Exploring Nonreciprocal Noise Transfer under Onsager-Casimir Symmetry in Synthetic-Field Optomechanics

TL;DR

The paper investigates nonreciprocal backaction noise in a closed-loop optomechanical system with synthetic magnetism generated by a loop phase $\phi_{\ell}$, while maintaining Onsager-Casimir symmetry. It develops a linearized quantum Langevin framework, analyzes internal and output noise PSDs via a drift matrix formalism, and introduces a loop-phase dependent nonreciprocity measure to quantify directional noise transfer between two identical mechanical resonators coupled to a cavity. Key findings show that $\phi_{\ell}$ enables nonreciprocal noise flow between the resonators, most pronounced away from the EPs and diminishes as $\mu$ grows toward EP, with intracavity and output spectra tunable between lower/upper bands; near EPs a double-peak PSD emerges, offering sensing advantages. The work also discusses feasible experimental implementations, highlighting strong intermechanical coupling and phase control as enabling technologies, and points to practical use in enhanced optomechanical sensing and directional noise routing.

Abstract

An optomechanical system of fundamental importance consists of two intercoupled mechanical resonators, which are radiation-pressure coupled individually to a photonic cavity. This closed-loop and overall lossy configuration possesses two exceptional points (EPs) and offers the realization of synthetic magnetism, controlled by the loop phase. To elucidate the intricate role of loop phase and EPs in this setting, we analyze the noise power spectral density profiles of internal as well as output fluctuations. In the presence of a synthetic magnetic field, the nonreciprocal routing of a signal is well known. Here, we further show that this also applies to nonreciprocal backaction noise flow when the time-reversal symmetry is broken, while the Onsager-Casimir symmetry still holds. To better quantify this phenomenon, we introduce a nonreciprocity measure that contrasts the time-reversed counterparts as a function of loop phase. We observe that nonreciprocal noise flow is enhanced for smaller intermechanical couplings at the expense of lower sensitivity, whereas for sensing purposes, using a higher intermechanical coupling constant is the more viable option.

Figures (15)

• Figure 1: Non-Hermitian closed-loop optomechanical system composed of a photonic cavity and two lossy mechanical resonators with the resonance frequencies $\omega_{c}$ and $\omega_m$, respectively. The photonic cavity is pumped via a coherent laser with amplitude $\varepsilon_{L}$. Loss rates are indicated with wavy arrows, and coupling rates with solid arrows.
• Figure 2: (a) Optical intracavity PSD, (b) noise contribution of the second mechanical resonator to the cavity-output noise spectrum for loop phases, $\phi_{\ell} = 0,~\pi/2,~\pi$, and $3\pi/2$.
• Figure 3: PSD of (a) first and (b) second mechanical resonators as a function of frequency for $\phi_{\ell}= \pi/2$ and $3\pi/2$.
• Figure 4: Noise transfer pathways between the two mechanical resonators. (a) Contribution of the second resonator’s fluctuations to the momentum-noise spectrum of the first resonator, (b) contribution of the first resonator’s fluctuations to the momentum-noise spectrum of the second resonator for $\phi_{\ell} = \pi/2$ and $3\pi/2$. The arrows in the insets depict the weight of noise transfer between mechanical resonators for $\phi_{\ell} = \pi/2$ and $3\pi/2$.
• Figure 5: Nonreciprocity measure $I_\Delta(\phi_{\ell})$ as a function of the loop phase $\phi_{\ell}$ (horizontal axis) and mechanical coupling constant normalized to second EP $|\mu/\mu_{EP,2}|$ (vertical axis). Dark-red regions indicate stronger nonreciprocity.