Nonreciprocity of intense light field and weak quantum signal in optomechanical systems with three-mode parametric interactions

TL;DR

The paper introduces a reconfigurable three-mode optomechanical platform that enables nonreciprocity for both strong classical fields and weak quantum signals. A single three-mode block achieves direction-dependent transmission through intrinsic nonlinear radiation pressure and optomechanical feedback, while a two-block hybrid system achieves unidirectional quantum routing via constructive/destructive quantum interference between direct hopping and indirect photon-phonon pathways, with auxiliary modes allowing adiabatic elimination to tailor dissipation. Key contributions include a fixed-point and bifurcation analysis for strong-field nonreciprocity, a quantum-interference scheme for single-photon isolation with tunable bandwidth and insertion loss, and a demonstration of significantly reduced control-field power compared to two-mode schemes in the sideband-resolved regime. The proposed approach offers a programmable, scalable path toward on-chip optical nonreciprocity applicable to hybrid quantum networks, with practical parameter regimes and reservoir-engineering-based tunability of performance metrics such as isolation, insertion loss, and nonreciprocal bandwidth.

Abstract

We demonstrate nonreciprocal optical transmission for both intense classical fields and weak quantum signals within a reconfigurable optomechanical platform driven by three-mode parametric interactions. The platform is modular, where each three-mode optomechanical system serves as a fundamental building block. Operating independently, a single block achieves nonreciprocity for classical fields. Specifically, asymmetric radiation pressure from intrinsic optomechanical nonlinearity induces nonreciprocal mechanical displacement, modulating the cavity intensity through optomechanical feedback. This enables full isolation of backward transmission without requiring parameter initialization. Alternatively, for quantum signals, the platform is reconfigured by activating photonic and phononic exchange channels between the two blocks. In this configuration, nonreciprocity arises from quantum interference between direct photon hopping and indirect conversion pathways. Constructive interference enables unidirectional low-loss transmission, while destructive interference completely suppresses the reverse direction. After adiabatically eliminating the auxiliary modes, the optimal nonreciprocal frequency and the trade-off between insertion loss and nonreciprocal bandwidth can be controlled by engineering optomechanically induced mechanical dissipation. Additionally, the three-mode-based device requires less control-field power than two-mode systems under resolved-sideband conditions, demonstrating versatile potential for optical nonreciprocity applications across classical and quantum domains.

Figures (10)

• Figure 1: (a) Optomechanical parametric coupling in a Fabry-Pérot cavity incorporating a central high-reflectivity mirror. Coupling between normal modes $a_1=(a_L+a_R)/\sqrt{2}$ (symmetric, red) and $a_2=(a_L-a_R)/\sqrt{2}$ (antisymmetric, blue) is induced by mechanical displacement $x$ of the middle mirror, where $a_L$ ($a_R$) describe the left (right) cavity mode. When applying forward input (inject into port 1) or backward input (inject into port 2), the corresponding mode $a_1$ or $a_2$ is selectively driven. (b) Schematic diagram of the two-port isolator, which serves as a fundamental building block, abstracted from the system in Fig. \ref{['schematic']}. (c) Schematic of the waveguide-mediated coupling of blocks. Operators $a_i$, $c_i$, $b_i$, $d_i$$(i=1,2)$ denote the carrier, signal, mechanical, and auxiliary modes in the i-th subsystem respectively. Coherently enhanced modes $a_i$ (carrier) and $d_i$ (auxiliary) govern the effective optomechanical couplings: $G_i$ via $a_i$; $G_{d,i}$ via $d_i$. Tunneling couplings mediate between (i) $c_1$-$c_2$ and (ii) $b_1$-$b_2$ mode pairs.
• Figure 2: (a),(b) The number of fixed points and (c),(d) the transmission rate at the fixed points are plotted as a function of renormalized injected strength $P$ and detuning $\Delta$. The renormalized optical and mechanical dissipation rates are $\kappa = 0.05, \gamma = 10^{-3}$. The left panels correspond to the forward input, while the right panels correspond to the backward input. In regions I, II, and III, there are one, three, and two fixed points, respectively. The black dashed line indicates a Hopf bifurcation, through which the stable spiral corresponding to the fixed point $X_{+}$ transitions into a limit cycle.
• Figure 3: The forward and backward temporal nonreciprocal transmission coefficients, $T_{21}$ (red solid curves) and $T_{12}$ (blue solid curves), are plotted for four representative points in the parameter space, denoted as A, B, C, and D in Fig. \ref{['Figure2']}. Owing to the weak clarity of the figures caused by the rapid oscillations of the transmission coefficient, extended temporal profiles corresponding to Fig. \ref{['Figure3']} are provided in Fig. \ref{['FigureA2']} (Appendix \ref{['appendix_C']})
• Figure 4: Forward ($T_+$, red solid) and backward ($T_-$, blue dashed) scattering probabilities versus signal frequency $\omega$. The phase parameter $\theta$ is fixed at $\pi/2$ (left panel) and $3\pi/2$ (right panel). Effective mechanical dissipation rates $\Gamma$ take values $\{\kappa/2, \kappa/10, \kappa/20, \kappa/50\}$ with auxiliary mode decay rates $\kappa_{d,1} = \kappa_{d,2} = 5\kappa$.
• Figure 5: The nonreciprocity bandwidth $\Delta \omega$ and optimal parameter $J_m$ (left axis), along with the insertion loss (dB) (right axis), are plotted as functions of the effective mechanical dissipation $\Gamma/\kappa$. The decay rares of auxiliary modes are set identical to those used in Fig. \ref{['Fig5']}