pi=1$ MHz, $O_{m2}/2\pi=60$ MHz, $O_{m31}/2 \pi=O_{m32}/2\pi= O_{m3}/2\pi= 48.5$ MHz, (b) $O_{m1}/2\pi=60$ MHz, $O_{m2}/2\pi=1$ MHz, $O_{m31}/2 \pi=O_{m32}/2\pi=O_{m3}/2\pi= 48.5$ MHz. (c)(d) The waterfall plots of transmission intensities T$_{1\rightarrow 2}$ and T$_{2\rightarrow 1}$ as a function of probe-drive field detuning $\Delta_{p}$ and $O_{m3}$ . The optomechanical couplings for (c), (d) are $O_{m1}/2\pi=1$ MHz, $O_{m2}/2\pi=60$ MHz. The general parameters are given as $\Delta_{a1}/2\pi=79.168$ GHz, $\Delta_{a2}/2\pi=79.160$ GHz, $\Delta_{a3}/2\pi=79.96$ GHz. Other values are same as mentioned in Figure 2a.
• Figure 4: Probe transmission intensities T$_{2\rightarrow 1}$ (red dash-dot) and T$_{1 \rightarrow 2}$ (black solid) as a function of probe-drive field detuning under different values of cavity decay rates: (a) $\kappa_{1}/2\pi=83$ MHz, $\kappa_{2}/2\pi=3$ MHz, $\kappa_{3}/2\pi=73$ MHz, and (b) $\kappa_{1}/2\pi=3$ MHz, $\kappa_{2}/2\pi=83$ MHz, $\kappa_{3}/2\pi=73$ MHz. The general parameters are given as, $\Delta_{1}=\Delta_{2}=\Delta_{3}=\omega_{m1}$, whereas other parameter values are same as in Figure 2a
• Figure 5: Dependence of transmission intensities T$_{2\rightarrow 1}$ (red dash-dot) and T$_{1 \rightarrow 2}$ (black solid) on the probe-drive field detuning $\Delta_p$ when (a) probe phases $\Phi_{p1}=\Phi_{p2}=0$, (b) $\Phi_{p1}=\Phi_{p2}=2\pi/3$, (c) $\Phi_{p1}=-2\pi/3,~ \Phi_{p2}=2\pi/3$. The general parameters are given as $\Delta_{1}=\Delta_{2}=\Delta_{3}=\omega_{m1}$, and other parameter values are same as in Figure 2(a).